Fig A1a variational double-bracket flow TLFIM L = 7.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from simple_exact_diagonalization_routines.local_matrix_class import *\n",
    "from scipy.linalg import expm\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "\n",
    "\n",
    "# System size\n",
    "L = 7\n",
    "\n",
    "# Create objects of Pauli operators\n",
    "X = X_class(L)\n",
    "Y = Y_class(L)\n",
    "Z = Z_class(L)\n",
    "S_plus = S_plus_class(L)\n",
    "S_minus = S_minus_class(L)\n",
    "\n",
    "# Trivial initialization of the right size matrix\n",
    "hamiltonian_name = \"TLFIM_L_\" +str(L)\n",
    "H_TLFIM = 0*np.eye( 2**L ) \n",
    "\n",
    "for x in range(L-1):\n",
    "    H_TLFIM = H_TLFIM + 2*X.at(x+1).dot(X.at(x+2)) + Z.at(x+1)+ X.at(x+1)\n",
    "H_TLFIM = H_TLFIM + Z.at(L)    + X.at(L) \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Flow step  0\n",
      "Found minimum norm =  61.02085248356292  for s =  0.0833984375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZZ  gave for s =  0.0833984375   minimal norm  61.02085248356292\n",
      "Found minimum norm =  59.90311992765712  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZ1  gave for s =  0.07285156250000001   minimal norm  59.90311992765712\n",
      "Found minimum norm =  59.30242179822068  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ1Z  gave for s =  0.0498046875   minimal norm  59.30242179822068\n",
      "Found minimum norm =  60.26933917912077  for s =  0.07675781250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ11  gave for s =  0.07675781250000001   minimal norm  60.26933917912077\n",
      "Found minimum norm =  59.30242179822068  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1ZZ  gave for s =  0.0498046875   minimal norm  59.30242179822068\n",
      "Found minimum norm =  57.9271386799706  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1Z1  gave for s =  0.0498046875   minimal norm  57.9271386799706\n",
      "Found minimum norm =  58.79165843997469  for s =  0.0646484375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ11Z  gave for s =  0.0646484375   minimal norm  58.79165843997469\n",
      "Found minimum norm =  60.62284717554087  for s =  0.08144531250000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ111  gave for s =  0.08144531250000002   minimal norm  60.62284717554087\n",
      "Found minimum norm =  59.302421798220664  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZZ  gave for s =  0.0498046875   minimal norm  59.302421798220664\n",
      "Found minimum norm =  57.951187167826255  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZ1  gave for s =  0.0498046875   minimal norm  57.951187167826255\n",
      "Found minimum norm =  56.46490276318451  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z1Z  gave for s =  0.0498046875   minimal norm  56.46490276318451\n",
      "Found minimum norm =  58.39539267855518  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z11  gave for s =  0.0498046875   minimal norm  58.39539267855518\n",
      "Found minimum norm =  58.79165843997469  for s =  0.0646484375\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11ZZ  gave for s =  0.0646484375   minimal norm  58.79165843997469\n",
      "Found minimum norm =  57.607321369375995  for s =  0.0587890625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11Z1  gave for s =  0.0587890625   minimal norm  57.607321369375995\n",
      "Found minimum norm =  59.17364702236818  for s =  0.06699218750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZ111Z  gave for s =  0.06699218750000001   minimal norm  59.17364702236818\n",
      "Found minimum norm =  60.95557195483594  for s =  0.0880859375\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1111  gave for s =  0.0880859375   minimal norm  60.95557195483594\n",
      "Found minimum norm =  59.30242179822068  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZZ  gave for s =  0.0498046875   minimal norm  59.30242179822068\n",
      "Found minimum norm =  57.95118716782624  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZ1  gave for s =  0.0498046875   minimal norm  57.95118716782624\n",
      "Found minimum norm =  56.63003996776743  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ1Z  gave for s =  0.048242187500000006   minimal norm  56.63003996776743\n",
      "Found minimum norm =  58.41924840833319  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ11  gave for s =  0.0498046875   minimal norm  58.41924840833319\n",
      "Found minimum norm =  56.464902763184504  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1ZZ  gave for s =  0.0498046875   minimal norm  56.464902763184504\n",
      "Found minimum norm =  55.1403854265222  for s =  0.0470703125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1Z1  gave for s =  0.0470703125   minimal norm  55.1403854265222\n",
      "Found minimum norm =  56.58327536004987  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z11Z  gave for s =  0.0498046875   minimal norm  56.58327536004987\n",
      "Found minimum norm =  58.8627339237514  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z111  gave for s =  0.0498046875   minimal norm  58.8627339237514\n",
      "Found minimum norm =  58.79165843997469  for s =  0.0646484375\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZZ  gave for s =  0.0646484375   minimal norm  58.79165843997469\n",
      "Found minimum norm =  57.651420771970784  for s =  0.0583984375\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZ1  gave for s =  0.0583984375   minimal norm  57.651420771970784\n",
      "Found minimum norm =  56.58327536004985  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z1Z  gave for s =  0.0498046875   minimal norm  56.58327536004985\n",
      "Found minimum norm =  57.999389037282526  for s =  0.0607421875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z11  gave for s =  0.0607421875   minimal norm  57.999389037282526\n",
      "Found minimum norm =  59.17364702236819  for s =  0.06699218750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ111ZZ  gave for s =  0.06699218750000001   minimal norm  59.17364702236819\n",
      "Found minimum norm =  57.99938903728253  for s =  0.0607421875\n",
      "Flow step output with generator type  single_commutator using string  ZZ111Z1  gave for s =  0.0607421875   minimal norm  57.99938903728253\n",
      "Found minimum norm =  59.547359141927494  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1111Z  gave for s =  0.0701171875   minimal norm  59.547359141927494\n",
      "Found minimum norm =  61.24619658809556  for s =  0.09824218750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ11111  gave for s =  0.09824218750000001   minimal norm  61.24619658809556\n",
      "Found minimum norm =  59.302421798220685  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZZ  gave for s =  0.0498046875   minimal norm  59.302421798220685\n",
      "Found minimum norm =  57.95118716782625  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZ1  gave for s =  0.0498046875   minimal norm  57.95118716782625\n",
      "Found minimum norm =  56.630039967767445  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ1Z  gave for s =  0.048242187500000006   minimal norm  56.630039967767445\n",
      "Found minimum norm =  58.41924840833319  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ11  gave for s =  0.0498046875   minimal norm  58.41924840833319\n",
      "Found minimum norm =  56.63003996776743  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1ZZ  gave for s =  0.048242187500000006   minimal norm  56.63003996776743\n",
      "Found minimum norm =  55.27749616988717  for s =  0.046289062500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1Z1  gave for s =  0.046289062500000006   minimal norm  55.27749616988717\n",
      "Found minimum norm =  56.60789475844434  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ11Z  gave for s =  0.0498046875   minimal norm  56.60789475844434\n",
      "Found minimum norm =  58.886400327157354  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ111  gave for s =  0.0498046875   minimal norm  58.886400327157354\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  56.46490276318451  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZZ  gave for s =  0.0498046875   minimal norm  56.46490276318451\n",
      "Found minimum norm =  55.160861156833285  for s =  0.0470703125\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZ1  gave for s =  0.0470703125   minimal norm  55.160861156833285\n",
      "Found minimum norm =  53.66261141087955  for s =  0.04355468750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z1Z  gave for s =  0.04355468750000001   minimal norm  53.66261141087955\n",
      "Found minimum norm =  55.590960300070144  for s =  0.0478515625\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z11  gave for s =  0.0478515625   minimal norm  55.590960300070144\n",
      "Found minimum norm =  56.58327536004986  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11ZZ  gave for s =  0.0498046875   minimal norm  56.58327536004986\n",
      "Found minimum norm =  55.26926564514319  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11Z1  gave for s =  0.048242187500000006   minimal norm  55.26926564514319\n",
      "Found minimum norm =  57.040453012090374  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z111Z  gave for s =  0.0498046875   minimal norm  57.040453012090374\n",
      "Found minimum norm =  59.139706837002336  for s =  0.058007812500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1111  gave for s =  0.058007812500000006   minimal norm  59.139706837002336\n",
      "Found minimum norm =  58.7916584399747  for s =  0.0646484375\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZZ  gave for s =  0.0646484375   minimal norm  58.7916584399747\n",
      "Found minimum norm =  57.651420771970784  for s =  0.0583984375\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZ1  gave for s =  0.0583984375   minimal norm  57.651420771970784\n",
      "Found minimum norm =  56.60789475844434  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ1Z  gave for s =  0.0498046875   minimal norm  56.60789475844434\n",
      "Found minimum norm =  58.04827190316681  for s =  0.0603515625\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ11  gave for s =  0.0603515625   minimal norm  58.04827190316681\n",
      "Found minimum norm =  56.58327536004986  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1ZZ  gave for s =  0.0498046875   minimal norm  56.58327536004986\n",
      "Found minimum norm =  55.2692656451432  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1Z1  gave for s =  0.048242187500000006   minimal norm  55.2692656451432\n",
      "Found minimum norm =  56.55082662398689  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z11Z  gave for s =  0.0498046875   minimal norm  56.55082662398689\n",
      "Found minimum norm =  58.38476100950885  for s =  0.0626953125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z111  gave for s =  0.0626953125   minimal norm  58.38476100950885\n",
      "Found minimum norm =  59.17364702236818  for s =  0.06699218750000001\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZZ  gave for s =  0.06699218750000001   minimal norm  59.17364702236818\n",
      "Found minimum norm =  58.04827190316681  for s =  0.0603515625\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZ1  gave for s =  0.0603515625   minimal norm  58.04827190316681\n",
      "Found minimum norm =  57.040453012090374  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z111Z1Z  gave for s =  0.0498046875   minimal norm  57.040453012090374\n",
      "Found minimum norm =  58.38476100950885  for s =  0.0626953125\n",
      "Flow step output with generator type  single_commutator using string  Z111Z11  gave for s =  0.0626953125   minimal norm  58.38476100950885\n",
      "Found minimum norm =  59.547359141927494  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  Z1111ZZ  gave for s =  0.0701171875   minimal norm  59.547359141927494\n",
      "Found minimum norm =  58.38476100950885  for s =  0.0626953125\n",
      "Flow step output with generator type  single_commutator using string  Z1111Z1  gave for s =  0.0626953125   minimal norm  58.38476100950885\n",
      "Found minimum norm =  59.910078782124415  for s =  0.07363281250000002\n",
      "Flow step output with generator type  single_commutator using string  Z11111Z  gave for s =  0.07363281250000002   minimal norm  59.910078782124415\n",
      "Found minimum norm =  59.35321766227213  for s =  0.0998046875\n",
      "Flow step output with generator type  single_commutator using string  Z111111  gave for s =  0.0998046875   minimal norm  59.35321766227213\n",
      "Found minimum norm =  59.90311992765712  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZZ  gave for s =  0.07285156250000001   minimal norm  59.90311992765712\n",
      "Found minimum norm =  58.7916584399747  for s =  0.0646484375\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZ1  gave for s =  0.0646484375   minimal norm  58.7916584399747\n",
      "Found minimum norm =  57.95118716782625  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ1Z  gave for s =  0.0498046875   minimal norm  57.95118716782625\n",
      "Found minimum norm =  59.1736470223682  for s =  0.06699218750000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ11  gave for s =  0.06699218750000001   minimal norm  59.1736470223682\n",
      "Found minimum norm =  57.95118716782625  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1ZZ  gave for s =  0.0498046875   minimal norm  57.95118716782625\n",
      "Found minimum norm =  56.58327536004987  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1Z1  gave for s =  0.0498046875   minimal norm  56.58327536004987\n",
      "Found minimum norm =  57.65142077197079  for s =  0.0583984375\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ11Z  gave for s =  0.0583984375   minimal norm  57.65142077197079\n",
      "Found minimum norm =  59.547359141927494  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ111  gave for s =  0.0701171875   minimal norm  59.547359141927494\n",
      "Found minimum norm =  57.95118716782625  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZZ  gave for s =  0.0498046875   minimal norm  57.95118716782625\n",
      "Found minimum norm =  56.607894758444324  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZ1  gave for s =  0.0498046875   minimal norm  56.607894758444324\n",
      "Found minimum norm =  55.16086115683328  for s =  0.0470703125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z1Z  gave for s =  0.0470703125   minimal norm  55.16086115683328\n",
      "Found minimum norm =  57.040453012090374  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z11  gave for s =  0.0498046875   minimal norm  57.040453012090374\n",
      "Found minimum norm =  57.651420771970784  for s =  0.0583984375\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11ZZ  gave for s =  0.0583984375   minimal norm  57.651420771970784\n",
      "Found minimum norm =  56.5508266239869  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11Z1  gave for s =  0.0498046875   minimal norm  56.5508266239869\n",
      "Found minimum norm =  58.04827190316681  for s =  0.0603515625\n",
      "Flow step output with generator type  single_commutator using string  1ZZ111Z  gave for s =  0.0603515625   minimal norm  58.04827190316681\n",
      "Found minimum norm =  59.91007878212443  for s =  0.07363281250000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1111  gave for s =  0.07363281250000002   minimal norm  59.91007878212443\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  57.92713867997059  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZZ  gave for s =  0.0498046875   minimal norm  57.92713867997059\n",
      "Found minimum norm =  56.58327536004986  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZ1  gave for s =  0.0498046875   minimal norm  56.58327536004986\n",
      "Found minimum norm =  55.27749616988718  for s =  0.046289062500000006\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ1Z  gave for s =  0.046289062500000006   minimal norm  55.27749616988718\n",
      "Found minimum norm =  57.040453012090374  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ11  gave for s =  0.0498046875   minimal norm  57.040453012090374\n",
      "Found minimum norm =  55.1403854265222  for s =  0.0470703125\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1ZZ  gave for s =  0.0470703125   minimal norm  55.1403854265222\n",
      "Found minimum norm =  53.79925054370304  for s =  0.04472656250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1Z1  gave for s =  0.04472656250000001   minimal norm  53.79925054370304\n",
      "Found minimum norm =  55.2692656451432  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z11Z  gave for s =  0.048242187500000006   minimal norm  55.2692656451432\n",
      "Found minimum norm =  57.479348910982324  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z111  gave for s =  0.0498046875   minimal norm  57.479348910982324\n",
      "Found minimum norm =  57.607321369375995  for s =  0.0587890625\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZZ  gave for s =  0.0587890625   minimal norm  57.607321369375995\n",
      "Found minimum norm =  56.55082662398689  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZ1  gave for s =  0.0498046875   minimal norm  56.55082662398689\n",
      "Found minimum norm =  55.2692656451432  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z1Z  gave for s =  0.048242187500000006   minimal norm  55.2692656451432\n",
      "Found minimum norm =  56.99441819827817  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z11  gave for s =  0.0498046875   minimal norm  56.99441819827817\n",
      "Found minimum norm =  57.99938903728255  for s =  0.0607421875\n",
      "Flow step output with generator type  single_commutator using string  1Z111ZZ  gave for s =  0.0607421875   minimal norm  57.99938903728255\n",
      "Found minimum norm =  56.99441819827817  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z111Z1  gave for s =  0.0498046875   minimal norm  56.99441819827817\n",
      "Found minimum norm =  58.38476100950885  for s =  0.0626953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1111Z  gave for s =  0.0626953125   minimal norm  58.38476100950885\n",
      "Found minimum norm =  57.35117920480263  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z11111  gave for s =  0.07285156250000001   minimal norm  57.35117920480263\n",
      "Found minimum norm =  60.26933917912078  for s =  0.07675781250000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZZ  gave for s =  0.07675781250000001   minimal norm  60.26933917912078\n",
      "Found minimum norm =  59.17364702236819  for s =  0.06699218750000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZ1  gave for s =  0.06699218750000001   minimal norm  59.17364702236819\n",
      "Found minimum norm =  58.41924840833319  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ1Z  gave for s =  0.0498046875   minimal norm  58.41924840833319\n",
      "Found minimum norm =  59.54735914192749  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ11  gave for s =  0.0701171875   minimal norm  59.54735914192749\n",
      "Found minimum norm =  58.41924840833319  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1ZZ  gave for s =  0.0498046875   minimal norm  58.41924840833319\n",
      "Found minimum norm =  57.040453012090374  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1Z1  gave for s =  0.0498046875   minimal norm  57.040453012090374\n",
      "Found minimum norm =  58.048271903166814  for s =  0.0603515625\n",
      "Flow step output with generator type  single_commutator using string  11ZZ11Z  gave for s =  0.0603515625   minimal norm  58.048271903166814\n",
      "Found minimum norm =  59.91007878212443  for s =  0.07363281250000002\n",
      "Flow step output with generator type  single_commutator using string  11ZZ111  gave for s =  0.07363281250000002   minimal norm  59.91007878212443\n",
      "Found minimum norm =  58.39539267855518  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZZ  gave for s =  0.0498046875   minimal norm  58.39539267855518\n",
      "Found minimum norm =  57.040453012090374  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZ1  gave for s =  0.0498046875   minimal norm  57.040453012090374\n",
      "Found minimum norm =  55.59096030007015  for s =  0.0478515625\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z1Z  gave for s =  0.0478515625   minimal norm  55.59096030007015\n",
      "Found minimum norm =  57.479348910982324  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z11  gave for s =  0.0498046875   minimal norm  57.479348910982324\n",
      "Found minimum norm =  57.99938903728253  for s =  0.0607421875\n",
      "Flow step output with generator type  single_commutator using string  11Z11ZZ  gave for s =  0.0607421875   minimal norm  57.99938903728253\n",
      "Found minimum norm =  56.99441819827817  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z11Z1  gave for s =  0.0498046875   minimal norm  56.99441819827817\n",
      "Found minimum norm =  58.38476100950885  for s =  0.0626953125\n",
      "Flow step output with generator type  single_commutator using string  11Z111Z  gave for s =  0.0626953125   minimal norm  58.38476100950885\n",
      "Found minimum norm =  57.35117920480263  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  11Z1111  gave for s =  0.07285156250000001   minimal norm  57.35117920480263\n",
      "Found minimum norm =  60.622847175540855  for s =  0.08144531250000002\n",
      "Flow step output with generator type  single_commutator using string  111ZZZZ  gave for s =  0.08144531250000002   minimal norm  60.622847175540855\n",
      "Found minimum norm =  59.54735914192749  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  111ZZZ1  gave for s =  0.0701171875   minimal norm  59.54735914192749\n",
      "Found minimum norm =  58.88640032715736  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111ZZ1Z  gave for s =  0.0498046875   minimal norm  58.88640032715736\n",
      "Found minimum norm =  59.91007878212442  for s =  0.07363281250000002\n",
      "Flow step output with generator type  single_commutator using string  111ZZ11  gave for s =  0.07363281250000002   minimal norm  59.91007878212442\n",
      "Found minimum norm =  58.8627339237514  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111Z1ZZ  gave for s =  0.0498046875   minimal norm  58.8627339237514\n",
      "Found minimum norm =  57.47934891098232  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111Z1Z1  gave for s =  0.0498046875   minimal norm  57.47934891098232\n",
      "Found minimum norm =  58.38476100950885  for s =  0.0626953125\n",
      "Flow step output with generator type  single_commutator using string  111Z11Z  gave for s =  0.0626953125   minimal norm  58.38476100950885\n",
      "Found minimum norm =  57.35117920480263  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  111Z111  gave for s =  0.07285156250000001   minimal norm  57.35117920480263\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  60.955571954835946  for s =  0.0880859375\n",
      "Flow step output with generator type  single_commutator using string  1111ZZZ  gave for s =  0.0880859375   minimal norm  60.955571954835946\n",
      "Found minimum norm =  59.91007878212442  for s =  0.07363281250000002\n",
      "Flow step output with generator type  single_commutator using string  1111ZZ1  gave for s =  0.07363281250000002   minimal norm  59.91007878212442\n",
      "Found minimum norm =  59.13970683700234  for s =  0.058007812500000006\n",
      "Flow step output with generator type  single_commutator using string  1111Z1Z  gave for s =  0.058007812500000006   minimal norm  59.13970683700234\n",
      "Found minimum norm =  57.35117920480263  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  1111Z11  gave for s =  0.07285156250000001   minimal norm  57.35117920480263\n",
      "Found minimum norm =  61.24619658809556  for s =  0.09824218750000001\n",
      "Flow step output with generator type  single_commutator using string  11111ZZ  gave for s =  0.09824218750000001   minimal norm  61.24619658809556\n",
      "Found minimum norm =  57.35117920480263  for s =  0.07285156250000001\n",
      "Flow step output with generator type  single_commutator using string  11111Z1  gave for s =  0.07285156250000001   minimal norm  57.35117920480263\n",
      "Found minimum norm =  59.353217662272144  for s =  0.0998046875\n",
      "Flow step output with generator type  single_commutator using string  111111Z  gave for s =  0.0998046875   minimal norm  59.353217662272144\n",
      "Found minimum norm =  62.99206299209449  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1111111  gave for s =  0.0001953125   minimal norm  62.99206299209449\n",
      "Found minimum norm =  47.7352772712826  for s =  0.03964843750000001\n",
      "Found that canonical is better because  47.7352772712826 53.66261141087955\n",
      "Found minimum norm =  47.7352772712826  for s =  0.03964843750000001\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  1\n",
      "Found minimum norm =  45.77904288494961  for s =  0.07910156250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZZ  gave for s =  0.07910156250000001   minimal norm  45.77904288494961\n",
      "Found minimum norm =  45.579201151616914  for s =  0.06894531250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZ1  gave for s =  0.06894531250000001   minimal norm  45.579201151616914\n",
      "Found minimum norm =  45.220179023149655  for s =  0.0666015625\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ1Z  gave for s =  0.0666015625   minimal norm  45.220179023149655\n",
      "Found minimum norm =  46.55072566671276  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ11  gave for s =  0.0498046875   minimal norm  46.55072566671276\n",
      "Found minimum norm =  45.765358743416016  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1ZZ  gave for s =  0.0498046875   minimal norm  45.765358743416016\n",
      "Found minimum norm =  44.832555954262645  for s =  0.06738281250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1Z1  gave for s =  0.06738281250000001   minimal norm  44.832555954262645\n",
      "Found minimum norm =  45.982247589745235  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ11Z  gave for s =  0.0498046875   minimal norm  45.982247589745235\n",
      "Found minimum norm =  46.7147811624073  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ111  gave for s =  0.0498046875   minimal norm  46.7147811624073\n",
      "Found minimum norm =  45.77130638865143  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZZ  gave for s =  0.0498046875   minimal norm  45.77130638865143\n",
      "Found minimum norm =  45.28158043840863  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZ1  gave for s =  0.0498046875   minimal norm  45.28158043840863\n",
      "Found minimum norm =  44.22573461133002  for s =  0.0646484375\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z1Z  gave for s =  0.0646484375   minimal norm  44.22573461133002\n",
      "Found minimum norm =  45.9603276240148  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z11  gave for s =  0.0498046875   minimal norm  45.9603276240148\n",
      "Found minimum norm =  46.17445881723275  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11ZZ  gave for s =  0.0498046875   minimal norm  46.17445881723275\n",
      "Found minimum norm =  45.82853674235827  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11Z1  gave for s =  0.0498046875   minimal norm  45.82853674235827\n",
      "Found minimum norm =  46.25445830122092  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ111Z  gave for s =  0.0498046875   minimal norm  46.25445830122092\n",
      "Found minimum norm =  46.65867053629414  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1111  gave for s =  0.0498046875   minimal norm  46.65867053629414\n",
      "Found minimum norm =  45.76535874341602  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZZ  gave for s =  0.0498046875   minimal norm  45.76535874341602\n",
      "Found minimum norm =  45.22630299260385  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZ1  gave for s =  0.0498046875   minimal norm  45.22630299260385\n",
      "Found minimum norm =  44.75599069726628  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ1Z  gave for s =  0.0498046875   minimal norm  44.75599069726628\n",
      "Found minimum norm =  45.91067201280675  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ11  gave for s =  0.0498046875   minimal norm  45.91067201280675\n",
      "Found minimum norm =  44.84902647452931  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1ZZ  gave for s =  0.0498046875   minimal norm  44.84902647452931\n",
      "Found minimum norm =  43.93724029171678  for s =  0.06386718749999999\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1Z1  gave for s =  0.06386718749999999   minimal norm  43.93724029171678\n",
      "Found minimum norm =  45.12711239468043  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z11Z  gave for s =  0.0498046875   minimal norm  45.12711239468043\n",
      "Found minimum norm =  46.418366650551214  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z111  gave for s =  0.0498046875   minimal norm  46.418366650551214\n",
      "Found minimum norm =  46.17445881723275  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZZ  gave for s =  0.0498046875   minimal norm  46.17445881723275\n",
      "Found minimum norm =  45.67409805203979  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZ1  gave for s =  0.0498046875   minimal norm  45.67409805203979\n",
      "Found minimum norm =  45.162916628384885  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z1Z  gave for s =  0.0498046875   minimal norm  45.162916628384885\n",
      "Found minimum norm =  46.400629955191626  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z11  gave for s =  0.0498046875   minimal norm  46.400629955191626\n",
      "Found minimum norm =  46.49167945952621  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ111ZZ  gave for s =  0.0498046875   minimal norm  46.49167945952621\n",
      "Found minimum norm =  46.17968998807477  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ111Z1  gave for s =  0.0498046875   minimal norm  46.17968998807477\n",
      "Found minimum norm =  46.6562131109623  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1111Z  gave for s =  0.0498046875   minimal norm  46.6562131109623\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  46.65335471825567  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11111  gave for s =  0.0498046875   minimal norm  46.65335471825567\n",
      "Found minimum norm =  45.220179023149655  for s =  0.0666015625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZZ  gave for s =  0.0666015625   minimal norm  45.220179023149655\n",
      "Found minimum norm =  45.10128617915345  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZ1  gave for s =  0.0498046875   minimal norm  45.10128617915345\n",
      "Found minimum norm =  44.62866474128635  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ1Z  gave for s =  0.0498046875   minimal norm  44.62866474128635\n",
      "Found minimum norm =  45.777066428877795  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ11  gave for s =  0.0498046875   minimal norm  45.777066428877795\n",
      "Found minimum norm =  44.755990697266284  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1ZZ  gave for s =  0.0498046875   minimal norm  44.755990697266284\n",
      "Found minimum norm =  44.28289810917976  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1Z1  gave for s =  0.0498046875   minimal norm  44.28289810917976\n",
      "Found minimum norm =  44.971284358095076  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ11Z  gave for s =  0.0498046875   minimal norm  44.971284358095076\n",
      "Found minimum norm =  46.25996853285605  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ111  gave for s =  0.0498046875   minimal norm  46.25996853285605\n",
      "Found minimum norm =  44.22573461133002  for s =  0.0646484375\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZZ  gave for s =  0.0646484375   minimal norm  44.22573461133002\n",
      "Found minimum norm =  44.16773642927599  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZ1  gave for s =  0.0498046875   minimal norm  44.16773642927599\n",
      "Found minimum norm =  42.909399290969844  for s =  0.0654296875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z1Z  gave for s =  0.0654296875   minimal norm  42.909399290969844\n",
      "Found minimum norm =  44.38064856092418  for s =  0.0658203125\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z11  gave for s =  0.0658203125   minimal norm  44.38064856092418\n",
      "Found minimum norm =  45.162916628384885  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11ZZ  gave for s =  0.0498046875   minimal norm  45.162916628384885\n",
      "Found minimum norm =  44.812111174263634  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11Z1  gave for s =  0.0498046875   minimal norm  44.812111174263634\n",
      "Found minimum norm =  44.983891153815904  for s =  0.0630859375\n",
      "Flow step output with generator type  single_commutator using string  Z1Z111Z  gave for s =  0.0630859375   minimal norm  44.983891153815904\n",
      "Found minimum norm =  46.158425790251556  for s =  0.07441406250000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1111  gave for s =  0.07441406250000002   minimal norm  46.158425790251556\n",
      "Found minimum norm =  45.98224758974523  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZZ  gave for s =  0.0498046875   minimal norm  45.98224758974523\n",
      "Found minimum norm =  45.431946197896956  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZ1  gave for s =  0.0498046875   minimal norm  45.431946197896956\n",
      "Found minimum norm =  44.971284358095076  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ1Z  gave for s =  0.0498046875   minimal norm  44.971284358095076\n",
      "Found minimum norm =  46.11697662154768  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ11  gave for s =  0.0498046875   minimal norm  46.11697662154768\n",
      "Found minimum norm =  45.12711239468043  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1ZZ  gave for s =  0.0498046875   minimal norm  45.12711239468043\n",
      "Found minimum norm =  44.698339790856295  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1Z1  gave for s =  0.0498046875   minimal norm  44.698339790856295\n",
      "Found minimum norm =  45.4073060221662  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z11Z  gave for s =  0.0498046875   minimal norm  45.4073060221662\n",
      "Found minimum norm =  46.629381146346226  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z111  gave for s =  0.0498046875   minimal norm  46.629381146346226\n",
      "Found minimum norm =  46.254458301220915  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZZ  gave for s =  0.0498046875   minimal norm  46.254458301220915\n",
      "Found minimum norm =  45.789000467671364  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZ1  gave for s =  0.0498046875   minimal norm  45.789000467671364\n",
      "Found minimum norm =  44.98389115381591  for s =  0.0630859375\n",
      "Flow step output with generator type  single_commutator using string  Z111Z1Z  gave for s =  0.0630859375   minimal norm  44.98389115381591\n",
      "Found minimum norm =  46.509301391239575  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z111Z11  gave for s =  0.0498046875   minimal norm  46.509301391239575\n",
      "Found minimum norm =  46.6562131109623  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1111ZZ  gave for s =  0.0498046875   minimal norm  46.6562131109623\n",
      "Found minimum norm =  46.06375298572771  for s =  0.0666015625\n",
      "Flow step output with generator type  single_commutator using string  Z1111Z1  gave for s =  0.0666015625   minimal norm  46.06375298572771\n",
      "Found minimum norm =  46.57514184719504  for s =  0.0677734375\n",
      "Flow step output with generator type  single_commutator using string  Z11111Z  gave for s =  0.0677734375   minimal norm  46.57514184719504\n",
      "Found minimum norm =  45.985889787151024  for s =  0.07675781250000001\n",
      "Flow step output with generator type  single_commutator using string  Z111111  gave for s =  0.07675781250000001   minimal norm  45.985889787151024\n",
      "Found minimum norm =  45.579201151616914  for s =  0.06894531250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZZ  gave for s =  0.06894531250000001   minimal norm  45.579201151616914\n",
      "Found minimum norm =  45.17655791246252  for s =  0.0623046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZ1  gave for s =  0.0623046875   minimal norm  45.17655791246252\n",
      "Found minimum norm =  45.10128617915344  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ1Z  gave for s =  0.0498046875   minimal norm  45.10128617915344\n",
      "Found minimum norm =  45.938749835226666  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ11  gave for s =  0.0498046875   minimal norm  45.938749835226666\n",
      "Found minimum norm =  45.22630299260385  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1ZZ  gave for s =  0.0498046875   minimal norm  45.22630299260385\n",
      "Found minimum norm =  44.78437169551557  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1Z1  gave for s =  0.0498046875   minimal norm  44.78437169551557\n",
      "Found minimum norm =  45.431946197896956  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ11Z  gave for s =  0.0498046875   minimal norm  45.431946197896956\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  46.033960284291574  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ111  gave for s =  0.0498046875   minimal norm  46.033960284291574\n",
      "Found minimum norm =  45.281580438408625  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZZ  gave for s =  0.0498046875   minimal norm  45.281580438408625\n",
      "Found minimum norm =  44.75394986400303  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZ1  gave for s =  0.0498046875   minimal norm  44.75394986400303\n",
      "Found minimum norm =  44.16773642927599  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z1Z  gave for s =  0.0498046875   minimal norm  44.16773642927599\n",
      "Found minimum norm =  45.494411128099436  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z11  gave for s =  0.0498046875   minimal norm  45.494411128099436\n",
      "Found minimum norm =  45.674098052039795  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11ZZ  gave for s =  0.0498046875   minimal norm  45.674098052039795\n",
      "Found minimum norm =  45.3249141266515  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11Z1  gave for s =  0.0498046875   minimal norm  45.3249141266515\n",
      "Found minimum norm =  45.78900046767136  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ111Z  gave for s =  0.0498046875   minimal norm  45.78900046767136\n",
      "Found minimum norm =  46.186109702378204  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1111  gave for s =  0.0498046875   minimal norm  46.186109702378204\n",
      "Found minimum norm =  44.832555954262645  for s =  0.06738281250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZZ  gave for s =  0.06738281250000001   minimal norm  44.832555954262645\n",
      "Found minimum norm =  44.78437169551557  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZ1  gave for s =  0.0498046875   minimal norm  44.78437169551557\n",
      "Found minimum norm =  44.28289810917977  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ1Z  gave for s =  0.0498046875   minimal norm  44.28289810917977\n",
      "Found minimum norm =  45.497101461139096  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ11  gave for s =  0.0498046875   minimal norm  45.497101461139096\n",
      "Found minimum norm =  43.93724029171678  for s =  0.06386718749999999\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1ZZ  gave for s =  0.06386718749999999   minimal norm  43.93724029171678\n",
      "Found minimum norm =  43.200793080800445  for s =  0.0677734375\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1Z1  gave for s =  0.0677734375   minimal norm  43.200793080800445\n",
      "Found minimum norm =  44.698339790856295  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z11Z  gave for s =  0.0498046875   minimal norm  44.698339790856295\n",
      "Found minimum norm =  45.473690277953885  for s =  0.07089843750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z111  gave for s =  0.07089843750000001   minimal norm  45.473690277953885\n",
      "Found minimum norm =  45.82853674235827  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZZ  gave for s =  0.0498046875   minimal norm  45.82853674235827\n",
      "Found minimum norm =  45.32491412665151  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZ1  gave for s =  0.0498046875   minimal norm  45.32491412665151\n",
      "Found minimum norm =  44.81211117426364  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z1Z  gave for s =  0.0498046875   minimal norm  44.81211117426364\n",
      "Found minimum norm =  46.05298149126945  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z11  gave for s =  0.0498046875   minimal norm  46.05298149126945\n",
      "Found minimum norm =  46.17968998807477  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z111ZZ  gave for s =  0.0498046875   minimal norm  46.17968998807477\n",
      "Found minimum norm =  45.590393773834215  for s =  0.06386718749999999\n",
      "Flow step output with generator type  single_commutator using string  1Z111Z1  gave for s =  0.06386718749999999   minimal norm  45.590393773834215\n",
      "Found minimum norm =  46.06375298572772  for s =  0.0666015625\n",
      "Flow step output with generator type  single_commutator using string  1Z1111Z  gave for s =  0.0666015625   minimal norm  46.06375298572772\n",
      "Found minimum norm =  45.020261911867294  for s =  0.07128906250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z11111  gave for s =  0.07128906250000001   minimal norm  45.020261911867294\n",
      "Found minimum norm =  46.55072566671276  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZZ  gave for s =  0.0498046875   minimal norm  46.55072566671276\n",
      "Found minimum norm =  45.93874983522666  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZ1  gave for s =  0.0498046875   minimal norm  45.93874983522666\n",
      "Found minimum norm =  45.77706642887779  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ1Z  gave for s =  0.0498046875   minimal norm  45.77706642887779\n",
      "Found minimum norm =  46.2710207510442  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ11  gave for s =  0.0498046875   minimal norm  46.2710207510442\n",
      "Found minimum norm =  45.91067201280674  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1ZZ  gave for s =  0.0498046875   minimal norm  45.91067201280674\n",
      "Found minimum norm =  45.497101461139096  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1Z1  gave for s =  0.0498046875   minimal norm  45.497101461139096\n",
      "Found minimum norm =  46.11697662154768  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ11Z  gave for s =  0.0498046875   minimal norm  46.11697662154768\n",
      "Found minimum norm =  46.410533930897515  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  11ZZ111  gave for s =  0.048242187500000006   minimal norm  46.410533930897515\n",
      "Found minimum norm =  45.9603276240148  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZZ  gave for s =  0.0498046875   minimal norm  45.9603276240148\n",
      "Found minimum norm =  45.494411128099436  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZ1  gave for s =  0.0498046875   minimal norm  45.494411128099436\n",
      "Found minimum norm =  44.38064856092418  for s =  0.0658203125\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z1Z  gave for s =  0.0658203125   minimal norm  44.38064856092418\n",
      "Found minimum norm =  46.14190024202076  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z11  gave for s =  0.0498046875   minimal norm  46.14190024202076\n",
      "Found minimum norm =  46.400629955191626  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z11ZZ  gave for s =  0.0498046875   minimal norm  46.400629955191626\n",
      "Found minimum norm =  46.052981491269456  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z11Z1  gave for s =  0.0498046875   minimal norm  46.052981491269456\n",
      "Found minimum norm =  46.509301391239575  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z111Z  gave for s =  0.0498046875   minimal norm  46.509301391239575\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  44.723171867401454  for s =  0.0615234375\n",
      "Flow step output with generator type  single_commutator using string  11Z1111  gave for s =  0.0615234375   minimal norm  44.723171867401454\n",
      "Found minimum norm =  46.7147811624073  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111ZZZZ  gave for s =  0.0498046875   minimal norm  46.7147811624073\n",
      "Found minimum norm =  46.03396028429158  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111ZZZ1  gave for s =  0.0498046875   minimal norm  46.03396028429158\n",
      "Found minimum norm =  46.25996853285605  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111ZZ1Z  gave for s =  0.0498046875   minimal norm  46.25996853285605\n",
      "Found minimum norm =  46.41053393089752  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  111ZZ11  gave for s =  0.048242187500000006   minimal norm  46.41053393089752\n",
      "Found minimum norm =  46.418366650551214  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111Z1ZZ  gave for s =  0.0498046875   minimal norm  46.418366650551214\n",
      "Found minimum norm =  45.473690277953885  for s =  0.07089843750000001\n",
      "Flow step output with generator type  single_commutator using string  111Z1Z1  gave for s =  0.07089843750000001   minimal norm  45.473690277953885\n",
      "Found minimum norm =  46.62938114634622  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111Z11Z  gave for s =  0.0498046875   minimal norm  46.62938114634622\n",
      "Found minimum norm =  44.669944713898055  for s =  0.061914062500000006\n",
      "Flow step output with generator type  single_commutator using string  111Z111  gave for s =  0.061914062500000006   minimal norm  44.669944713898055\n",
      "Found minimum norm =  46.65867053629414  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1111ZZZ  gave for s =  0.0498046875   minimal norm  46.65867053629414\n",
      "Found minimum norm =  46.186109702378204  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1111ZZ1  gave for s =  0.0498046875   minimal norm  46.186109702378204\n",
      "Found minimum norm =  46.158425790251556  for s =  0.07441406250000002\n",
      "Flow step output with generator type  single_commutator using string  1111Z1Z  gave for s =  0.07441406250000002   minimal norm  46.158425790251556\n",
      "Found minimum norm =  44.72317186740146  for s =  0.0615234375\n",
      "Flow step output with generator type  single_commutator using string  1111Z11  gave for s =  0.0615234375   minimal norm  44.72317186740146\n",
      "Found minimum norm =  46.65335471825568  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11111ZZ  gave for s =  0.0498046875   minimal norm  46.65335471825568\n",
      "Found minimum norm =  45.020261911867294  for s =  0.07128906250000001\n",
      "Flow step output with generator type  single_commutator using string  11111Z1  gave for s =  0.07128906250000001   minimal norm  45.020261911867294\n",
      "Found minimum norm =  45.985889787151024  for s =  0.07675781250000001\n",
      "Flow step output with generator type  single_commutator using string  111111Z  gave for s =  0.07675781250000001   minimal norm  45.985889787151024\n",
      "Found minimum norm =  47.7352772712826  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1111111  gave for s =  0.0001953125   minimal norm  47.7352772712826\n",
      "Found minimum norm =  39.29658561128848  for s =  0.020507812500000003\n",
      "Found that canonical is better because  39.29658561128848 42.909399290969844\n",
      "Found minimum norm =  39.29658561128848  for s =  0.020507812500000003\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  2\n",
      "Found minimum norm =  38.85733292083084  for s =  0.040429687500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZZ  gave for s =  0.040429687500000006   minimal norm  38.85733292083084\n",
      "Found minimum norm =  38.637567968558386  for s =  0.0451171875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZ1  gave for s =  0.0451171875   minimal norm  38.637567968558386\n",
      "Found minimum norm =  38.65884247743653  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ1Z  gave for s =  0.0498046875   minimal norm  38.65884247743653\n",
      "Found minimum norm =  38.81534091047969  for s =  0.03574218750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ11  gave for s =  0.03574218750000001   minimal norm  38.81534091047969\n",
      "Found minimum norm =  38.80960155770249  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1ZZ  gave for s =  0.0498046875   minimal norm  38.80960155770249\n",
      "Found minimum norm =  38.71177382751104  for s =  0.0490234375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1Z1  gave for s =  0.0490234375   minimal norm  38.71177382751104\n",
      "Found minimum norm =  39.07596322984887  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ11Z  gave for s =  0.0373046875   minimal norm  39.07596322984887\n",
      "Found minimum norm =  38.73539898507418  for s =  0.0349609375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ111  gave for s =  0.0349609375   minimal norm  38.73539898507418\n",
      "Found minimum norm =  38.797409891865236  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZZ  gave for s =  0.0498046875   minimal norm  38.797409891865236\n",
      "Found minimum norm =  38.46640052030191  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZ1  gave for s =  0.0498046875   minimal norm  38.46640052030191\n",
      "Found minimum norm =  38.359417222276406  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z1Z  gave for s =  0.0498046875   minimal norm  38.359417222276406\n",
      "Found minimum norm =  39.08126213078582  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z11  gave for s =  0.0373046875   minimal norm  39.08126213078582\n",
      "Found minimum norm =  39.2434007335387  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11ZZ  gave for s =  0.024804687500000002   minimal norm  39.2434007335387\n",
      "Found minimum norm =  39.18666110253891  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11Z1  gave for s =  0.024804687500000002   minimal norm  39.18666110253891\n",
      "Found minimum norm =  39.2273304233223  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ111Z  gave for s =  0.024804687500000002   minimal norm  39.2273304233223\n",
      "Found minimum norm =  38.40230533530976  for s =  0.042382812500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1111  gave for s =  0.042382812500000006   minimal norm  38.40230533530976\n",
      "Found minimum norm =  38.80960155770249  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZZ  gave for s =  0.0498046875   minimal norm  38.80960155770249\n",
      "Found minimum norm =  38.555051346696345  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZ1  gave for s =  0.0498046875   minimal norm  38.555051346696345\n",
      "Found minimum norm =  37.99218934538115  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ1Z  gave for s =  0.0498046875   minimal norm  37.99218934538115\n",
      "Found minimum norm =  38.98550976860907  for s =  0.0458984375\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ11  gave for s =  0.0458984375   minimal norm  38.98550976860907\n",
      "Found minimum norm =  38.46049668033178  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1ZZ  gave for s =  0.0498046875   minimal norm  38.46049668033178\n",
      "Found minimum norm =  38.35816363218563  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1Z1  gave for s =  0.0498046875   minimal norm  38.35816363218563\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  38.7140916019663  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z11Z  gave for s =  0.048242187500000006   minimal norm  38.7140916019663\n",
      "Found minimum norm =  39.162147948655026  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z111  gave for s =  0.024804687500000002   minimal norm  39.162147948655026\n",
      "Found minimum norm =  39.2434007335387  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZZ  gave for s =  0.024804687500000002   minimal norm  39.2434007335387\n",
      "Found minimum norm =  39.08307887565195  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZ1  gave for s =  0.0373046875   minimal norm  39.08307887565195\n",
      "Found minimum norm =  38.90809440621677  for s =  0.0419921875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z1Z  gave for s =  0.0419921875   minimal norm  38.90809440621677\n",
      "Found minimum norm =  39.26366178669623  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z11  gave for s =  0.012304687500000001   minimal norm  39.26366178669623\n",
      "Found minimum norm =  39.294903066097866  for s =  0.0076171875\n",
      "Flow step output with generator type  single_commutator using string  ZZ111ZZ  gave for s =  0.0076171875   minimal norm  39.294903066097866\n",
      "Found minimum norm =  39.28365580171565  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ111Z1  gave for s =  0.016992187500000002   minimal norm  39.28365580171565\n",
      "Found minimum norm =  39.27450541358511  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ1111Z  gave for s =  0.024804687500000002   minimal norm  39.27450541358511\n",
      "Found minimum norm =  38.54233624150311  for s =  0.0427734375\n",
      "Flow step output with generator type  single_commutator using string  ZZ11111  gave for s =  0.0427734375   minimal norm  38.54233624150311\n",
      "Found minimum norm =  38.65884247743653  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZZ  gave for s =  0.0498046875   minimal norm  38.65884247743653\n",
      "Found minimum norm =  38.38669544465382  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZ1  gave for s =  0.0498046875   minimal norm  38.38669544465382\n",
      "Found minimum norm =  37.978066972142145  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ1Z  gave for s =  0.0498046875   minimal norm  37.978066972142145\n",
      "Found minimum norm =  38.8481753584112  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ11  gave for s =  0.04550781250000001   minimal norm  38.8481753584112\n",
      "Found minimum norm =  37.99218934538114  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1ZZ  gave for s =  0.0498046875   minimal norm  37.99218934538114\n",
      "Found minimum norm =  37.90850729862753  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1Z1  gave for s =  0.0498046875   minimal norm  37.90850729862753\n",
      "Found minimum norm =  38.36365100468964  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ11Z  gave for s =  0.0498046875   minimal norm  38.36365100468964\n",
      "Found minimum norm =  38.92329600517171  for s =  0.0439453125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ111  gave for s =  0.0439453125   minimal norm  38.92329600517171\n",
      "Found minimum norm =  38.35941722227641  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZZ  gave for s =  0.0498046875   minimal norm  38.35941722227641\n",
      "Found minimum norm =  37.97182954141522  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZ1  gave for s =  0.0498046875   minimal norm  37.97182954141522\n",
      "Found minimum norm =  37.77380903710877  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z1Z  gave for s =  0.0498046875   minimal norm  37.77380903710877\n",
      "Found minimum norm =  38.75457292587737  for s =  0.0458984375\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z11  gave for s =  0.0458984375   minimal norm  38.75457292587737\n",
      "Found minimum norm =  38.90809440621676  for s =  0.0419921875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11ZZ  gave for s =  0.0419921875   minimal norm  38.90809440621676\n",
      "Found minimum norm =  38.796918989553475  for s =  0.04355468750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11Z1  gave for s =  0.04355468750000001   minimal norm  38.796918989553475\n",
      "Found minimum norm =  38.82408589399464  for s =  0.046289062500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1Z111Z  gave for s =  0.046289062500000006   minimal norm  38.82408589399464\n",
      "Found minimum norm =  38.91135329897212  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1111  gave for s =  0.03886718750000001   minimal norm  38.91135329897212\n",
      "Found minimum norm =  39.07596322984887  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZZ  gave for s =  0.0373046875   minimal norm  39.07596322984887\n",
      "Found minimum norm =  38.855139497139106  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZ1  gave for s =  0.04550781250000001   minimal norm  38.855139497139106\n",
      "Found minimum norm =  38.363651004689636  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ1Z  gave for s =  0.0498046875   minimal norm  38.363651004689636\n",
      "Found minimum norm =  39.14025804509115  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ11  gave for s =  0.0330078125   minimal norm  39.14025804509115\n",
      "Found minimum norm =  38.71409160196631  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1ZZ  gave for s =  0.048242187500000006   minimal norm  38.71409160196631\n",
      "Found minimum norm =  38.61989891525525  for s =  0.047460937499999994\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1Z1  gave for s =  0.047460937499999994   minimal norm  38.61989891525525\n",
      "Found minimum norm =  38.95883912381337  for s =  0.04160156250000001\n",
      "Flow step output with generator type  single_commutator using string  Z11Z11Z  gave for s =  0.04160156250000001   minimal norm  38.95883912381337\n",
      "Found minimum norm =  39.10720897252747  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11Z111  gave for s =  0.024804687500000002   minimal norm  39.10720897252747\n",
      "Found minimum norm =  39.2273304233223  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZZ  gave for s =  0.024804687500000002   minimal norm  39.2273304233223\n",
      "Found minimum norm =  39.008305181363475  for s =  0.044335937500000006\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZ1  gave for s =  0.044335937500000006   minimal norm  39.008305181363475\n",
      "Found minimum norm =  38.82408589399464  for s =  0.046289062500000006\n",
      "Flow step output with generator type  single_commutator using string  Z111Z1Z  gave for s =  0.046289062500000006   minimal norm  38.82408589399464\n",
      "Found minimum norm =  39.286971438269  for s =  0.009179687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z111Z11  gave for s =  0.009179687500000002   minimal norm  39.286971438269\n",
      "Found minimum norm =  39.27450541358512  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1111ZZ  gave for s =  0.024804687500000002   minimal norm  39.27450541358512\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  39.2562986240784  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1111Z1  gave for s =  0.024804687500000002   minimal norm  39.2562986240784\n",
      "Found minimum norm =  39.129595824101926  for s =  0.0486328125\n",
      "Flow step output with generator type  single_commutator using string  Z11111Z  gave for s =  0.0486328125   minimal norm  39.129595824101926\n",
      "Found minimum norm =  38.03945096684848  for s =  0.0697265625\n",
      "Flow step output with generator type  single_commutator using string  Z111111  gave for s =  0.0697265625   minimal norm  38.03945096684848\n",
      "Found minimum norm =  38.637567968558386  for s =  0.0451171875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZZ  gave for s =  0.0451171875   minimal norm  38.637567968558386\n",
      "Found minimum norm =  38.35926808229903  for s =  0.04941406250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZ1  gave for s =  0.04941406250000001   minimal norm  38.35926808229903\n",
      "Found minimum norm =  38.38669544465382  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ1Z  gave for s =  0.0498046875   minimal norm  38.38669544465382\n",
      "Found minimum norm =  38.59508724321767  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ11  gave for s =  0.0412109375   minimal norm  38.59508724321767\n",
      "Found minimum norm =  38.555051346696345  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1ZZ  gave for s =  0.0498046875   minimal norm  38.555051346696345\n",
      "Found minimum norm =  38.40469832120014  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1Z1  gave for s =  0.0498046875   minimal norm  38.40469832120014\n",
      "Found minimum norm =  38.8551394971391  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ11Z  gave for s =  0.04550781250000001   minimal norm  38.8551394971391\n",
      "Found minimum norm =  38.33254799691208  for s =  0.0431640625\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ111  gave for s =  0.0431640625   minimal norm  38.33254799691208\n",
      "Found minimum norm =  38.4664005203019  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZZ  gave for s =  0.0498046875   minimal norm  38.4664005203019\n",
      "Found minimum norm =  38.10772162639998  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZ1  gave for s =  0.0498046875   minimal norm  38.10772162639998\n",
      "Found minimum norm =  37.97182954141522  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z1Z  gave for s =  0.0498046875   minimal norm  37.97182954141522\n",
      "Found minimum norm =  38.75191157202829  for s =  0.0486328125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z11  gave for s =  0.0486328125   minimal norm  38.75191157202829\n",
      "Found minimum norm =  39.08307887565195  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11ZZ  gave for s =  0.0373046875   minimal norm  39.08307887565195\n",
      "Found minimum norm =  38.94536114380647  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11Z1  gave for s =  0.0412109375   minimal norm  38.94536114380647\n",
      "Found minimum norm =  39.00830518136348  for s =  0.044335937500000006\n",
      "Flow step output with generator type  single_commutator using string  1ZZ111Z  gave for s =  0.044335937500000006   minimal norm  39.00830518136348\n",
      "Found minimum norm =  38.44423078035598  for s =  0.0478515625\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1111  gave for s =  0.0478515625   minimal norm  38.44423078035598\n",
      "Found minimum norm =  38.71177382751103  for s =  0.0490234375\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZZ  gave for s =  0.0490234375   minimal norm  38.71177382751103\n",
      "Found minimum norm =  38.404698321200144  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZ1  gave for s =  0.0498046875   minimal norm  38.404698321200144\n",
      "Found minimum norm =  37.90850729862754  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ1Z  gave for s =  0.0498046875   minimal norm  37.90850729862754\n",
      "Found minimum norm =  38.79005609865963  for s =  0.0466796875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ11  gave for s =  0.0466796875   minimal norm  38.79005609865963\n",
      "Found minimum norm =  38.35816363218563  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1ZZ  gave for s =  0.0498046875   minimal norm  38.35816363218563\n",
      "Found minimum norm =  38.22174774436791  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1Z1  gave for s =  0.0498046875   minimal norm  38.22174774436791\n",
      "Found minimum norm =  38.61989891525525  for s =  0.047460937499999994\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z11Z  gave for s =  0.047460937499999994   minimal norm  38.61989891525525\n",
      "Found minimum norm =  38.94249351708379  for s =  0.03691406250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z111  gave for s =  0.03691406250000001   minimal norm  38.94249351708379\n",
      "Found minimum norm =  39.186661102538906  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZZ  gave for s =  0.024804687500000002   minimal norm  39.186661102538906\n",
      "Found minimum norm =  38.94536114380647  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZ1  gave for s =  0.0412109375   minimal norm  38.94536114380647\n",
      "Found minimum norm =  38.796918989553475  for s =  0.04355468750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z1Z  gave for s =  0.04355468750000001   minimal norm  38.796918989553475\n",
      "Found minimum norm =  39.10805178832632  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z11  gave for s =  0.024804687500000002   minimal norm  39.10805178832632\n",
      "Found minimum norm =  39.28365580171565  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z111ZZ  gave for s =  0.016992187500000002   minimal norm  39.28365580171565\n",
      "Found minimum norm =  39.25035708686  for s =  0.0236328125\n",
      "Flow step output with generator type  single_commutator using string  1Z111Z1  gave for s =  0.0236328125   minimal norm  39.25035708686\n",
      "Found minimum norm =  39.25629862407839  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z1111Z  gave for s =  0.024804687500000002   minimal norm  39.25629862407839\n",
      "Found minimum norm =  37.298499005764164  for s =  0.058007812500000006\n",
      "Flow step output with generator type  single_commutator using string  1Z11111  gave for s =  0.058007812500000006   minimal norm  37.298499005764164\n",
      "Found minimum norm =  38.815340910479684  for s =  0.03574218750000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZZ  gave for s =  0.03574218750000001   minimal norm  38.815340910479684\n",
      "Found minimum norm =  38.59508724321766  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZ1  gave for s =  0.0412109375   minimal norm  38.59508724321766\n",
      "Found minimum norm =  38.84817535841119  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ1Z  gave for s =  0.04550781250000001   minimal norm  38.84817535841119\n",
      "Found minimum norm =  38.50608633229191  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ11  gave for s =  0.0373046875   minimal norm  38.50608633229191\n",
      "Found minimum norm =  38.98550976860907  for s =  0.0458984375\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1ZZ  gave for s =  0.0458984375   minimal norm  38.98550976860907\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  38.790056098659626  for s =  0.0466796875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1Z1  gave for s =  0.0466796875   minimal norm  38.790056098659626\n",
      "Found minimum norm =  39.14025804509115  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  11ZZ11Z  gave for s =  0.0330078125   minimal norm  39.14025804509115\n",
      "Found minimum norm =  38.62114251461759  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  11ZZ111  gave for s =  0.0353515625   minimal norm  38.62114251461759\n",
      "Found minimum norm =  39.081262130785824  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZZ  gave for s =  0.0373046875   minimal norm  39.081262130785824\n",
      "Found minimum norm =  38.75191157202829  for s =  0.0486328125\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZ1  gave for s =  0.0486328125   minimal norm  38.75191157202829\n",
      "Found minimum norm =  38.75457292587737  for s =  0.0458984375\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z1Z  gave for s =  0.0458984375   minimal norm  38.75457292587737\n",
      "Found minimum norm =  39.07178259447152  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z11  gave for s =  0.024804687500000002   minimal norm  39.07178259447152\n",
      "Found minimum norm =  39.263661786696225  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  11Z11ZZ  gave for s =  0.012304687500000001   minimal norm  39.263661786696225\n",
      "Found minimum norm =  39.108051788326314  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z11Z1  gave for s =  0.024804687500000002   minimal norm  39.108051788326314\n",
      "Found minimum norm =  39.286971438269006  for s =  0.009179687500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z111Z  gave for s =  0.009179687500000002   minimal norm  39.286971438269006\n",
      "Found minimum norm =  37.13080621543432  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1111  gave for s =  0.0498046875   minimal norm  37.13080621543432\n",
      "Found minimum norm =  38.73539898507418  for s =  0.0349609375\n",
      "Flow step output with generator type  single_commutator using string  111ZZZZ  gave for s =  0.0349609375   minimal norm  38.73539898507418\n",
      "Found minimum norm =  38.332547996912076  for s =  0.0431640625\n",
      "Flow step output with generator type  single_commutator using string  111ZZZ1  gave for s =  0.0431640625   minimal norm  38.332547996912076\n",
      "Found minimum norm =  38.92329600517171  for s =  0.0439453125\n",
      "Flow step output with generator type  single_commutator using string  111ZZ1Z  gave for s =  0.0439453125   minimal norm  38.92329600517171\n",
      "Found minimum norm =  38.62114251461759  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  111ZZ11  gave for s =  0.0353515625   minimal norm  38.62114251461759\n",
      "Found minimum norm =  39.162147948655026  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  111Z1ZZ  gave for s =  0.024804687500000002   minimal norm  39.162147948655026\n",
      "Found minimum norm =  38.94249351708378  for s =  0.03691406250000001\n",
      "Flow step output with generator type  single_commutator using string  111Z1Z1  gave for s =  0.03691406250000001   minimal norm  38.94249351708378\n",
      "Found minimum norm =  39.10720897252746  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  111Z11Z  gave for s =  0.024804687500000002   minimal norm  39.10720897252746\n",
      "Found minimum norm =  36.95367255072213  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111Z111  gave for s =  0.0498046875   minimal norm  36.95367255072213\n",
      "Found minimum norm =  38.40230533530976  for s =  0.042382812500000006\n",
      "Flow step output with generator type  single_commutator using string  1111ZZZ  gave for s =  0.042382812500000006   minimal norm  38.40230533530976\n",
      "Found minimum norm =  38.444230780355966  for s =  0.0478515625\n",
      "Flow step output with generator type  single_commutator using string  1111ZZ1  gave for s =  0.0478515625   minimal norm  38.444230780355966\n",
      "Found minimum norm =  38.911353298972124  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  1111Z1Z  gave for s =  0.03886718750000001   minimal norm  38.911353298972124\n",
      "Found minimum norm =  37.13080621543432  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1111Z11  gave for s =  0.0498046875   minimal norm  37.13080621543432\n",
      "Found minimum norm =  38.54233624150311  for s =  0.0427734375\n",
      "Flow step output with generator type  single_commutator using string  11111ZZ  gave for s =  0.0427734375   minimal norm  38.54233624150311\n",
      "Found minimum norm =  37.298499005764164  for s =  0.058007812500000006\n",
      "Flow step output with generator type  single_commutator using string  11111Z1  gave for s =  0.058007812500000006   minimal norm  37.298499005764164\n",
      "Found minimum norm =  38.03945096684848  for s =  0.0697265625\n",
      "Flow step output with generator type  single_commutator using string  111111Z  gave for s =  0.0697265625   minimal norm  38.03945096684848\n",
      "Found minimum norm =  39.29658561128848  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1111111  gave for s =  0.0001953125   minimal norm  39.29658561128848\n",
      "Found minimum norm =  33.89018167136041  for s =  0.011132812500000002\n",
      "Found that canonical is better because  33.89018167136041 36.95367255072213\n",
      "Found minimum norm =  33.89018167136041  for s =  0.011132812500000002\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  3\n",
      "Found minimum norm =  33.68641601163334  for s =  0.0212890625\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZZ  gave for s =  0.0212890625   minimal norm  33.68641601163334\n",
      "Found minimum norm =  33.61123152960535  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZ1  gave for s =  0.024804687500000002   minimal norm  33.61123152960535\n",
      "Found minimum norm =  33.82818462148975  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ1Z  gave for s =  0.024804687500000002   minimal norm  33.82818462148975\n",
      "Found minimum norm =  33.52139025660881  for s =  0.0279296875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ11  gave for s =  0.0279296875   minimal norm  33.52139025660881\n",
      "Found minimum norm =  33.89047545032335  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1ZZ  gave for s =  0.0001953125   minimal norm  33.89047545032335\n",
      "Found minimum norm =  33.728383910968134  for s =  0.03964843750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1Z1  gave for s =  0.03964843750000001   minimal norm  33.728383910968134\n",
      "Found minimum norm =  33.87018249111329  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ11Z  gave for s =  0.012304687500000001   minimal norm  33.87018249111329\n",
      "Found minimum norm =  33.39113448889926  for s =  0.0306640625\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ111  gave for s =  0.0306640625   minimal norm  33.39113448889926\n",
      "Found minimum norm =  33.890499010905714  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZZ  gave for s =  0.0001953125   minimal norm  33.890499010905714\n",
      "Found minimum norm =  33.66704476442566  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZ1  gave for s =  0.0498046875   minimal norm  33.66704476442566\n",
      "Found minimum norm =  33.44128762044374  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z1Z  gave for s =  0.0498046875   minimal norm  33.44128762044374\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  33.820588649112324  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z11  gave for s =  0.024804687500000002   minimal norm  33.820588649112324\n",
      "Found minimum norm =  33.883999021907734  for s =  0.005664062500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11ZZ  gave for s =  0.005664062500000001   minimal norm  33.883999021907734\n",
      "Found minimum norm =  33.83757949611086  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11Z1  gave for s =  0.0181640625   minimal norm  33.83757949611086\n",
      "Found minimum norm =  33.881543317168145  for s =  0.009960937500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZ111Z  gave for s =  0.009960937500000003   minimal norm  33.881543317168145\n",
      "Found minimum norm =  33.25957708097293  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1111  gave for s =  0.03886718750000001   minimal norm  33.25957708097293\n",
      "Found minimum norm =  33.89047545032335  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZZ  gave for s =  0.0001953125   minimal norm  33.89047545032335\n",
      "Found minimum norm =  33.80581310473592  for s =  0.04160156250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZ1  gave for s =  0.04160156250000001   minimal norm  33.80581310473592\n",
      "Found minimum norm =  33.17889712981974  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ1Z  gave for s =  0.0498046875   minimal norm  33.17889712981974\n",
      "Found minimum norm =  33.89080186067848  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ11  gave for s =  0.0001953125   minimal norm  33.89080186067848\n",
      "Found minimum norm =  33.517291470491074  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1ZZ  gave for s =  0.0498046875   minimal norm  33.517291470491074\n",
      "Found minimum norm =  33.28247349673378  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1Z1  gave for s =  0.0498046875   minimal norm  33.28247349673378\n",
      "Found minimum norm =  33.73220423742375  for s =  0.0392578125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z11Z  gave for s =  0.0392578125   minimal norm  33.73220423742375\n",
      "Found minimum norm =  33.810941279834516  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z111  gave for s =  0.019335937500000004   minimal norm  33.810941279834516\n",
      "Found minimum norm =  33.88399902190773  for s =  0.005664062500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZZ  gave for s =  0.005664062500000001   minimal norm  33.88399902190773\n",
      "Found minimum norm =  33.84075770491588  for s =  0.0220703125\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZ1  gave for s =  0.0220703125   minimal norm  33.84075770491588\n",
      "Found minimum norm =  33.832612144457926  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z1Z  gave for s =  0.024804687500000002   minimal norm  33.832612144457926\n",
      "Found minimum norm =  33.81156335320702  for s =  0.014257812500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z11  gave for s =  0.014257812500000001   minimal norm  33.81156335320702\n",
      "Found minimum norm =  33.887288704704176  for s =  0.0037109375\n",
      "Flow step output with generator type  single_commutator using string  ZZ111ZZ  gave for s =  0.0037109375   minimal norm  33.887288704704176\n",
      "Found minimum norm =  33.87252678633701  for s =  0.0107421875\n",
      "Flow step output with generator type  single_commutator using string  ZZ111Z1  gave for s =  0.0107421875   minimal norm  33.87252678633701\n",
      "Found minimum norm =  33.88542727628804  for s =  0.0072265625\n",
      "Flow step output with generator type  single_commutator using string  ZZ1111Z  gave for s =  0.0072265625   minimal norm  33.88542727628804\n",
      "Found minimum norm =  33.26318633665401  for s =  0.042382812500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZ11111  gave for s =  0.042382812500000006   minimal norm  33.26318633665401\n",
      "Found minimum norm =  33.82818462148975  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZZ  gave for s =  0.024804687500000002   minimal norm  33.82818462148975\n",
      "Found minimum norm =  33.69514453845986  for s =  0.0392578125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZ1  gave for s =  0.0392578125   minimal norm  33.69514453845986\n",
      "Found minimum norm =  33.20405871143503  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ1Z  gave for s =  0.0498046875   minimal norm  33.20405871143503\n",
      "Found minimum norm =  33.722069498039964  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ11  gave for s =  0.0373046875   minimal norm  33.722069498039964\n",
      "Found minimum norm =  33.17889712981973  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1ZZ  gave for s =  0.0498046875   minimal norm  33.17889712981973\n",
      "Found minimum norm =  32.908010391744064  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1Z1  gave for s =  0.0498046875   minimal norm  32.908010391744064\n",
      "Found minimum norm =  33.42234492060359  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ11Z  gave for s =  0.0498046875   minimal norm  33.42234492060359\n",
      "Found minimum norm =  33.74101398619027  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ111  gave for s =  0.0373046875   minimal norm  33.74101398619027\n",
      "Found minimum norm =  33.441287620443745  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZZ  gave for s =  0.0498046875   minimal norm  33.441287620443745\n",
      "Found minimum norm =  33.05991700331822  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZ1  gave for s =  0.0498046875   minimal norm  33.05991700331822\n",
      "Found minimum norm =  32.92246507392022  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z1Z  gave for s =  0.0498046875   minimal norm  32.92246507392022\n",
      "Found minimum norm =  33.526405612294816  for s =  0.0458984375\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z11  gave for s =  0.0458984375   minimal norm  33.526405612294816\n",
      "Found minimum norm =  33.832612144457926  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11ZZ  gave for s =  0.024804687500000002   minimal norm  33.832612144457926\n",
      "Found minimum norm =  33.6858920911802  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11Z1  gave for s =  0.0373046875   minimal norm  33.6858920911802\n",
      "Found minimum norm =  33.71243212938345  for s =  0.040429687500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1Z111Z  gave for s =  0.040429687500000006   minimal norm  33.71243212938345\n",
      "Found minimum norm =  33.483531246480446  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1111  gave for s =  0.038476562500000006   minimal norm  33.483531246480446\n",
      "Found minimum norm =  33.87018249111328  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZZ  gave for s =  0.012304687500000001   minimal norm  33.87018249111328\n",
      "Found minimum norm =  33.779084119628365  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZ1  gave for s =  0.024804687500000002   minimal norm  33.779084119628365\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  33.42234492060359  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ1Z  gave for s =  0.0498046875   minimal norm  33.42234492060359\n",
      "Found minimum norm =  33.72553937824915  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ11  gave for s =  0.0322265625   minimal norm  33.72553937824915\n",
      "Found minimum norm =  33.73220423742375  for s =  0.0392578125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1ZZ  gave for s =  0.0392578125   minimal norm  33.73220423742375\n",
      "Found minimum norm =  33.51707232864328  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1Z1  gave for s =  0.04550781250000001   minimal norm  33.51707232864328\n",
      "Found minimum norm =  33.8522497074349  for s =  0.0232421875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z11Z  gave for s =  0.0232421875   minimal norm  33.8522497074349\n",
      "Found minimum norm =  33.58455261522626  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11Z111  gave for s =  0.024804687500000002   minimal norm  33.58455261522626\n",
      "Found minimum norm =  33.881543317168145  for s =  0.009960937500000003\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZZ  gave for s =  0.009960937500000003   minimal norm  33.881543317168145\n",
      "Found minimum norm =  33.760658153805906  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZ1  gave for s =  0.0373046875   minimal norm  33.760658153805906\n",
      "Found minimum norm =  33.712432129383444  for s =  0.040429687500000006\n",
      "Flow step output with generator type  single_commutator using string  Z111Z1Z  gave for s =  0.040429687500000006   minimal norm  33.712432129383444\n",
      "Found minimum norm =  33.83788067004946  for s =  0.014257812500000001\n",
      "Flow step output with generator type  single_commutator using string  Z111Z11  gave for s =  0.014257812500000001   minimal norm  33.83788067004946\n",
      "Found minimum norm =  33.88542727628804  for s =  0.0072265625\n",
      "Flow step output with generator type  single_commutator using string  Z1111ZZ  gave for s =  0.0072265625   minimal norm  33.88542727628804\n",
      "Found minimum norm =  33.84847809202142  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  Z1111Z1  gave for s =  0.0240234375   minimal norm  33.84847809202142\n",
      "Found minimum norm =  33.80882584926275  for s =  0.03964843750000001\n",
      "Flow step output with generator type  single_commutator using string  Z11111Z  gave for s =  0.03964843750000001   minimal norm  33.80882584926275\n",
      "Found minimum norm =  32.83964018799411  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  Z111111  gave for s =  0.0701171875   minimal norm  32.83964018799411\n",
      "Found minimum norm =  33.61123152960534  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZZ  gave for s =  0.024804687500000002   minimal norm  33.61123152960534\n",
      "Found minimum norm =  33.49833654256  for s =  0.0314453125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZ1  gave for s =  0.0314453125   minimal norm  33.49833654256\n",
      "Found minimum norm =  33.69514453845986  for s =  0.0392578125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ1Z  gave for s =  0.0392578125   minimal norm  33.69514453845986\n",
      "Found minimum norm =  33.38766285760953  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ11  gave for s =  0.0341796875   minimal norm  33.38766285760953\n",
      "Found minimum norm =  33.805813104735925  for s =  0.04160156250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1ZZ  gave for s =  0.04160156250000001   minimal norm  33.805813104735925\n",
      "Found minimum norm =  33.405669250491734  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1Z1  gave for s =  0.0498046875   minimal norm  33.405669250491734\n",
      "Found minimum norm =  33.77908411962836  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ11Z  gave for s =  0.024804687500000002   minimal norm  33.77908411962836\n",
      "Found minimum norm =  33.26829178072278  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ111  gave for s =  0.0373046875   minimal norm  33.26829178072278\n",
      "Found minimum norm =  33.667044764425654  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZZ  gave for s =  0.0498046875   minimal norm  33.667044764425654\n",
      "Found minimum norm =  33.35033176020376  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZ1  gave for s =  0.0498046875   minimal norm  33.35033176020376\n",
      "Found minimum norm =  33.05991700331821  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z1Z  gave for s =  0.0498046875   minimal norm  33.05991700331821\n",
      "Found minimum norm =  33.59674464276107  for s =  0.0466796875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z11  gave for s =  0.0466796875   minimal norm  33.59674464276107\n",
      "Found minimum norm =  33.84075770491587  for s =  0.0220703125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11ZZ  gave for s =  0.0220703125   minimal norm  33.84075770491587\n",
      "Found minimum norm =  33.63282019167943  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11Z1  gave for s =  0.0373046875   minimal norm  33.63282019167943\n",
      "Found minimum norm =  33.760658153805906  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ111Z  gave for s =  0.0373046875   minimal norm  33.760658153805906\n",
      "Found minimum norm =  33.36092620026174  for s =  0.0439453125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1111  gave for s =  0.0439453125   minimal norm  33.36092620026174\n",
      "Found minimum norm =  33.72838391096814  for s =  0.03964843750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZZ  gave for s =  0.03964843750000001   minimal norm  33.72838391096814\n",
      "Found minimum norm =  33.405669250491734  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZ1  gave for s =  0.0498046875   minimal norm  33.405669250491734\n",
      "Found minimum norm =  32.90801039174406  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ1Z  gave for s =  0.0498046875   minimal norm  32.90801039174406\n",
      "Found minimum norm =  33.44539970069745  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ11  gave for s =  0.0498046875   minimal norm  33.44539970069745\n",
      "Found minimum norm =  33.28247349673378  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1ZZ  gave for s =  0.0498046875   minimal norm  33.28247349673378\n",
      "Found minimum norm =  32.93536056374803  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1Z1  gave for s =  0.0498046875   minimal norm  32.93536056374803\n",
      "Found minimum norm =  33.51707232864329  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z11Z  gave for s =  0.04550781250000001   minimal norm  33.51707232864329\n",
      "Found minimum norm =  33.5856270952704  for s =  0.03691406250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z111  gave for s =  0.03691406250000001   minimal norm  33.5856270952704\n",
      "Found minimum norm =  33.83757949611086  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZZ  gave for s =  0.0181640625   minimal norm  33.83757949611086\n",
      "Found minimum norm =  33.632820191679436  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZ1  gave for s =  0.0373046875   minimal norm  33.632820191679436\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  33.68589209118019  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z1Z  gave for s =  0.0373046875   minimal norm  33.68589209118019\n",
      "Found minimum norm =  33.57354093870352  for s =  0.0279296875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z11  gave for s =  0.0279296875   minimal norm  33.57354093870352\n",
      "Found minimum norm =  33.87252678633701  for s =  0.0107421875\n",
      "Flow step output with generator type  single_commutator using string  1Z111ZZ  gave for s =  0.0107421875   minimal norm  33.87252678633701\n",
      "Found minimum norm =  33.80352753837967  for s =  0.0244140625\n",
      "Flow step output with generator type  single_commutator using string  1Z111Z1  gave for s =  0.0244140625   minimal norm  33.80352753837967\n",
      "Found minimum norm =  33.84847809202143  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  1Z1111Z  gave for s =  0.0240234375   minimal norm  33.84847809202143\n",
      "Found minimum norm =  32.47450958256992  for s =  0.0583984375\n",
      "Flow step output with generator type  single_commutator using string  1Z11111  gave for s =  0.0583984375   minimal norm  32.47450958256992\n",
      "Found minimum norm =  33.52139025660881  for s =  0.0279296875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZZ  gave for s =  0.0279296875   minimal norm  33.52139025660881\n",
      "Found minimum norm =  33.38766285760952  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZ1  gave for s =  0.0341796875   minimal norm  33.38766285760952\n",
      "Found minimum norm =  33.722069498039964  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ1Z  gave for s =  0.0373046875   minimal norm  33.722069498039964\n",
      "Found minimum norm =  33.245235595702134  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ11  gave for s =  0.038476562500000006   minimal norm  33.245235595702134\n",
      "Found minimum norm =  33.89080186067848  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1ZZ  gave for s =  0.0001953125   minimal norm  33.89080186067848\n",
      "Found minimum norm =  33.44539970069746  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1Z1  gave for s =  0.0498046875   minimal norm  33.44539970069746\n",
      "Found minimum norm =  33.72553937824916  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  11ZZ11Z  gave for s =  0.0322265625   minimal norm  33.72553937824916\n",
      "Found minimum norm =  33.419271800742145  for s =  0.0361328125\n",
      "Flow step output with generator type  single_commutator using string  11ZZ111  gave for s =  0.0361328125   minimal norm  33.419271800742145\n",
      "Found minimum norm =  33.820588649112324  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZZ  gave for s =  0.024804687500000002   minimal norm  33.820588649112324\n",
      "Found minimum norm =  33.59674464276107  for s =  0.0466796875\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZ1  gave for s =  0.0466796875   minimal norm  33.59674464276107\n",
      "Found minimum norm =  33.52640561229481  for s =  0.0458984375\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z1Z  gave for s =  0.0458984375   minimal norm  33.52640561229481\n",
      "Found minimum norm =  33.62663932249355  for s =  0.0306640625\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z11  gave for s =  0.0306640625   minimal norm  33.62663932249355\n",
      "Found minimum norm =  33.81156335320702  for s =  0.014257812500000001\n",
      "Flow step output with generator type  single_commutator using string  11Z11ZZ  gave for s =  0.014257812500000001   minimal norm  33.81156335320702\n",
      "Found minimum norm =  33.57354093870352  for s =  0.0279296875\n",
      "Flow step output with generator type  single_commutator using string  11Z11Z1  gave for s =  0.0279296875   minimal norm  33.57354093870352\n",
      "Found minimum norm =  33.83788067004946  for s =  0.014257812500000001\n",
      "Flow step output with generator type  single_commutator using string  11Z111Z  gave for s =  0.014257812500000001   minimal norm  33.83788067004946\n",
      "Found minimum norm =  32.520061149145526  for s =  0.0466796875\n",
      "Flow step output with generator type  single_commutator using string  11Z1111  gave for s =  0.0466796875   minimal norm  32.520061149145526\n",
      "Found minimum norm =  33.39113448889926  for s =  0.0306640625\n",
      "Flow step output with generator type  single_commutator using string  111ZZZZ  gave for s =  0.0306640625   minimal norm  33.39113448889926\n",
      "Found minimum norm =  33.26829178072278  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  111ZZZ1  gave for s =  0.0373046875   minimal norm  33.26829178072278\n",
      "Found minimum norm =  33.74101398619027  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  111ZZ1Z  gave for s =  0.0373046875   minimal norm  33.74101398619027\n",
      "Found minimum norm =  33.419271800742145  for s =  0.0361328125\n",
      "Flow step output with generator type  single_commutator using string  111ZZ11  gave for s =  0.0361328125   minimal norm  33.419271800742145\n",
      "Found minimum norm =  33.810941279834516  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  111Z1ZZ  gave for s =  0.019335937500000004   minimal norm  33.810941279834516\n",
      "Found minimum norm =  33.5856270952704  for s =  0.03691406250000001\n",
      "Flow step output with generator type  single_commutator using string  111Z1Z1  gave for s =  0.03691406250000001   minimal norm  33.5856270952704\n",
      "Found minimum norm =  33.58455261522626  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  111Z11Z  gave for s =  0.024804687500000002   minimal norm  33.58455261522626\n",
      "Found minimum norm =  32.342975329553084  for s =  0.044335937500000006\n",
      "Flow step output with generator type  single_commutator using string  111Z111  gave for s =  0.044335937500000006   minimal norm  32.342975329553084\n",
      "Found minimum norm =  33.25957708097293  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  1111ZZZ  gave for s =  0.03886718750000001   minimal norm  33.25957708097293\n",
      "Found minimum norm =  33.36092620026174  for s =  0.0439453125\n",
      "Flow step output with generator type  single_commutator using string  1111ZZ1  gave for s =  0.0439453125   minimal norm  33.36092620026174\n",
      "Found minimum norm =  33.483531246480446  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  1111Z1Z  gave for s =  0.038476562500000006   minimal norm  33.483531246480446\n",
      "Found minimum norm =  32.52006114914553  for s =  0.0466796875\n",
      "Flow step output with generator type  single_commutator using string  1111Z11  gave for s =  0.0466796875   minimal norm  32.52006114914553\n",
      "Found minimum norm =  33.263186336654016  for s =  0.042382812500000006\n",
      "Flow step output with generator type  single_commutator using string  11111ZZ  gave for s =  0.042382812500000006   minimal norm  33.263186336654016\n",
      "Found minimum norm =  32.47450958256992  for s =  0.0583984375\n",
      "Flow step output with generator type  single_commutator using string  11111Z1  gave for s =  0.0583984375   minimal norm  32.47450958256992\n",
      "Found minimum norm =  32.83964018799411  for s =  0.0701171875\n",
      "Flow step output with generator type  single_commutator using string  111111Z  gave for s =  0.0701171875   minimal norm  32.83964018799411\n",
      "Found minimum norm =  33.89018167136041  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1111111  gave for s =  0.0001953125   minimal norm  33.89018167136041\n",
      "Found minimum norm =  30.926559079849504  for s =  0.0076171875\n",
      "Found that canonical is better because  30.926559079849504 32.342975329553084\n",
      "Found minimum norm =  30.926559079849504  for s =  0.0076171875\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  4\n",
      "Found minimum norm =  30.622442247097943  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZZ  gave for s =  0.024804687500000002   minimal norm  30.622442247097943\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  30.542680705105145  for s =  0.0283203125\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZ1  gave for s =  0.0283203125   minimal norm  30.542680705105145\n",
      "Found minimum norm =  30.85278059474829  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ1Z  gave for s =  0.019335937500000004   minimal norm  30.85278059474829\n",
      "Found minimum norm =  30.49151885320239  for s =  0.0294921875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ11  gave for s =  0.0294921875   minimal norm  30.49151885320239\n",
      "Found minimum norm =  30.923607206196337  for s =  0.0041015625\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1ZZ  gave for s =  0.0041015625   minimal norm  30.923607206196337\n",
      "Found minimum norm =  30.75754527132715  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1Z1  gave for s =  0.0341796875   minimal norm  30.75754527132715\n",
      "Found minimum norm =  30.856728284416647  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ11Z  gave for s =  0.016992187500000002   minimal norm  30.856728284416647\n",
      "Found minimum norm =  30.48515155511364  for s =  0.0294921875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ111  gave for s =  0.0294921875   minimal norm  30.48515155511364\n",
      "Found minimum norm =  30.92686306971702  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZZ  gave for s =  0.0001953125   minimal norm  30.92686306971702\n",
      "Found minimum norm =  30.915345308822985  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZ1  gave for s =  0.024804687500000002   minimal norm  30.915345308822985\n",
      "Found minimum norm =  30.657440683827993  for s =  0.0451171875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z1Z  gave for s =  0.0451171875   minimal norm  30.657440683827993\n",
      "Found minimum norm =  30.832627618766328  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z11  gave for s =  0.024804687500000002   minimal norm  30.832627618766328\n",
      "Found minimum norm =  30.894940514464793  for s =  0.0107421875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11ZZ  gave for s =  0.0107421875   minimal norm  30.894940514464793\n",
      "Found minimum norm =  30.780533059682732  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11Z1  gave for s =  0.024804687500000002   minimal norm  30.780533059682732\n",
      "Found minimum norm =  30.883411234973295  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ111Z  gave for s =  0.016992187500000002   minimal norm  30.883411234973295\n",
      "Found minimum norm =  30.53058483788387  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1111  gave for s =  0.0322265625   minimal norm  30.53058483788387\n",
      "Found minimum norm =  30.923607206196333  for s =  0.0041015625\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZZ  gave for s =  0.0041015625   minimal norm  30.923607206196333\n",
      "Found minimum norm =  30.906123172333743  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZ1  gave for s =  0.018554687500000003   minimal norm  30.906123172333743\n",
      "Found minimum norm =  30.60227676112674  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ1Z  gave for s =  0.0498046875   minimal norm  30.60227676112674\n",
      "Found minimum norm =  30.927197554980932  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ11  gave for s =  0.0001953125   minimal norm  30.927197554980932\n",
      "Found minimum norm =  30.76808245845021  for s =  0.03964843750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1ZZ  gave for s =  0.03964843750000001   minimal norm  30.76808245845021\n",
      "Found minimum norm =  30.428525597800068  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1Z1  gave for s =  0.0498046875   minimal norm  30.428525597800068\n",
      "Found minimum norm =  30.712448272086583  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z11Z  gave for s =  0.0373046875   minimal norm  30.712448272086583\n",
      "Found minimum norm =  30.81706707964252  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z111  gave for s =  0.019726562500000003   minimal norm  30.81706707964252\n",
      "Found minimum norm =  30.894940514464796  for s =  0.0107421875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZZ  gave for s =  0.0107421875   minimal norm  30.894940514464796\n",
      "Found minimum norm =  30.803572199930574  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZ1  gave for s =  0.024804687500000002   minimal norm  30.803572199930574\n",
      "Found minimum norm =  30.78437087167673  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z1Z  gave for s =  0.024804687500000002   minimal norm  30.78437087167673\n",
      "Found minimum norm =  30.709602632275214  for s =  0.0220703125\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z11  gave for s =  0.0220703125   minimal norm  30.709602632275214\n",
      "Found minimum norm =  30.87901843574916  for s =  0.0119140625\n",
      "Flow step output with generator type  single_commutator using string  ZZ111ZZ  gave for s =  0.0119140625   minimal norm  30.87901843574916\n",
      "Found minimum norm =  30.797317937322443  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ111Z1  gave for s =  0.022851562500000002   minimal norm  30.797317937322443\n",
      "Found minimum norm =  30.899140728574267  for s =  0.0119140625\n",
      "Flow step output with generator type  single_commutator using string  ZZ1111Z  gave for s =  0.0119140625   minimal norm  30.899140728574267\n",
      "Found minimum norm =  30.463910749723244  for s =  0.034570312500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZ11111  gave for s =  0.034570312500000006   minimal norm  30.463910749723244\n",
      "Found minimum norm =  30.852780594748292  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZZ  gave for s =  0.019335937500000004   minimal norm  30.852780594748292\n",
      "Found minimum norm =  30.734019252457724  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZ1  gave for s =  0.0322265625   minimal norm  30.734019252457724\n",
      "Found minimum norm =  30.466455652998256  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ1Z  gave for s =  0.0498046875   minimal norm  30.466455652998256\n",
      "Found minimum norm =  30.738702455973012  for s =  0.0333984375\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ11  gave for s =  0.0333984375   minimal norm  30.738702455973012\n",
      "Found minimum norm =  30.60227676112674  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1ZZ  gave for s =  0.0498046875   minimal norm  30.60227676112674\n",
      "Found minimum norm =  30.120989559311383  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1Z1  gave for s =  0.0498046875   minimal norm  30.120989559311383\n",
      "Found minimum norm =  30.541748007113732  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ11Z  gave for s =  0.0498046875   minimal norm  30.541748007113732\n",
      "Found minimum norm =  30.842902871490093  for s =  0.0310546875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ111  gave for s =  0.0310546875   minimal norm  30.842902871490093\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  30.657440683828  for s =  0.0451171875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZZ  gave for s =  0.0451171875   minimal norm  30.657440683828\n",
      "Found minimum norm =  30.240855511982037  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZ1  gave for s =  0.0498046875   minimal norm  30.240855511982037\n",
      "Found minimum norm =  30.2590161447598  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z1Z  gave for s =  0.0498046875   minimal norm  30.2590161447598\n",
      "Found minimum norm =  30.448358763505105  for s =  0.0470703125\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z11  gave for s =  0.0470703125   minimal norm  30.448358763505105\n",
      "Found minimum norm =  30.784370871676735  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11ZZ  gave for s =  0.024804687500000002   minimal norm  30.784370871676735\n",
      "Found minimum norm =  30.501696992859895  for s =  0.0419921875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11Z1  gave for s =  0.0419921875   minimal norm  30.501696992859895\n",
      "Found minimum norm =  30.69915747929268  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z111Z  gave for s =  0.0373046875   minimal norm  30.69915747929268\n",
      "Found minimum norm =  30.49561479935033  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1111  gave for s =  0.0353515625   minimal norm  30.49561479935033\n",
      "Found minimum norm =  30.85672828441665  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZZ  gave for s =  0.016992187500000002   minimal norm  30.85672828441665\n",
      "Found minimum norm =  30.739492366448488  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZ1  gave for s =  0.0330078125   minimal norm  30.739492366448488\n",
      "Found minimum norm =  30.54174800711373  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ1Z  gave for s =  0.0498046875   minimal norm  30.54174800711373\n",
      "Found minimum norm =  30.613576217565242  for s =  0.04355468750000001\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ11  gave for s =  0.04355468750000001   minimal norm  30.613576217565242\n",
      "Found minimum norm =  30.712448272086586  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1ZZ  gave for s =  0.0373046875   minimal norm  30.712448272086586\n",
      "Found minimum norm =  30.347084929555724  for s =  0.0486328125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1Z1  gave for s =  0.0486328125   minimal norm  30.347084929555724\n",
      "Found minimum norm =  30.78147830961557  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11Z11Z  gave for s =  0.024804687500000002   minimal norm  30.78147830961557\n",
      "Found minimum norm =  30.478045614043307  for s =  0.029882812499999998\n",
      "Flow step output with generator type  single_commutator using string  Z11Z111  gave for s =  0.029882812499999998   minimal norm  30.478045614043307\n",
      "Found minimum norm =  30.883411234973295  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZZ  gave for s =  0.016992187500000002   minimal norm  30.883411234973295\n",
      "Found minimum norm =  30.64806160860136  for s =  0.0419921875\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZ1  gave for s =  0.0419921875   minimal norm  30.64806160860136\n",
      "Found minimum norm =  30.699157479292676  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  Z111Z1Z  gave for s =  0.0373046875   minimal norm  30.699157479292676\n",
      "Found minimum norm =  30.71939619447373  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z111Z11  gave for s =  0.024804687500000002   minimal norm  30.71939619447373\n",
      "Found minimum norm =  30.89914072857427  for s =  0.0119140625\n",
      "Flow step output with generator type  single_commutator using string  Z1111ZZ  gave for s =  0.0119140625   minimal norm  30.89914072857427\n",
      "Found minimum norm =  30.792155384854123  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  Z1111Z1  gave for s =  0.0330078125   minimal norm  30.792155384854123\n",
      "Found minimum norm =  30.833306966207683  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  Z11111Z  gave for s =  0.0353515625   minimal norm  30.833306966207683\n",
      "Found minimum norm =  30.13022611240304  for s =  0.0642578125\n",
      "Flow step output with generator type  single_commutator using string  Z111111  gave for s =  0.0642578125   minimal norm  30.13022611240304\n",
      "Found minimum norm =  30.54268070510514  for s =  0.0283203125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZZ  gave for s =  0.0283203125   minimal norm  30.54268070510514\n",
      "Found minimum norm =  30.42058687296751  for s =  0.0333984375\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZ1  gave for s =  0.0333984375   minimal norm  30.42058687296751\n",
      "Found minimum norm =  30.73401925245772  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ1Z  gave for s =  0.0322265625   minimal norm  30.73401925245772\n",
      "Found minimum norm =  30.39659173663435  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ11  gave for s =  0.0341796875   minimal norm  30.39659173663435\n",
      "Found minimum norm =  30.906123172333743  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1ZZ  gave for s =  0.018554687500000003   minimal norm  30.906123172333743\n",
      "Found minimum norm =  30.460699309323555  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1Z1  gave for s =  0.0498046875   minimal norm  30.460699309323555\n",
      "Found minimum norm =  30.739492366448477  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ11Z  gave for s =  0.0330078125   minimal norm  30.739492366448477\n",
      "Found minimum norm =  30.482328993718884  for s =  0.03378906250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ111  gave for s =  0.03378906250000001   minimal norm  30.482328993718884\n",
      "Found minimum norm =  30.91534530882299  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZZ  gave for s =  0.024804687500000002   minimal norm  30.91534530882299\n",
      "Found minimum norm =  30.568297747444316  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZ1  gave for s =  0.0498046875   minimal norm  30.568297747444316\n",
      "Found minimum norm =  30.24085551198203  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z1Z  gave for s =  0.0498046875   minimal norm  30.24085551198203\n",
      "Found minimum norm =  30.546289273724636  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z11  gave for s =  0.0498046875   minimal norm  30.546289273724636\n",
      "Found minimum norm =  30.803572199930574  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11ZZ  gave for s =  0.024804687500000002   minimal norm  30.803572199930574\n",
      "Found minimum norm =  30.426004625986124  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11Z1  gave for s =  0.04550781250000001   minimal norm  30.426004625986124\n",
      "Found minimum norm =  30.64806160860136  for s =  0.0419921875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ111Z  gave for s =  0.0419921875   minimal norm  30.64806160860136\n",
      "Found minimum norm =  30.55067948919286  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1111  gave for s =  0.0373046875   minimal norm  30.55067948919286\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  30.757545271327146  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZZ  gave for s =  0.0341796875   minimal norm  30.757545271327146\n",
      "Found minimum norm =  30.460699309323555  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZ1  gave for s =  0.0498046875   minimal norm  30.460699309323555\n",
      "Found minimum norm =  30.120989559311376  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ1Z  gave for s =  0.0498046875   minimal norm  30.120989559311376\n",
      "Found minimum norm =  30.472812162096876  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ11  gave for s =  0.0498046875   minimal norm  30.472812162096876\n",
      "Found minimum norm =  30.428525597800054  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1ZZ  gave for s =  0.0498046875   minimal norm  30.428525597800054\n",
      "Found minimum norm =  29.866323485101113  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1Z1  gave for s =  0.0498046875   minimal norm  29.866323485101113\n",
      "Found minimum norm =  30.347084929555727  for s =  0.0486328125\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z11Z  gave for s =  0.0486328125   minimal norm  30.347084929555727\n",
      "Found minimum norm =  30.52437137041312  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z111  gave for s =  0.03886718750000001   minimal norm  30.52437137041312\n",
      "Found minimum norm =  30.780533059682732  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZZ  gave for s =  0.024804687500000002   minimal norm  30.780533059682732\n",
      "Found minimum norm =  30.426004625986128  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZ1  gave for s =  0.04550781250000001   minimal norm  30.426004625986128\n",
      "Found minimum norm =  30.501696992859888  for s =  0.0419921875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z1Z  gave for s =  0.0419921875   minimal norm  30.501696992859888\n",
      "Found minimum norm =  30.370354273488633  for s =  0.03574218750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z11  gave for s =  0.03574218750000001   minimal norm  30.370354273488633\n",
      "Found minimum norm =  30.79731793732244  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z111ZZ  gave for s =  0.022851562500000002   minimal norm  30.79731793732244\n",
      "Found minimum norm =  30.54914815318184  for s =  0.040039062500000014\n",
      "Flow step output with generator type  single_commutator using string  1Z111Z1  gave for s =  0.040039062500000014   minimal norm  30.54914815318184\n",
      "Found minimum norm =  30.792155384854112  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  1Z1111Z  gave for s =  0.0330078125   minimal norm  30.792155384854112\n",
      "Found minimum norm =  29.905708179913724  for s =  0.0529296875\n",
      "Flow step output with generator type  single_commutator using string  1Z11111  gave for s =  0.0529296875   minimal norm  29.905708179913724\n",
      "Found minimum norm =  30.49151885320239  for s =  0.0294921875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZZ  gave for s =  0.0294921875   minimal norm  30.49151885320239\n",
      "Found minimum norm =  30.396591736634353  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZ1  gave for s =  0.0341796875   minimal norm  30.396591736634353\n",
      "Found minimum norm =  30.738702455973005  for s =  0.0333984375\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ1Z  gave for s =  0.0333984375   minimal norm  30.738702455973005\n",
      "Found minimum norm =  30.46618269882563  for s =  0.034570312500000006\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ11  gave for s =  0.034570312500000006   minimal norm  30.46618269882563\n",
      "Found minimum norm =  30.927197554980932  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1ZZ  gave for s =  0.0001953125   minimal norm  30.927197554980932\n",
      "Found minimum norm =  30.472812162096872  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1Z1  gave for s =  0.0498046875   minimal norm  30.472812162096872\n",
      "Found minimum norm =  30.613576217565246  for s =  0.04355468750000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZ11Z  gave for s =  0.04355468750000001   minimal norm  30.613576217565246\n",
      "Found minimum norm =  30.598185266265787  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZ111  gave for s =  0.03886718750000001   minimal norm  30.598185266265787\n",
      "Found minimum norm =  30.832627618766328  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZZ  gave for s =  0.024804687500000002   minimal norm  30.832627618766328\n",
      "Found minimum norm =  30.546289273724646  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZ1  gave for s =  0.0498046875   minimal norm  30.546289273724646\n",
      "Found minimum norm =  30.448358763505098  for s =  0.0470703125\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z1Z  gave for s =  0.0470703125   minimal norm  30.448358763505098\n",
      "Found minimum norm =  30.4750650301452  for s =  0.04160156250000001\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z11  gave for s =  0.04160156250000001   minimal norm  30.4750650301452\n",
      "Found minimum norm =  30.709602632275217  for s =  0.0220703125\n",
      "Flow step output with generator type  single_commutator using string  11Z11ZZ  gave for s =  0.0220703125   minimal norm  30.709602632275217\n",
      "Found minimum norm =  30.370354273488637  for s =  0.03574218750000001\n",
      "Flow step output with generator type  single_commutator using string  11Z11Z1  gave for s =  0.03574218750000001   minimal norm  30.370354273488637\n",
      "Found minimum norm =  30.719396194473727  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z111Z  gave for s =  0.024804687500000002   minimal norm  30.719396194473727\n",
      "Found minimum norm =  29.967103249086378  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  11Z1111  gave for s =  0.038476562500000006   minimal norm  29.967103249086378\n",
      "Found minimum norm =  30.485151555113635  for s =  0.0294921875\n",
      "Flow step output with generator type  single_commutator using string  111ZZZZ  gave for s =  0.0294921875   minimal norm  30.485151555113635\n",
      "Found minimum norm =  30.482328993718887  for s =  0.03378906250000001\n",
      "Flow step output with generator type  single_commutator using string  111ZZZ1  gave for s =  0.03378906250000001   minimal norm  30.482328993718887\n",
      "Found minimum norm =  30.84290287149009  for s =  0.0310546875\n",
      "Flow step output with generator type  single_commutator using string  111ZZ1Z  gave for s =  0.0310546875   minimal norm  30.84290287149009\n",
      "Found minimum norm =  30.59818526626579  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  111ZZ11  gave for s =  0.03886718750000001   minimal norm  30.59818526626579\n",
      "Found minimum norm =  30.81706707964252  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  111Z1ZZ  gave for s =  0.019726562500000003   minimal norm  30.81706707964252\n",
      "Found minimum norm =  30.524371370413125  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  111Z1Z1  gave for s =  0.03886718750000001   minimal norm  30.524371370413125\n",
      "Found minimum norm =  30.478045614043292  for s =  0.029882812499999998\n",
      "Flow step output with generator type  single_commutator using string  111Z11Z  gave for s =  0.029882812499999998   minimal norm  30.478045614043292\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  29.83340341073155  for s =  0.03691406250000001\n",
      "Flow step output with generator type  single_commutator using string  111Z111  gave for s =  0.03691406250000001   minimal norm  29.83340341073155\n",
      "Found minimum norm =  30.530584837883865  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  1111ZZZ  gave for s =  0.0322265625   minimal norm  30.530584837883865\n",
      "Found minimum norm =  30.55067948919285  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  1111ZZ1  gave for s =  0.0373046875   minimal norm  30.55067948919285\n",
      "Found minimum norm =  30.495614799350328  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  1111Z1Z  gave for s =  0.0353515625   minimal norm  30.495614799350328\n",
      "Found minimum norm =  29.967103249086378  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  1111Z11  gave for s =  0.038476562500000006   minimal norm  29.967103249086378\n",
      "Found minimum norm =  30.46391074972324  for s =  0.034570312500000006\n",
      "Flow step output with generator type  single_commutator using string  11111ZZ  gave for s =  0.034570312500000006   minimal norm  30.46391074972324\n",
      "Found minimum norm =  29.905708179913727  for s =  0.0529296875\n",
      "Flow step output with generator type  single_commutator using string  11111Z1  gave for s =  0.0529296875   minimal norm  29.905708179913727\n",
      "Found minimum norm =  30.13022611240304  for s =  0.0642578125\n",
      "Flow step output with generator type  single_commutator using string  111111Z  gave for s =  0.0642578125   minimal norm  30.13022611240304\n",
      "Found minimum norm =  30.926559079849504  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1111111  gave for s =  0.0001953125   minimal norm  30.926559079849504\n",
      "Found minimum norm =  29.303320693190436  for s =  0.004882812500000001\n",
      "Found that canonical is better because  29.303320693190436 29.83340341073155\n",
      "Found minimum norm =  29.303320693190436  for s =  0.004882812500000001\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  5\n",
      "Found minimum norm =  28.991848341914977  for s =  0.0302734375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZZ  gave for s =  0.0302734375   minimal norm  28.991848341914977\n",
      "Found minimum norm =  28.92432711583218  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZ1  gave for s =  0.0353515625   minimal norm  28.92432711583218\n",
      "Found minimum norm =  29.188955319661748  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ1Z  gave for s =  0.024804687500000002   minimal norm  29.188955319661748\n",
      "Found minimum norm =  28.984819282667544  for s =  0.028710937500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ11  gave for s =  0.028710937500000002   minimal norm  28.984819282667544\n",
      "Found minimum norm =  29.272903276232125  for s =  0.009960937500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1ZZ  gave for s =  0.009960937500000003   minimal norm  29.272903276232125\n",
      "Found minimum norm =  29.081935184779677  for s =  0.031835937499999994\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1Z1  gave for s =  0.031835937499999994   minimal norm  29.081935184779677\n",
      "Found minimum norm =  29.18206875449086  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ11Z  gave for s =  0.021679687500000003   minimal norm  29.18206875449086\n",
      "Found minimum norm =  28.962865721890786  for s =  0.0275390625\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ111  gave for s =  0.0275390625   minimal norm  28.962865721890786\n",
      "Found minimum norm =  29.28752119307545  for s =  0.0076171875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZZ  gave for s =  0.0076171875   minimal norm  29.28752119307545\n",
      "Found minimum norm =  29.226599359677714  for s =  0.0220703125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZ1  gave for s =  0.0220703125   minimal norm  29.226599359677714\n",
      "Found minimum norm =  29.015823734760634  for s =  0.040039062500000014\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z1Z  gave for s =  0.040039062500000014   minimal norm  29.015823734760634\n",
      "Found minimum norm =  29.161190290709094  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z11  gave for s =  0.024804687500000002   minimal norm  29.161190290709094\n",
      "Found minimum norm =  29.267611455327952  for s =  0.013085937500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11ZZ  gave for s =  0.013085937500000002   minimal norm  29.267611455327952\n",
      "Found minimum norm =  29.112132883450318  for s =  0.0361328125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11Z1  gave for s =  0.0361328125   minimal norm  29.112132883450318\n",
      "Found minimum norm =  29.22550187637062  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZ111Z  gave for s =  0.021679687500000003   minimal norm  29.22550187637062\n",
      "Found minimum norm =  29.021991381083918  for s =  0.0279296875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1111  gave for s =  0.0279296875   minimal norm  29.021991381083918\n",
      "Found minimum norm =  29.272903276232125  for s =  0.009960937500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZZ  gave for s =  0.009960937500000003   minimal norm  29.272903276232125\n",
      "Found minimum norm =  29.20989748434765  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZ1  gave for s =  0.022851562500000002   minimal norm  29.20989748434765\n",
      "Found minimum norm =  29.074068452514766  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ1Z  gave for s =  0.03886718750000001   minimal norm  29.074068452514766\n",
      "Found minimum norm =  29.2916598360194  for s =  0.008398437500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ11  gave for s =  0.008398437500000001   minimal norm  29.2916598360194\n",
      "Found minimum norm =  29.09217912905009  for s =  0.04082031250000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1ZZ  gave for s =  0.04082031250000001   minimal norm  29.09217912905009\n",
      "Found minimum norm =  28.743175842164344  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1Z1  gave for s =  0.0498046875   minimal norm  28.743175842164344\n",
      "Found minimum norm =  28.94957063345404  for s =  0.0470703125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z11Z  gave for s =  0.0470703125   minimal norm  28.94957063345404\n",
      "Found minimum norm =  29.216446222176167  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z111  gave for s =  0.020898437500000002   minimal norm  29.216446222176167\n",
      "Found minimum norm =  29.267611455327952  for s =  0.013085937500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZZ  gave for s =  0.013085937500000002   minimal norm  29.267611455327952\n",
      "Found minimum norm =  29.17526538671532  for s =  0.0306640625\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZ1  gave for s =  0.0306640625   minimal norm  29.17526538671532\n",
      "Found minimum norm =  28.994703403349092  for s =  0.0427734375\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z1Z  gave for s =  0.0427734375   minimal norm  28.994703403349092\n",
      "Found minimum norm =  29.131153502686704  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z11  gave for s =  0.024804687500000002   minimal norm  29.131153502686704\n",
      "Found minimum norm =  29.204645412780117  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ111ZZ  gave for s =  0.016992187500000002   minimal norm  29.204645412780117\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  29.07362820962194  for s =  0.0302734375\n",
      "Flow step output with generator type  single_commutator using string  ZZ111Z1  gave for s =  0.0302734375   minimal norm  29.07362820962194\n",
      "Found minimum norm =  29.21530355721149  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1111Z  gave for s =  0.017773437500000003   minimal norm  29.21530355721149\n",
      "Found minimum norm =  28.972836215288893  for s =  0.0275390625\n",
      "Flow step output with generator type  single_commutator using string  ZZ11111  gave for s =  0.0275390625   minimal norm  28.972836215288893\n",
      "Found minimum norm =  29.18895531966175  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZZ  gave for s =  0.024804687500000002   minimal norm  29.18895531966175\n",
      "Found minimum norm =  28.979250586735045  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZ1  gave for s =  0.038476562500000006   minimal norm  28.979250586735045\n",
      "Found minimum norm =  28.849980190112284  for s =  0.046289062500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ1Z  gave for s =  0.046289062500000006   minimal norm  28.849980190112284\n",
      "Found minimum norm =  29.076342264383882  for s =  0.0310546875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ11  gave for s =  0.0310546875   minimal norm  29.076342264383882\n",
      "Found minimum norm =  29.074068452514773  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1ZZ  gave for s =  0.03886718750000001   minimal norm  29.074068452514773\n",
      "Found minimum norm =  28.527445308388618  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1Z1  gave for s =  0.0498046875   minimal norm  28.527445308388618\n",
      "Found minimum norm =  28.821214950044432  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ11Z  gave for s =  0.0498046875   minimal norm  28.821214950044432\n",
      "Found minimum norm =  29.18158682504684  for s =  0.03378906250000001\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ111  gave for s =  0.03378906250000001   minimal norm  29.18158682504684\n",
      "Found minimum norm =  29.01582373476064  for s =  0.040039062500000014\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZZ  gave for s =  0.040039062500000014   minimal norm  29.01582373476064\n",
      "Found minimum norm =  28.5951446958103  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZ1  gave for s =  0.0498046875   minimal norm  28.5951446958103\n",
      "Found minimum norm =  28.418850774898843  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z1Z  gave for s =  0.0498046875   minimal norm  28.418850774898843\n",
      "Found minimum norm =  28.670492892221542  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z11  gave for s =  0.0498046875   minimal norm  28.670492892221542\n",
      "Found minimum norm =  28.994703403349096  for s =  0.0427734375\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11ZZ  gave for s =  0.0427734375   minimal norm  28.994703403349096\n",
      "Found minimum norm =  28.589982281281927  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11Z1  gave for s =  0.0498046875   minimal norm  28.589982281281927\n",
      "Found minimum norm =  28.918314354565286  for s =  0.04472656250000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z111Z  gave for s =  0.04472656250000001   minimal norm  28.918314354565286\n",
      "Found minimum norm =  28.93743661464362  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1111  gave for s =  0.0341796875   minimal norm  28.93743661464362\n",
      "Found minimum norm =  29.18206875449086  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZZ  gave for s =  0.021679687500000003   minimal norm  29.18206875449086\n",
      "Found minimum norm =  29.03345944722254  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZ1  gave for s =  0.0412109375   minimal norm  29.03345944722254\n",
      "Found minimum norm =  28.82121495004443  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ1Z  gave for s =  0.0498046875   minimal norm  28.82121495004443\n",
      "Found minimum norm =  29.024759785163834  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ11  gave for s =  0.04550781250000001   minimal norm  29.024759785163834\n",
      "Found minimum norm =  28.94957063345404  for s =  0.0470703125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1ZZ  gave for s =  0.0470703125   minimal norm  28.94957063345404\n",
      "Found minimum norm =  28.496878920532353  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1Z1  gave for s =  0.0498046875   minimal norm  28.496878920532353\n",
      "Found minimum norm =  28.978938001596685  for s =  0.040039062500000014\n",
      "Flow step output with generator type  single_commutator using string  Z11Z11Z  gave for s =  0.040039062500000014   minimal norm  28.978938001596685\n",
      "Found minimum norm =  28.84631029478982  for s =  0.034570312500000006\n",
      "Flow step output with generator type  single_commutator using string  Z11Z111  gave for s =  0.034570312500000006   minimal norm  28.84631029478982\n",
      "Found minimum norm =  29.22550187637062  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZZ  gave for s =  0.021679687500000003   minimal norm  29.22550187637062\n",
      "Found minimum norm =  28.93157726273199  for s =  0.04355468750000001\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZ1  gave for s =  0.04355468750000001   minimal norm  28.93157726273199\n",
      "Found minimum norm =  28.918314354565293  for s =  0.04472656250000001\n",
      "Flow step output with generator type  single_commutator using string  Z111Z1Z  gave for s =  0.04472656250000001   minimal norm  28.918314354565293\n",
      "Found minimum norm =  28.99409869063146  for s =  0.0314453125\n",
      "Flow step output with generator type  single_commutator using string  Z111Z11  gave for s =  0.0314453125   minimal norm  28.99409869063146\n",
      "Found minimum norm =  29.21530355721149  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1111ZZ  gave for s =  0.017773437500000003   minimal norm  29.21530355721149\n",
      "Found minimum norm =  29.0384737822311  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  Z1111Z1  gave for s =  0.0412109375   minimal norm  29.0384737822311\n",
      "Found minimum norm =  29.143587178323507  for s =  0.03378906250000001\n",
      "Flow step output with generator type  single_commutator using string  Z11111Z  gave for s =  0.03378906250000001   minimal norm  29.143587178323507\n",
      "Found minimum norm =  28.716438132200153  for s =  0.04941406250000001\n",
      "Flow step output with generator type  single_commutator using string  Z111111  gave for s =  0.04941406250000001   minimal norm  28.716438132200153\n",
      "Found minimum norm =  28.924327115832178  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZZ  gave for s =  0.0353515625   minimal norm  28.924327115832178\n",
      "Found minimum norm =  28.764014529922243  for s =  0.04355468750000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZ1  gave for s =  0.04355468750000001   minimal norm  28.764014529922243\n",
      "Found minimum norm =  28.97925058673504  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ1Z  gave for s =  0.038476562500000006   minimal norm  28.97925058673504\n",
      "Found minimum norm =  28.871458138775004  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ11  gave for s =  0.0353515625   minimal norm  28.871458138775004\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  29.20989748434764  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1ZZ  gave for s =  0.022851562500000002   minimal norm  29.20989748434764\n",
      "Found minimum norm =  28.780521393738823  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1Z1  gave for s =  0.0498046875   minimal norm  28.780521393738823\n",
      "Found minimum norm =  29.03345944722251  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ11Z  gave for s =  0.0412109375   minimal norm  29.03345944722251\n",
      "Found minimum norm =  28.975866763200507  for s =  0.032617187500000006\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ111  gave for s =  0.032617187500000006   minimal norm  28.975866763200507\n",
      "Found minimum norm =  29.2265993596777  for s =  0.0220703125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZZ  gave for s =  0.0220703125   minimal norm  29.2265993596777\n",
      "Found minimum norm =  28.994153354385375  for s =  0.0439453125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZ1  gave for s =  0.0439453125   minimal norm  28.994153354385375\n",
      "Found minimum norm =  28.595144695810262  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z1Z  gave for s =  0.0498046875   minimal norm  28.595144695810262\n",
      "Found minimum norm =  28.91508086475285  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z11  gave for s =  0.0498046875   minimal norm  28.91508086475285\n",
      "Found minimum norm =  29.175265386715314  for s =  0.0306640625\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11ZZ  gave for s =  0.0306640625   minimal norm  29.175265386715314\n",
      "Found minimum norm =  28.70038725615129  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11Z1  gave for s =  0.0498046875   minimal norm  28.70038725615129\n",
      "Found minimum norm =  28.931577262732006  for s =  0.04355468750000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ111Z  gave for s =  0.04355468750000001   minimal norm  28.931577262732006\n",
      "Found minimum norm =  29.013976098324385  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1111  gave for s =  0.0330078125   minimal norm  29.013976098324385\n",
      "Found minimum norm =  29.081935184779667  for s =  0.031835937499999994\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZZ  gave for s =  0.031835937499999994   minimal norm  29.081935184779667\n",
      "Found minimum norm =  28.780521393738816  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZ1  gave for s =  0.0498046875   minimal norm  28.780521393738816\n",
      "Found minimum norm =  28.527445308388568  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ1Z  gave for s =  0.0498046875   minimal norm  28.527445308388568\n",
      "Found minimum norm =  28.93458505312777  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ11  gave for s =  0.0498046875   minimal norm  28.93458505312777\n",
      "Found minimum norm =  28.74317584216431  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1ZZ  gave for s =  0.0498046875   minimal norm  28.74317584216431\n",
      "Found minimum norm =  28.141161645074114  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1Z1  gave for s =  0.0498046875   minimal norm  28.141161645074114\n",
      "Found minimum norm =  28.496878920532374  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z11Z  gave for s =  0.0498046875   minimal norm  28.496878920532374\n",
      "Found minimum norm =  28.861968579656097  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z111  gave for s =  0.048242187500000006   minimal norm  28.861968579656097\n",
      "Found minimum norm =  29.112132883450307  for s =  0.0361328125\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZZ  gave for s =  0.0361328125   minimal norm  29.112132883450307\n",
      "Found minimum norm =  28.70038725615128  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZ1  gave for s =  0.0498046875   minimal norm  28.70038725615128\n",
      "Found minimum norm =  28.589982281281937  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z1Z  gave for s =  0.0498046875   minimal norm  28.589982281281937\n",
      "Found minimum norm =  28.676315010627377  for s =  0.047460937499999994\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z11  gave for s =  0.047460937499999994   minimal norm  28.676315010627377\n",
      "Found minimum norm =  29.073628209621933  for s =  0.0302734375\n",
      "Flow step output with generator type  single_commutator using string  1Z111ZZ  gave for s =  0.0302734375   minimal norm  29.073628209621933\n",
      "Found minimum norm =  28.702656735319472  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z111Z1  gave for s =  0.0498046875   minimal norm  28.702656735319472\n",
      "Found minimum norm =  29.03847378223107  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  1Z1111Z  gave for s =  0.0412109375   minimal norm  29.03847378223107\n",
      "Found minimum norm =  28.530027660222313  for s =  0.0458984375\n",
      "Flow step output with generator type  single_commutator using string  1Z11111  gave for s =  0.0458984375   minimal norm  28.530027660222313\n",
      "Found minimum norm =  28.98481928266754  for s =  0.028710937500000002\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZZ  gave for s =  0.028710937500000002   minimal norm  28.98481928266754\n",
      "Found minimum norm =  28.871458138775004  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZ1  gave for s =  0.0353515625   minimal norm  28.871458138775004\n",
      "Found minimum norm =  29.076342264383868  for s =  0.0310546875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ1Z  gave for s =  0.0310546875   minimal norm  29.076342264383868\n",
      "Found minimum norm =  28.948180312090976  for s =  0.026757812500000002\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ11  gave for s =  0.026757812500000002   minimal norm  28.948180312090976\n",
      "Found minimum norm =  29.2916598360194  for s =  0.008398437500000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1ZZ  gave for s =  0.008398437500000001   minimal norm  29.2916598360194\n",
      "Found minimum norm =  28.93458505312776  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1Z1  gave for s =  0.0498046875   minimal norm  28.93458505312776\n",
      "Found minimum norm =  29.024759785163837  for s =  0.04550781250000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZ11Z  gave for s =  0.04550781250000001   minimal norm  29.024759785163837\n",
      "Found minimum norm =  29.08462716740487  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ111  gave for s =  0.0498046875   minimal norm  29.08462716740487\n",
      "Found minimum norm =  29.161190290709087  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZZ  gave for s =  0.024804687500000002   minimal norm  29.161190290709087\n",
      "Found minimum norm =  28.915080864752845  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZ1  gave for s =  0.0498046875   minimal norm  28.915080864752845\n",
      "Found minimum norm =  28.67049289222155  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z1Z  gave for s =  0.0498046875   minimal norm  28.67049289222155\n",
      "Found minimum norm =  28.700009476326752  for s =  0.06894531250000001\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z11  gave for s =  0.06894531250000001   minimal norm  28.700009476326752\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  29.131153502686697  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z11ZZ  gave for s =  0.024804687500000002   minimal norm  29.131153502686697\n",
      "Found minimum norm =  28.67631501062737  for s =  0.047460937499999994\n",
      "Flow step output with generator type  single_commutator using string  11Z11Z1  gave for s =  0.047460937499999994   minimal norm  28.67631501062737\n",
      "Found minimum norm =  28.994098690631443  for s =  0.0314453125\n",
      "Flow step output with generator type  single_commutator using string  11Z111Z  gave for s =  0.0314453125   minimal norm  28.994098690631443\n",
      "Found minimum norm =  28.591777864581545  for s =  0.032617187500000006\n",
      "Flow step output with generator type  single_commutator using string  11Z1111  gave for s =  0.032617187500000006   minimal norm  28.591777864581545\n",
      "Found minimum norm =  28.96286572189078  for s =  0.0275390625\n",
      "Flow step output with generator type  single_commutator using string  111ZZZZ  gave for s =  0.0275390625   minimal norm  28.96286572189078\n",
      "Found minimum norm =  28.975866763200507  for s =  0.032617187500000006\n",
      "Flow step output with generator type  single_commutator using string  111ZZZ1  gave for s =  0.032617187500000006   minimal norm  28.975866763200507\n",
      "Found minimum norm =  29.18158682504683  for s =  0.03378906250000001\n",
      "Flow step output with generator type  single_commutator using string  111ZZ1Z  gave for s =  0.03378906250000001   minimal norm  29.18158682504683\n",
      "Found minimum norm =  29.084627167404886  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111ZZ11  gave for s =  0.0498046875   minimal norm  29.084627167404886\n",
      "Found minimum norm =  29.216446222176163  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  111Z1ZZ  gave for s =  0.020898437500000002   minimal norm  29.216446222176163\n",
      "Found minimum norm =  28.8619685796561  for s =  0.048242187500000006\n",
      "Flow step output with generator type  single_commutator using string  111Z1Z1  gave for s =  0.048242187500000006   minimal norm  28.8619685796561\n",
      "Found minimum norm =  28.84631029478979  for s =  0.034570312500000006\n",
      "Flow step output with generator type  single_commutator using string  111Z11Z  gave for s =  0.034570312500000006   minimal norm  28.84631029478979\n",
      "Found minimum norm =  28.523897619072805  for s =  0.032617187500000006\n",
      "Flow step output with generator type  single_commutator using string  111Z111  gave for s =  0.032617187500000006   minimal norm  28.523897619072805\n",
      "Found minimum norm =  29.021991381083907  for s =  0.0279296875\n",
      "Flow step output with generator type  single_commutator using string  1111ZZZ  gave for s =  0.0279296875   minimal norm  29.021991381083907\n",
      "Found minimum norm =  29.01397609832438  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  1111ZZ1  gave for s =  0.0330078125   minimal norm  29.01397609832438\n",
      "Found minimum norm =  28.9374366146436  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  1111Z1Z  gave for s =  0.0341796875   minimal norm  28.9374366146436\n",
      "Found minimum norm =  28.591777864581545  for s =  0.032617187500000006\n",
      "Flow step output with generator type  single_commutator using string  1111Z11  gave for s =  0.032617187500000006   minimal norm  28.591777864581545\n",
      "Found minimum norm =  28.97283621528888  for s =  0.0275390625\n",
      "Flow step output with generator type  single_commutator using string  11111ZZ  gave for s =  0.0275390625   minimal norm  28.97283621528888\n",
      "Found minimum norm =  28.53002766022231  for s =  0.0458984375\n",
      "Flow step output with generator type  single_commutator using string  11111Z1  gave for s =  0.0458984375   minimal norm  28.53002766022231\n",
      "Found minimum norm =  28.716438132200164  for s =  0.04941406250000001\n",
      "Flow step output with generator type  single_commutator using string  111111Z  gave for s =  0.04941406250000001   minimal norm  28.716438132200164\n",
      "Found minimum norm =  29.303320693190436  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1111111  gave for s =  0.0001953125   minimal norm  29.303320693190436\n",
      "Found minimum norm =  28.358581587484128  for s =  0.0033203125000000003\n",
      "Found that canonical is worse because  28.358581587484128 28.141161645074114\n",
      "Found minimum norm =  28.141161645074114  for s =  0.0498046875\n",
      "Flowing forwards with type  single_commutator\n",
      "[]\n",
      "Flow step  6\n",
      "Found minimum norm =  27.83820251354902  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZZ  gave for s =  0.024804687500000002   minimal norm  27.83820251354902\n",
      "Found minimum norm =  27.807070488119187  for s =  0.0271484375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZ1  gave for s =  0.0271484375   minimal norm  27.807070488119187\n",
      "Found minimum norm =  28.047222021853653  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ1Z  gave for s =  0.016992187500000002   minimal norm  28.047222021853653\n",
      "Found minimum norm =  27.809019756116825  for s =  0.0236328125\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ11  gave for s =  0.0236328125   minimal norm  27.809019756116825\n",
      "Found minimum norm =  28.05025760490671  for s =  0.0138671875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1ZZ  gave for s =  0.0138671875   minimal norm  28.05025760490671\n",
      "Found minimum norm =  27.964015708893513  for s =  0.020117187500000005\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1Z1  gave for s =  0.020117187500000005   minimal norm  27.964015708893513\n",
      "Found minimum norm =  27.996037046267745  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ11Z  gave for s =  0.0166015625   minimal norm  27.996037046267745\n",
      "Found minimum norm =  27.733823054738107  for s =  0.0271484375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ111  gave for s =  0.0271484375   minimal norm  27.733823054738107\n",
      "Found minimum norm =  28.11536739581965  for s =  0.0076171875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZZ  gave for s =  0.0076171875   minimal norm  28.11536739581965\n",
      "Found minimum norm =  28.10605836150104  for s =  0.009179687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZ1  gave for s =  0.009179687500000002   minimal norm  28.10605836150104\n",
      "Found minimum norm =  28.02241432192752  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z1Z  gave for s =  0.0166015625   minimal norm  28.02241432192752\n",
      "Found minimum norm =  28.0312739079745  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z11  gave for s =  0.0181640625   minimal norm  28.0312739079745\n",
      "Found minimum norm =  28.06200615798744  for s =  0.0134765625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11ZZ  gave for s =  0.0134765625   minimal norm  28.06200615798744\n",
      "Found minimum norm =  28.0578838405556  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11Z1  gave for s =  0.0166015625   minimal norm  28.0578838405556\n",
      "Found minimum norm =  28.08965064804696  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZ111Z  gave for s =  0.012304687500000001   minimal norm  28.08965064804696\n",
      "Found minimum norm =  27.790310861241434  for s =  0.0236328125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1111  gave for s =  0.0236328125   minimal norm  27.790310861241434\n",
      "Found minimum norm =  28.050257604906715  for s =  0.0138671875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZZ  gave for s =  0.0138671875   minimal norm  28.050257604906715\n",
      "Found minimum norm =  28.024620348993768  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZ1  gave for s =  0.0173828125   minimal norm  28.024620348993768\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  28.041711847836883  for s =  0.0158203125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ1Z  gave for s =  0.0158203125   minimal norm  28.041711847836883\n",
      "Found minimum norm =  28.092958455262117  for s =  0.011132812500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ11  gave for s =  0.011132812500000002   minimal norm  28.092958455262117\n",
      "Found minimum norm =  28.094626892113713  for s =  0.0138671875\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1ZZ  gave for s =  0.0138671875   minimal norm  28.094626892113713\n",
      "Found minimum norm =  28.141274817294022  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1Z1  gave for s =  0.0001953125   minimal norm  28.141274817294022\n",
      "Found minimum norm =  28.03972488118232  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z11Z  gave for s =  0.019335937500000004   minimal norm  28.03972488118232\n",
      "Found minimum norm =  27.96744003557083  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z111  gave for s =  0.020507812500000003   minimal norm  27.96744003557083\n",
      "Found minimum norm =  28.062006157987444  for s =  0.0134765625\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZZ  gave for s =  0.0134765625   minimal norm  28.062006157987444\n",
      "Found minimum norm =  28.042129081588197  for s =  0.0162109375\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZ1  gave for s =  0.0162109375   minimal norm  28.042129081588197\n",
      "Found minimum norm =  28.03201524173591  for s =  0.018945312500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z1Z  gave for s =  0.018945312500000002   minimal norm  28.03201524173591\n",
      "Found minimum norm =  27.90793340918666  for s =  0.0220703125\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z11  gave for s =  0.0220703125   minimal norm  27.90793340918666\n",
      "Found minimum norm =  28.016466312116634  for s =  0.0162109375\n",
      "Flow step output with generator type  single_commutator using string  ZZ111ZZ  gave for s =  0.0162109375   minimal norm  28.016466312116634\n",
      "Found minimum norm =  27.903817879228278  for s =  0.022460937500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ111Z1  gave for s =  0.022460937500000003   minimal norm  27.903817879228278\n",
      "Found minimum norm =  28.022930647174185  for s =  0.0146484375\n",
      "Flow step output with generator type  single_commutator using string  ZZ1111Z  gave for s =  0.0146484375   minimal norm  28.022930647174185\n",
      "Found minimum norm =  27.73632805663194  for s =  0.026367187500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ11111  gave for s =  0.026367187500000003   minimal norm  27.73632805663194\n",
      "Found minimum norm =  28.047222021853656  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZZ  gave for s =  0.016992187500000002   minimal norm  28.047222021853656\n",
      "Found minimum norm =  27.98499444109351  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZ1  gave for s =  0.0181640625   minimal norm  27.98499444109351\n",
      "Found minimum norm =  28.04800915414507  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ1Z  gave for s =  0.0166015625   minimal norm  28.04800915414507\n",
      "Found minimum norm =  28.01646479315199  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ11  gave for s =  0.018554687500000003   minimal norm  28.01646479315199\n",
      "Found minimum norm =  28.041711847836876  for s =  0.0158203125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1ZZ  gave for s =  0.0158203125   minimal norm  28.041711847836876\n",
      "Found minimum norm =  27.920109953762086  for s =  0.0291015625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1Z1  gave for s =  0.0291015625   minimal norm  27.920109953762086\n",
      "Found minimum norm =  28.04911456356602  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ11Z  gave for s =  0.017773437500000003   minimal norm  28.04911456356602\n",
      "Found minimum norm =  27.992323560242074  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ111  gave for s =  0.0181640625   minimal norm  27.992323560242074\n",
      "Found minimum norm =  28.02241432192752  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZZ  gave for s =  0.0166015625   minimal norm  28.02241432192752\n",
      "Found minimum norm =  28.120476786367142  for s =  0.008398437500000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZ1  gave for s =  0.008398437500000001   minimal norm  28.120476786367142\n",
      "Found minimum norm =  28.075977048521484  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z1Z  gave for s =  0.012304687500000001   minimal norm  28.075977048521484\n",
      "Found minimum norm =  27.96848038291922  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z11  gave for s =  0.019335937500000004   minimal norm  27.96848038291922\n",
      "Found minimum norm =  28.03201524173592  for s =  0.018945312500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11ZZ  gave for s =  0.018945312500000002   minimal norm  28.03201524173592\n",
      "Found minimum norm =  27.9046967533046  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11Z1  gave for s =  0.021679687500000003   minimal norm  27.9046967533046\n",
      "Found minimum norm =  28.020751905393883  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  Z1Z111Z  gave for s =  0.0181640625   minimal norm  28.020751905393883\n",
      "Found minimum norm =  27.867081740121613  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1111  gave for s =  0.024804687500000002   minimal norm  27.867081740121613\n",
      "Found minimum norm =  27.99603704626774  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZZ  gave for s =  0.0166015625   minimal norm  27.99603704626774\n",
      "Found minimum norm =  27.972679731387778  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZ1  gave for s =  0.020898437500000002   minimal norm  27.972679731387778\n",
      "Found minimum norm =  28.04911456356603  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ1Z  gave for s =  0.017773437500000003   minimal norm  28.04911456356603\n",
      "Found minimum norm =  27.952175273013793  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ11  gave for s =  0.021679687500000003   minimal norm  27.952175273013793\n",
      "Found minimum norm =  28.039724881182327  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1ZZ  gave for s =  0.019335937500000004   minimal norm  28.039724881182327\n",
      "Found minimum norm =  28.13152410021533  for s =  0.0052734375\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1Z1  gave for s =  0.0052734375   minimal norm  28.13152410021533\n",
      "Found minimum norm =  28.012553555606914  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11Z11Z  gave for s =  0.016992187500000002   minimal norm  28.012553555606914\n",
      "Found minimum norm =  27.827896932169367  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  Z11Z111  gave for s =  0.0240234375   minimal norm  27.827896932169367\n",
      "Found minimum norm =  28.08965064804696  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZZ  gave for s =  0.012304687500000001   minimal norm  28.08965064804696\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  27.958794758014207  for s =  0.0212890625\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZ1  gave for s =  0.0212890625   minimal norm  27.958794758014207\n",
      "Found minimum norm =  28.02075190539388  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  Z111Z1Z  gave for s =  0.0181640625   minimal norm  28.02075190539388\n",
      "Found minimum norm =  27.95201101564313  for s =  0.020117187500000005\n",
      "Flow step output with generator type  single_commutator using string  Z111Z11  gave for s =  0.020117187500000005   minimal norm  27.95201101564313\n",
      "Found minimum norm =  28.022930647174178  for s =  0.0146484375\n",
      "Flow step output with generator type  single_commutator using string  Z1111ZZ  gave for s =  0.0146484375   minimal norm  28.022930647174178\n",
      "Found minimum norm =  27.99024589423712  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1111Z1  gave for s =  0.019726562500000003   minimal norm  27.99024589423712\n",
      "Found minimum norm =  28.050407201549344  for s =  0.0146484375\n",
      "Flow step output with generator type  single_commutator using string  Z11111Z  gave for s =  0.0146484375   minimal norm  28.050407201549344\n",
      "Found minimum norm =  27.614509669765916  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  Z111111  gave for s =  0.0322265625   minimal norm  27.614509669765916\n",
      "Found minimum norm =  27.80707048811919  for s =  0.0271484375\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZZ  gave for s =  0.0271484375   minimal norm  27.80707048811919\n",
      "Found minimum norm =  27.809578617735085  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZ1  gave for s =  0.0240234375   minimal norm  27.809578617735085\n",
      "Found minimum norm =  27.984994441093463  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ1Z  gave for s =  0.0181640625   minimal norm  27.984994441093463\n",
      "Found minimum norm =  27.718492254085824  for s =  0.028710937500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ11  gave for s =  0.028710937500000002   minimal norm  27.718492254085824\n",
      "Found minimum norm =  28.02462034899372  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1ZZ  gave for s =  0.0173828125   minimal norm  28.02462034899372\n",
      "Found minimum norm =  28.141549273816096  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1Z1  gave for s =  0.0001953125   minimal norm  28.141549273816096\n",
      "Found minimum norm =  27.972679731387796  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ11Z  gave for s =  0.020898437500000002   minimal norm  27.972679731387796\n",
      "Found minimum norm =  27.748309061684434  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ111  gave for s =  0.024804687500000002   minimal norm  27.748309061684434\n",
      "Found minimum norm =  28.10605836150101  for s =  0.009179687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZZ  gave for s =  0.009179687500000002   minimal norm  28.10605836150101\n",
      "Found minimum norm =  28.12718963059332  for s =  0.0068359375\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZ1  gave for s =  0.0068359375   minimal norm  28.12718963059332\n",
      "Found minimum norm =  28.12047678636717  for s =  0.008398437500000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z1Z  gave for s =  0.008398437500000001   minimal norm  28.12047678636717\n",
      "Found minimum norm =  27.957629427203738  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z11  gave for s =  0.021679687500000003   minimal norm  27.957629427203738\n",
      "Found minimum norm =  28.042129081588225  for s =  0.0162109375\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11ZZ  gave for s =  0.0162109375   minimal norm  28.042129081588225\n",
      "Found minimum norm =  28.12839331757294  for s =  0.0052734375\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11Z1  gave for s =  0.0052734375   minimal norm  28.12839331757294\n",
      "Found minimum norm =  27.95879475801417  for s =  0.0212890625\n",
      "Flow step output with generator type  single_commutator using string  1ZZ111Z  gave for s =  0.0212890625   minimal norm  27.95879475801417\n",
      "Found minimum norm =  27.89553902891937  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1111  gave for s =  0.024804687500000002   minimal norm  27.89553902891937\n",
      "Found minimum norm =  27.96401570889347  for s =  0.020117187500000005\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZZ  gave for s =  0.020117187500000005   minimal norm  27.96401570889347\n",
      "Found minimum norm =  28.141549273816096  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZ1  gave for s =  0.0001953125   minimal norm  28.141549273816096\n",
      "Found minimum norm =  27.920109953762072  for s =  0.0291015625\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ1Z  gave for s =  0.0291015625   minimal norm  27.920109953762072\n",
      "Found minimum norm =  28.10571384295567  for s =  0.0095703125\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ11  gave for s =  0.0095703125   minimal norm  28.10571384295567\n",
      "Found minimum norm =  28.141274817294022  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1ZZ  gave for s =  0.0001953125   minimal norm  28.141274817294022\n",
      "Found minimum norm =  27.682744007566583  for s =  0.0259765625\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1Z1  gave for s =  0.0259765625   minimal norm  27.682744007566583\n",
      "Found minimum norm =  28.131524100215312  for s =  0.0052734375\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z11Z  gave for s =  0.0052734375   minimal norm  28.131524100215312\n",
      "Found minimum norm =  27.97258559156555  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z111  gave for s =  0.024804687500000002   minimal norm  27.97258559156555\n",
      "Found minimum norm =  28.05788384055562  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZZ  gave for s =  0.0166015625   minimal norm  28.05788384055562\n",
      "Found minimum norm =  28.128393317572943  for s =  0.0052734375\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZ1  gave for s =  0.0052734375   minimal norm  28.128393317572943\n",
      "Found minimum norm =  27.90469675330456  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z1Z  gave for s =  0.021679687500000003   minimal norm  27.90469675330456\n",
      "Found minimum norm =  27.732960015698627  for s =  0.0310546875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z11  gave for s =  0.0310546875   minimal norm  27.732960015698627\n",
      "Found minimum norm =  27.90381787922825  for s =  0.022460937500000003\n",
      "Flow step output with generator type  single_commutator using string  1Z111ZZ  gave for s =  0.022460937500000003   minimal norm  27.90381787922825\n",
      "Found minimum norm =  28.127234698720162  for s =  0.0087890625\n",
      "Flow step output with generator type  single_commutator using string  1Z111Z1  gave for s =  0.0087890625   minimal norm  28.127234698720162\n",
      "Found minimum norm =  27.990245894237127  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  1Z1111Z  gave for s =  0.019726562500000003   minimal norm  27.990245894237127\n",
      "Found minimum norm =  27.48646264477786  for s =  0.0306640625\n",
      "Flow step output with generator type  single_commutator using string  1Z11111  gave for s =  0.0306640625   minimal norm  27.48646264477786\n",
      "Found minimum norm =  27.809019756116797  for s =  0.0236328125\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZZ  gave for s =  0.0236328125   minimal norm  27.809019756116797\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  27.718492254085824  for s =  0.028710937500000002\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZ1  gave for s =  0.028710937500000002   minimal norm  27.718492254085824\n",
      "Found minimum norm =  28.016464793152004  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ1Z  gave for s =  0.018554687500000003   minimal norm  28.016464793152004\n",
      "Found minimum norm =  27.7419767022416  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ11  gave for s =  0.0240234375   minimal norm  27.7419767022416\n",
      "Found minimum norm =  28.092958455262135  for s =  0.011132812500000002\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1ZZ  gave for s =  0.011132812500000002   minimal norm  28.092958455262135\n",
      "Found minimum norm =  28.105713842955666  for s =  0.0095703125\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1Z1  gave for s =  0.0095703125   minimal norm  28.105713842955666\n",
      "Found minimum norm =  27.952175273013765  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZ11Z  gave for s =  0.021679687500000003   minimal norm  27.952175273013765\n",
      "Found minimum norm =  27.915301939459855  for s =  0.0333984375\n",
      "Flow step output with generator type  single_commutator using string  11ZZ111  gave for s =  0.0333984375   minimal norm  27.915301939459855\n",
      "Found minimum norm =  28.031273907974512  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZZ  gave for s =  0.0181640625   minimal norm  28.031273907974512\n",
      "Found minimum norm =  27.957629427203734  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZ1  gave for s =  0.021679687500000003   minimal norm  27.957629427203734\n",
      "Found minimum norm =  27.96848038291918  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z1Z  gave for s =  0.019335937500000004   minimal norm  27.96848038291918\n",
      "Found minimum norm =  27.799887181025323  for s =  0.04082031250000001\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z11  gave for s =  0.04082031250000001   minimal norm  27.799887181025323\n",
      "Found minimum norm =  27.907933409186633  for s =  0.0220703125\n",
      "Flow step output with generator type  single_commutator using string  11Z11ZZ  gave for s =  0.0220703125   minimal norm  27.907933409186633\n",
      "Found minimum norm =  27.73296001569863  for s =  0.0310546875\n",
      "Flow step output with generator type  single_commutator using string  11Z11Z1  gave for s =  0.0310546875   minimal norm  27.73296001569863\n",
      "Found minimum norm =  27.952011015643148  for s =  0.020117187500000005\n",
      "Flow step output with generator type  single_commutator using string  11Z111Z  gave for s =  0.020117187500000005   minimal norm  27.952011015643148\n",
      "Found minimum norm =  27.348784735405598  for s =  0.0291015625\n",
      "Flow step output with generator type  single_commutator using string  11Z1111  gave for s =  0.0291015625   minimal norm  27.348784735405598\n",
      "Found minimum norm =  27.733823054738096  for s =  0.0271484375\n",
      "Flow step output with generator type  single_commutator using string  111ZZZZ  gave for s =  0.0271484375   minimal norm  27.733823054738096\n",
      "Found minimum norm =  27.748309061684438  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  111ZZZ1  gave for s =  0.024804687500000002   minimal norm  27.748309061684438\n",
      "Found minimum norm =  27.992323560242042  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  111ZZ1Z  gave for s =  0.0181640625   minimal norm  27.992323560242042\n",
      "Found minimum norm =  27.915301939459855  for s =  0.0333984375\n",
      "Flow step output with generator type  single_commutator using string  111ZZ11  gave for s =  0.0333984375   minimal norm  27.915301939459855\n",
      "Found minimum norm =  27.96744003557081  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  111Z1ZZ  gave for s =  0.020507812500000003   minimal norm  27.96744003557081\n",
      "Found minimum norm =  27.972585591565558  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  111Z1Z1  gave for s =  0.024804687500000002   minimal norm  27.972585591565558\n",
      "Found minimum norm =  27.827896932169363  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  111Z11Z  gave for s =  0.0240234375   minimal norm  27.827896932169363\n",
      "Found minimum norm =  27.22514272572706  for s =  0.029882812499999998\n",
      "Flow step output with generator type  single_commutator using string  111Z111  gave for s =  0.029882812499999998   minimal norm  27.22514272572706\n",
      "Found minimum norm =  27.79031086124141  for s =  0.0236328125\n",
      "Flow step output with generator type  single_commutator using string  1111ZZZ  gave for s =  0.0236328125   minimal norm  27.79031086124141\n",
      "Found minimum norm =  27.895539028919362  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1111ZZ1  gave for s =  0.024804687500000002   minimal norm  27.895539028919362\n",
      "Found minimum norm =  27.867081740121613  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1111Z1Z  gave for s =  0.024804687500000002   minimal norm  27.867081740121613\n",
      "Found minimum norm =  27.348784735405605  for s =  0.0291015625\n",
      "Flow step output with generator type  single_commutator using string  1111Z11  gave for s =  0.0291015625   minimal norm  27.348784735405605\n",
      "Found minimum norm =  27.736328056631923  for s =  0.026367187500000003\n",
      "Flow step output with generator type  single_commutator using string  11111ZZ  gave for s =  0.026367187500000003   minimal norm  27.736328056631923\n",
      "Found minimum norm =  27.486462644777856  for s =  0.0306640625\n",
      "Flow step output with generator type  single_commutator using string  11111Z1  gave for s =  0.0306640625   minimal norm  27.486462644777856\n",
      "Found minimum norm =  27.614509669765923  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  111111Z  gave for s =  0.0322265625   minimal norm  27.614509669765923\n",
      "Found minimum norm =  28.141161645074114  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1111111  gave for s =  0.0001953125   minimal norm  28.141161645074114\n",
      "Found minimum norm =  27.12533963530527  for s =  0.0025390625000000005\n",
      "Found that canonical is better because  27.12533963530527 27.22514272572706\n",
      "Found minimum norm =  27.12533963530527  for s =  0.0025390625000000005\n",
      "Flowing forwards with type  canonical\n",
      "[]\n",
      "Flow step  7\n",
      "Found minimum norm =  26.809862263604934  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZZ  gave for s =  0.0240234375   minimal norm  26.809862263604934\n",
      "Found minimum norm =  26.779415039322974  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZ1  gave for s =  0.0353515625   minimal norm  26.779415039322974\n",
      "Found minimum norm =  27.011439520404362  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ1Z  gave for s =  0.022851562500000002   minimal norm  27.011439520404362\n",
      "Found minimum norm =  26.845996312472106  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ11  gave for s =  0.021679687500000003   minimal norm  26.845996312472106\n",
      "Found minimum norm =  27.081756890523756  for s =  0.0134765625\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1ZZ  gave for s =  0.0134765625   minimal norm  27.081756890523756\n",
      "Found minimum norm =  26.91967489101826  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1Z1  gave for s =  0.021679687500000003   minimal norm  26.91967489101826\n",
      "Found minimum norm =  26.95772541018642  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ11Z  gave for s =  0.019335937500000004   minimal norm  26.95772541018642\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  26.840709287522394  for s =  0.0333984375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ111  gave for s =  0.0333984375   minimal norm  26.840709287522394\n",
      "Found minimum norm =  27.11537415663973  for s =  0.0060546875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZZ  gave for s =  0.0060546875   minimal norm  27.11537415663973\n",
      "Found minimum norm =  27.086830078039938  for s =  0.0095703125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZ1  gave for s =  0.0095703125   minimal norm  27.086830078039938\n",
      "Found minimum norm =  27.005178318104353  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z1Z  gave for s =  0.017773437500000003   minimal norm  27.005178318104353\n",
      "Found minimum norm =  27.087161490147352  for s =  0.0158203125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z11  gave for s =  0.0158203125   minimal norm  27.087161490147352\n",
      "Found minimum norm =  27.011183261130082  for s =  0.0158203125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11ZZ  gave for s =  0.0158203125   minimal norm  27.011183261130082\n",
      "Found minimum norm =  27.066801970706553  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11Z1  gave for s =  0.022851562500000002   minimal norm  27.066801970706553\n",
      "Found minimum norm =  27.05869711368265  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ111Z  gave for s =  0.0173828125   minimal norm  27.05869711368265\n",
      "Found minimum norm =  26.815201234926622  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1111  gave for s =  0.021679687500000003   minimal norm  26.815201234926622\n",
      "Found minimum norm =  27.081756890523756  for s =  0.0134765625\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZZ  gave for s =  0.0134765625   minimal norm  27.081756890523756\n",
      "Found minimum norm =  27.002970436392285  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZ1  gave for s =  0.0173828125   minimal norm  27.002970436392285\n",
      "Found minimum norm =  26.978535421793804  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ1Z  gave for s =  0.019726562500000003   minimal norm  26.978535421793804\n",
      "Found minimum norm =  27.124957647825237  for s =  0.0017578125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ11  gave for s =  0.0017578125   minimal norm  27.124957647825237\n",
      "Found minimum norm =  26.9988854636318  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1ZZ  gave for s =  0.019335937500000004   minimal norm  26.9988854636318\n",
      "Found minimum norm =  27.12632851374279  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1Z1  gave for s =  0.0001953125   minimal norm  27.12632851374279\n",
      "Found minimum norm =  27.025922376429772  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z11Z  gave for s =  0.024804687500000002   minimal norm  27.025922376429772\n",
      "Found minimum norm =  26.976035018094045  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z111  gave for s =  0.016992187500000002   minimal norm  26.976035018094045\n",
      "Found minimum norm =  27.011183261130082  for s =  0.0158203125\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZZ  gave for s =  0.0158203125   minimal norm  27.011183261130082\n",
      "Found minimum norm =  27.014178908021776  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZ1  gave for s =  0.024804687500000002   minimal norm  27.014178908021776\n",
      "Found minimum norm =  26.98827141470607  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z1Z  gave for s =  0.024804687500000002   minimal norm  26.98827141470607\n",
      "Found minimum norm =  26.95768339226733  for s =  0.018945312500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z11  gave for s =  0.018945312500000002   minimal norm  26.95768339226733\n",
      "Found minimum norm =  27.050336656761434  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  ZZ111ZZ  gave for s =  0.0173828125   minimal norm  27.050336656761434\n",
      "Found minimum norm =  26.89034283458062  for s =  0.022460937500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ111Z1  gave for s =  0.022460937500000003   minimal norm  26.89034283458062\n",
      "Found minimum norm =  26.96827169407107  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  ZZ1111Z  gave for s =  0.0181640625   minimal norm  26.96827169407107\n",
      "Found minimum norm =  26.791892317573463  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11111  gave for s =  0.0341796875   minimal norm  26.791892317573463\n",
      "Found minimum norm =  27.011439520404366  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZZ  gave for s =  0.022851562500000002   minimal norm  27.011439520404366\n",
      "Found minimum norm =  26.936060744191842  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZ1  gave for s =  0.020898437500000002   minimal norm  26.936060744191842\n",
      "Found minimum norm =  27.004117346470668  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ1Z  gave for s =  0.018554687500000003   minimal norm  27.004117346470668\n",
      "Found minimum norm =  27.093790752013586  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ11  gave for s =  0.016992187500000002   minimal norm  27.093790752013586\n",
      "Found minimum norm =  26.978535421793797  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1ZZ  gave for s =  0.019726562500000003   minimal norm  26.978535421793797\n",
      "Found minimum norm =  26.813411364827605  for s =  0.0451171875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1Z1  gave for s =  0.0451171875   minimal norm  26.813411364827605\n",
      "Found minimum norm =  26.983998002592447  for s =  0.0294921875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ11Z  gave for s =  0.0294921875   minimal norm  26.983998002592447\n",
      "Found minimum norm =  26.94626818080183  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ111  gave for s =  0.0181640625   minimal norm  26.94626818080183\n",
      "Found minimum norm =  27.00517831810435  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZZ  gave for s =  0.017773437500000003   minimal norm  27.00517831810435\n",
      "Found minimum norm =  27.118362657187525  for s =  0.008398437500000001\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZ1  gave for s =  0.008398437500000001   minimal norm  27.118362657187525\n",
      "Found minimum norm =  27.028200466161817  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z1Z  gave for s =  0.020898437500000002   minimal norm  27.028200466161817\n",
      "Found minimum norm =  26.9658693926461  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z11  gave for s =  0.017773437500000003   minimal norm  26.9658693926461\n",
      "Found minimum norm =  26.988271414706073  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11ZZ  gave for s =  0.024804687500000002   minimal norm  26.988271414706073\n",
      "Found minimum norm =  26.881079297597434  for s =  0.022460937500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11Z1  gave for s =  0.022460937500000003   minimal norm  26.881079297597434\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  26.967522719613346  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1Z111Z  gave for s =  0.019726562500000003   minimal norm  26.967522719613346\n",
      "Found minimum norm =  26.901404898632915  for s =  0.040429687500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1111  gave for s =  0.040429687500000006   minimal norm  26.901404898632915\n",
      "Found minimum norm =  26.957725410186413  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZZ  gave for s =  0.019335937500000004   minimal norm  26.957725410186413\n",
      "Found minimum norm =  26.91451197789827  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZ1  gave for s =  0.0330078125   minimal norm  26.91451197789827\n",
      "Found minimum norm =  26.983998002592443  for s =  0.0294921875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ1Z  gave for s =  0.0294921875   minimal norm  26.983998002592443\n",
      "Found minimum norm =  26.93330864725343  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ11  gave for s =  0.019726562500000003   minimal norm  26.93330864725343\n",
      "Found minimum norm =  27.02592237642977  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1ZZ  gave for s =  0.024804687500000002   minimal norm  27.02592237642977\n",
      "Found minimum norm =  27.10556139918203  for s =  0.0072265625\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1Z1  gave for s =  0.0072265625   minimal norm  27.10556139918203\n",
      "Found minimum norm =  26.938929415763763  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11Z11Z  gave for s =  0.020898437500000002   minimal norm  26.938929415763763\n",
      "Found minimum norm =  26.89064547744742  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z111  gave for s =  0.0373046875   minimal norm  26.89064547744742\n",
      "Found minimum norm =  27.058697113682648  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZZ  gave for s =  0.0173828125   minimal norm  27.058697113682648\n",
      "Found minimum norm =  26.939341159388817  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZ1  gave for s =  0.020507812500000003   minimal norm  26.939341159388817\n",
      "Found minimum norm =  26.967522719613346  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  Z111Z1Z  gave for s =  0.019726562500000003   minimal norm  26.967522719613346\n",
      "Found minimum norm =  26.968501164762763  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  Z111Z11  gave for s =  0.0322265625   minimal norm  26.968501164762763\n",
      "Found minimum norm =  26.968271694071063  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  Z1111ZZ  gave for s =  0.0181640625   minimal norm  26.968271694071063\n",
      "Found minimum norm =  26.860132280152566  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  Z1111Z1  gave for s =  0.0412109375   minimal norm  26.860132280152566\n",
      "Found minimum norm =  27.00356980506201  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  Z11111Z  gave for s =  0.0240234375   minimal norm  27.00356980506201\n",
      "Found minimum norm =  26.65566623643109  for s =  0.026757812500000002\n",
      "Flow step output with generator type  single_commutator using string  Z111111  gave for s =  0.026757812500000002   minimal norm  26.65566623643109\n",
      "Found minimum norm =  26.779415039322924  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZZ  gave for s =  0.0353515625   minimal norm  26.779415039322924\n",
      "Found minimum norm =  26.753565026045877  for s =  0.0259765625\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZ1  gave for s =  0.0259765625   minimal norm  26.753565026045877\n",
      "Found minimum norm =  26.93606074419178  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ1Z  gave for s =  0.020898437500000002   minimal norm  26.93606074419178\n",
      "Found minimum norm =  26.8167299802156  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ11  gave for s =  0.0412109375   minimal norm  26.8167299802156\n",
      "Found minimum norm =  27.002970436392218  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1ZZ  gave for s =  0.0173828125   minimal norm  27.002970436392218\n",
      "Found minimum norm =  27.127007004653645  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1Z1  gave for s =  0.0001953125   minimal norm  27.127007004653645\n",
      "Found minimum norm =  26.91451197789825  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ11Z  gave for s =  0.0330078125   minimal norm  26.91451197789825\n",
      "Found minimum norm =  26.776954766971222  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ111  gave for s =  0.022851562500000002   minimal norm  26.776954766971222\n",
      "Found minimum norm =  27.086830078039885  for s =  0.0095703125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZZ  gave for s =  0.0095703125   minimal norm  27.086830078039885\n",
      "Found minimum norm =  27.125853671750342  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZ1  gave for s =  0.0001953125   minimal norm  27.125853671750342\n",
      "Found minimum norm =  27.11836265718757  for s =  0.008398437500000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z1Z  gave for s =  0.008398437500000001   minimal norm  27.11836265718757\n",
      "Found minimum norm =  26.957858494819455  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z11  gave for s =  0.0181640625   minimal norm  26.957858494819455\n",
      "Found minimum norm =  27.014178908021808  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11ZZ  gave for s =  0.024804687500000002   minimal norm  27.014178908021808\n",
      "Found minimum norm =  27.105405402243928  for s =  0.0064453125000000005\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11Z1  gave for s =  0.0064453125000000005   minimal norm  27.105405402243928\n",
      "Found minimum norm =  26.93934115938876  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  1ZZ111Z  gave for s =  0.020507812500000003   minimal norm  26.93934115938876\n",
      "Found minimum norm =  26.946049038800105  for s =  0.04472656250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1111  gave for s =  0.04472656250000001   minimal norm  26.946049038800105\n",
      "Found minimum norm =  26.919674891018207  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZZ  gave for s =  0.021679687500000003   minimal norm  26.919674891018207\n",
      "Found minimum norm =  27.127007004653642  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZ1  gave for s =  0.0001953125   minimal norm  27.127007004653642\n",
      "Found minimum norm =  26.81341136482745  for s =  0.0451171875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ1Z  gave for s =  0.0451171875   minimal norm  26.81341136482745\n",
      "Found minimum norm =  27.073832170664602  for s =  0.009960937500000003\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ11  gave for s =  0.009960937500000003   minimal norm  27.073832170664602\n",
      "Found minimum norm =  27.12632851374279  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1ZZ  gave for s =  0.0001953125   minimal norm  27.12632851374279\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  26.61510630649272  for s =  0.0271484375\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1Z1  gave for s =  0.0271484375   minimal norm  26.61510630649272\n",
      "Found minimum norm =  27.105561399181983  for s =  0.0072265625\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z11Z  gave for s =  0.0072265625   minimal norm  27.105561399181983\n",
      "Found minimum norm =  26.90365128371832  for s =  0.0693359375\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z111  gave for s =  0.0693359375   minimal norm  26.90365128371832\n",
      "Found minimum norm =  27.06680197070659  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZZ  gave for s =  0.022851562500000002   minimal norm  27.06680197070659\n",
      "Found minimum norm =  27.105405402243935  for s =  0.0064453125000000005\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZ1  gave for s =  0.0064453125000000005   minimal norm  27.105405402243935\n",
      "Found minimum norm =  26.88107929759739  for s =  0.022460937500000003\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z1Z  gave for s =  0.022460937500000003   minimal norm  26.88107929759739\n",
      "Found minimum norm =  26.605212987560037  for s =  0.0615234375\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z11  gave for s =  0.0615234375   minimal norm  26.605212987560037\n",
      "Found minimum norm =  26.89034283458057  for s =  0.022460937500000003\n",
      "Flow step output with generator type  single_commutator using string  1Z111ZZ  gave for s =  0.022460937500000003   minimal norm  26.89034283458057\n",
      "Found minimum norm =  27.120757257331654  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z111Z1  gave for s =  0.0498046875   minimal norm  27.120757257331654\n",
      "Found minimum norm =  26.860132280152474  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  1Z1111Z  gave for s =  0.0412109375   minimal norm  26.860132280152474\n",
      "Found minimum norm =  26.602962275760376  for s =  0.026367187500000003\n",
      "Flow step output with generator type  single_commutator using string  1Z11111  gave for s =  0.026367187500000003   minimal norm  26.602962275760376\n",
      "Found minimum norm =  26.84599631247205  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZZ  gave for s =  0.021679687500000003   minimal norm  26.84599631247205\n",
      "Found minimum norm =  26.816729980215612  for s =  0.0412109375\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZ1  gave for s =  0.0412109375   minimal norm  26.816729980215612\n",
      "Found minimum norm =  27.093790752013646  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ1Z  gave for s =  0.016992187500000002   minimal norm  27.093790752013646\n",
      "Found minimum norm =  26.9071357053877  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ11  gave for s =  0.018554687500000003   minimal norm  26.9071357053877\n",
      "Found minimum norm =  27.124957647825248  for s =  0.0017578125\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1ZZ  gave for s =  0.0017578125   minimal norm  27.124957647825248\n",
      "Found minimum norm =  27.073832170664595  for s =  0.009960937500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1Z1  gave for s =  0.009960937500000003   minimal norm  27.073832170664595\n",
      "Found minimum norm =  26.933308647253373  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZ11Z  gave for s =  0.019726562500000003   minimal norm  26.933308647253373\n",
      "Found minimum norm =  26.977600604391675  for s =  0.0451171875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ111  gave for s =  0.0451171875   minimal norm  26.977600604391675\n",
      "Found minimum norm =  27.087161490147412  for s =  0.0158203125\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZZ  gave for s =  0.0158203125   minimal norm  27.087161490147412\n",
      "Found minimum norm =  26.957858494819458  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZ1  gave for s =  0.0181640625   minimal norm  26.957858494819458\n",
      "Found minimum norm =  26.965869392646034  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z1Z  gave for s =  0.017773437500000003   minimal norm  26.965869392646034\n",
      "Found minimum norm =  26.79643500683364  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z11  gave for s =  0.0498046875   minimal norm  26.79643500683364\n",
      "Found minimum norm =  26.957683392267274  for s =  0.018945312500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z11ZZ  gave for s =  0.018945312500000002   minimal norm  26.957683392267274\n",
      "Found minimum norm =  26.605212987559998  for s =  0.0615234375\n",
      "Flow step output with generator type  single_commutator using string  11Z11Z1  gave for s =  0.0615234375   minimal norm  26.605212987559998\n",
      "Found minimum norm =  26.968501164762756  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  11Z111Z  gave for s =  0.0322265625   minimal norm  26.968501164762756\n",
      "Found minimum norm =  26.641713859602287  for s =  0.025585937500000003\n",
      "Flow step output with generator type  single_commutator using string  11Z1111  gave for s =  0.025585937500000003   minimal norm  26.641713859602287\n",
      "Found minimum norm =  26.840709287522373  for s =  0.0333984375\n",
      "Flow step output with generator type  single_commutator using string  111ZZZZ  gave for s =  0.0333984375   minimal norm  26.840709287522373\n",
      "Found minimum norm =  26.77695476697123  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  111ZZZ1  gave for s =  0.022851562500000002   minimal norm  26.77695476697123\n",
      "Found minimum norm =  26.946268180801777  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  111ZZ1Z  gave for s =  0.0181640625   minimal norm  26.946268180801777\n",
      "Found minimum norm =  26.977600604391686  for s =  0.0451171875\n",
      "Flow step output with generator type  single_commutator using string  111ZZ11  gave for s =  0.0451171875   minimal norm  26.977600604391686\n",
      "Found minimum norm =  26.976035018093988  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  111Z1ZZ  gave for s =  0.016992187500000002   minimal norm  26.976035018093988\n",
      "Found minimum norm =  26.903651283718336  for s =  0.0693359375\n",
      "Flow step output with generator type  single_commutator using string  111Z1Z1  gave for s =  0.0693359375   minimal norm  26.903651283718336\n",
      "Found minimum norm =  26.890645477447368  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  111Z11Z  gave for s =  0.0373046875   minimal norm  26.890645477447368\n",
      "Found minimum norm =  26.529486560618874  for s =  0.026757812500000002\n",
      "Flow step output with generator type  single_commutator using string  111Z111  gave for s =  0.026757812500000002   minimal norm  26.529486560618874\n",
      "Found minimum norm =  26.815201234926572  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  1111ZZZ  gave for s =  0.021679687500000003   minimal norm  26.815201234926572\n",
      "Found minimum norm =  26.946049038800123  for s =  0.04472656250000001\n",
      "Flow step output with generator type  single_commutator using string  1111ZZ1  gave for s =  0.04472656250000001   minimal norm  26.946049038800123\n",
      "Found minimum norm =  26.901404898632833  for s =  0.040429687500000006\n",
      "Flow step output with generator type  single_commutator using string  1111Z1Z  gave for s =  0.040429687500000006   minimal norm  26.901404898632833\n",
      "Found minimum norm =  26.641713859602294  for s =  0.025585937500000003\n",
      "Flow step output with generator type  single_commutator using string  1111Z11  gave for s =  0.025585937500000003   minimal norm  26.641713859602294\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  26.791892317573435  for s =  0.0341796875\n",
      "Flow step output with generator type  single_commutator using string  11111ZZ  gave for s =  0.0341796875   minimal norm  26.791892317573435\n",
      "Found minimum norm =  26.602962275760383  for s =  0.026367187500000003\n",
      "Flow step output with generator type  single_commutator using string  11111Z1  gave for s =  0.026367187500000003   minimal norm  26.602962275760383\n",
      "Found minimum norm =  26.655666236431074  for s =  0.026757812500000002\n",
      "Flow step output with generator type  single_commutator using string  111111Z  gave for s =  0.026757812500000002   minimal norm  26.655666236431074\n",
      "Found minimum norm =  27.12533963530527  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1111111  gave for s =  0.0001953125   minimal norm  27.12533963530527\n",
      "Found minimum norm =  26.535703440152897  for s =  0.0017578125\n",
      "Found that canonical is worse because  26.535703440152897 26.529486560618874\n",
      "Found minimum norm =  26.529486560618874  for s =  0.026757812500000002\n",
      "Flowing forwards with type  single_commutator\n",
      "[]\n",
      "Flow step  8\n",
      "Found minimum norm =  26.245941417035148  for s =  0.0294921875\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZZ  gave for s =  0.0294921875   minimal norm  26.245941417035148\n",
      "Found minimum norm =  26.125863649186446  for s =  0.047460937499999994\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZ1  gave for s =  0.047460937499999994   minimal norm  26.125863649186446\n",
      "Found minimum norm =  26.42945770133961  for s =  0.0302734375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ1Z  gave for s =  0.0302734375   minimal norm  26.42945770133961\n",
      "Found minimum norm =  26.333755624115994  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ11  gave for s =  0.0240234375   minimal norm  26.333755624115994\n",
      "Found minimum norm =  26.51561938204077  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1ZZ  gave for s =  0.012304687500000001   minimal norm  26.51561938204077\n",
      "Found minimum norm =  26.343516299962864  for s =  0.029882812499999998\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1Z1  gave for s =  0.029882812499999998   minimal norm  26.343516299962864\n",
      "Found minimum norm =  26.422739601174083  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ11Z  gave for s =  0.021679687500000003   minimal norm  26.422739601174083\n",
      "Found minimum norm =  26.33898109820433  for s =  0.0361328125\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ111  gave for s =  0.0361328125   minimal norm  26.33898109820433\n",
      "Found minimum norm =  26.530013922713128  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZZ  gave for s =  0.0001953125   minimal norm  26.530013922713128\n",
      "Found minimum norm =  26.529740859056634  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZ1  gave for s =  0.0001953125   minimal norm  26.529740859056634\n",
      "Found minimum norm =  26.481858003863167  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z1Z  gave for s =  0.0173828125   minimal norm  26.481858003863167\n",
      "Found minimum norm =  26.524486294223927  for s =  0.010351562500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z11  gave for s =  0.010351562500000001   minimal norm  26.524486294223927\n",
      "Found minimum norm =  26.480676553687076  for s =  0.015039062499999999\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11ZZ  gave for s =  0.015039062499999999   minimal norm  26.480676553687076\n",
      "Found minimum norm =  26.48226666929982  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11Z1  gave for s =  0.0373046875   minimal norm  26.48226666929982\n",
      "Found minimum norm =  26.49168373478302  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZ111Z  gave for s =  0.020507812500000003   minimal norm  26.49168373478302\n",
      "Found minimum norm =  26.216242487295325  for s =  0.0283203125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1111  gave for s =  0.0283203125   minimal norm  26.216242487295325\n",
      "Found minimum norm =  26.51561938204077  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZZ  gave for s =  0.012304687500000001   minimal norm  26.51561938204077\n",
      "Found minimum norm =  26.445690414113443  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZ1  gave for s =  0.020507812500000003   minimal norm  26.445690414113443\n",
      "Found minimum norm =  26.413211150712122  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ1Z  gave for s =  0.024804687500000002   minimal norm  26.413211150712122\n",
      "Found minimum norm =  26.530046856101357  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ11  gave for s =  0.0001953125   minimal norm  26.530046856101357\n",
      "Found minimum norm =  26.447464036581827  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1ZZ  gave for s =  0.022851562500000002   minimal norm  26.447464036581827\n",
      "Found minimum norm =  26.531233964062032  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1Z1  gave for s =  0.0001953125   minimal norm  26.531233964062032\n",
      "Found minimum norm =  26.463827159966858  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z11Z  gave for s =  0.0330078125   minimal norm  26.463827159966858\n",
      "Found minimum norm =  26.48236792505212  for s =  0.013085937500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z111  gave for s =  0.013085937500000002   minimal norm  26.48236792505212\n",
      "Found minimum norm =  26.480676553687072  for s =  0.015039062499999999\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZZ  gave for s =  0.015039062499999999   minimal norm  26.480676553687072\n",
      "Found minimum norm =  26.444901479781205  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZ1  gave for s =  0.0373046875   minimal norm  26.444901479781205\n",
      "Found minimum norm =  26.355141518693102  for s =  0.042382812500000006\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z1Z  gave for s =  0.042382812500000006   minimal norm  26.355141518693102\n",
      "Found minimum norm =  26.4219289810752  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z11  gave for s =  0.020898437500000002   minimal norm  26.4219289810752\n",
      "Found minimum norm =  26.470498761379616  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  ZZ111ZZ  gave for s =  0.0240234375   minimal norm  26.470498761379616\n",
      "Found minimum norm =  26.346233746169066  for s =  0.0283203125\n",
      "Flow step output with generator type  single_commutator using string  ZZ111Z1  gave for s =  0.0283203125   minimal norm  26.346233746169066\n",
      "Found minimum norm =  26.42509521872147  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1111Z  gave for s =  0.020507812500000003   minimal norm  26.42509521872147\n",
      "Found minimum norm =  26.094181075568933  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11111  gave for s =  0.0498046875   minimal norm  26.094181075568933\n",
      "Found minimum norm =  26.42945770133961  for s =  0.0302734375\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZZ  gave for s =  0.0302734375   minimal norm  26.42945770133961\n",
      "Found minimum norm =  26.402955182829356  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZ1  gave for s =  0.024804687500000002   minimal norm  26.402955182829356\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  26.491965150731215  for s =  0.0158203125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ1Z  gave for s =  0.0158203125   minimal norm  26.491965150731215\n",
      "Found minimum norm =  26.529557416109068  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ11  gave for s =  0.0001953125   minimal norm  26.529557416109068\n",
      "Found minimum norm =  26.413211150712115  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1ZZ  gave for s =  0.024804687500000002   minimal norm  26.413211150712115\n",
      "Found minimum norm =  26.004188498995887  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1Z1  gave for s =  0.0498046875   minimal norm  26.004188498995887\n",
      "Found minimum norm =  26.350064475603038  for s =  0.0458984375\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ11Z  gave for s =  0.0458984375   minimal norm  26.350064475603038\n",
      "Found minimum norm =  26.449671566758255  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ111  gave for s =  0.0173828125   minimal norm  26.449671566758255\n",
      "Found minimum norm =  26.481858003863167  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZZ  gave for s =  0.0173828125   minimal norm  26.481858003863167\n",
      "Found minimum norm =  26.53006776973742  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZ1  gave for s =  0.0001953125   minimal norm  26.53006776973742\n",
      "Found minimum norm =  26.442155168491084  for s =  0.029882812499999998\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z1Z  gave for s =  0.029882812499999998   minimal norm  26.442155168491084\n",
      "Found minimum norm =  26.44006074489406  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z11  gave for s =  0.019335937500000004   minimal norm  26.44006074489406\n",
      "Found minimum norm =  26.355141518693095  for s =  0.042382812500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11ZZ  gave for s =  0.042382812500000006   minimal norm  26.355141518693095\n",
      "Found minimum norm =  26.36283361043501  for s =  0.0271484375\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11Z1  gave for s =  0.0271484375   minimal norm  26.36283361043501\n",
      "Found minimum norm =  26.409028035120137  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z111Z  gave for s =  0.024804687500000002   minimal norm  26.409028035120137\n",
      "Found minimum norm =  26.158338945922985  for s =  0.0646484375\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1111  gave for s =  0.0646484375   minimal norm  26.158338945922985\n",
      "Found minimum norm =  26.42273960117408  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZZ  gave for s =  0.021679687500000003   minimal norm  26.42273960117408\n",
      "Found minimum norm =  26.24090733129786  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZ1  gave for s =  0.0498046875   minimal norm  26.24090733129786\n",
      "Found minimum norm =  26.350064475603034  for s =  0.0458984375\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ1Z  gave for s =  0.0458984375   minimal norm  26.350064475603034\n",
      "Found minimum norm =  26.388698579295873  for s =  0.022460937500000003\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ11  gave for s =  0.022460937500000003   minimal norm  26.388698579295873\n",
      "Found minimum norm =  26.463827159966858  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1ZZ  gave for s =  0.0330078125   minimal norm  26.463827159966858\n",
      "Found minimum norm =  26.529686832896196  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1Z1  gave for s =  0.0001953125   minimal norm  26.529686832896196\n",
      "Found minimum norm =  26.422980823507856  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  Z11Z11Z  gave for s =  0.021679687500000003   minimal norm  26.422980823507856\n",
      "Found minimum norm =  26.337840424070542  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z11Z111  gave for s =  0.0498046875   minimal norm  26.337840424070542\n",
      "Found minimum norm =  26.491683734783017  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZZ  gave for s =  0.020507812500000003   minimal norm  26.491683734783017\n",
      "Found minimum norm =  26.398787278846548  for s =  0.0244140625\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZ1  gave for s =  0.0244140625   minimal norm  26.398787278846548\n",
      "Found minimum norm =  26.40902803512014  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z111Z1Z  gave for s =  0.024804687500000002   minimal norm  26.40902803512014\n",
      "Found minimum norm =  26.309948309838084  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z111Z11  gave for s =  0.0498046875   minimal norm  26.309948309838084\n",
      "Found minimum norm =  26.425095218721466  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1111ZZ  gave for s =  0.020507812500000003   minimal norm  26.425095218721466\n",
      "Found minimum norm =  26.21542277217584  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  Z1111Z1  gave for s =  0.0498046875   minimal norm  26.21542277217584\n",
      "Found minimum norm =  26.40628061103604  for s =  0.038476562500000006\n",
      "Flow step output with generator type  single_commutator using string  Z11111Z  gave for s =  0.038476562500000006   minimal norm  26.40628061103604\n",
      "Found minimum norm =  26.034894624060378  for s =  0.03574218750000001\n",
      "Flow step output with generator type  single_commutator using string  Z111111  gave for s =  0.03574218750000001   minimal norm  26.034894624060378\n",
      "Found minimum norm =  26.125863649186353  for s =  0.047460937499999994\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZZ  gave for s =  0.047460937499999994   minimal norm  26.125863649186353\n",
      "Found minimum norm =  26.193653966859582  for s =  0.03378906250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZ1  gave for s =  0.03378906250000001   minimal norm  26.193653966859582\n",
      "Found minimum norm =  26.40295518282933  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ1Z  gave for s =  0.024804687500000002   minimal norm  26.40295518282933\n",
      "Found minimum norm =  26.1292542520772  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ11  gave for s =  0.0498046875   minimal norm  26.1292542520772\n",
      "Found minimum norm =  26.445690414113418  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1ZZ  gave for s =  0.020507812500000003   minimal norm  26.445690414113418\n",
      "Found minimum norm =  26.531652484353504  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1Z1  gave for s =  0.0001953125   minimal norm  26.531652484353504\n",
      "Found minimum norm =  26.24090733129776  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ11Z  gave for s =  0.0498046875   minimal norm  26.24090733129776\n",
      "Found minimum norm =  26.31950635535973  for s =  0.0244140625\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ111  gave for s =  0.0244140625   minimal norm  26.31950635535973\n",
      "Found minimum norm =  26.52974085905663  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZZ  gave for s =  0.0001953125   minimal norm  26.52974085905663\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  26.531059679335577  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZ1  gave for s =  0.0001953125   minimal norm  26.531059679335577\n",
      "Found minimum norm =  26.53006776973742  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z1Z  gave for s =  0.0001953125   minimal norm  26.53006776973742\n",
      "Found minimum norm =  26.441535800916892  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z11  gave for s =  0.018554687500000003   minimal norm  26.441535800916892\n",
      "Found minimum norm =  26.444901479781183  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11ZZ  gave for s =  0.0373046875   minimal norm  26.444901479781183\n",
      "Found minimum norm =  26.530142297197827  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11Z1  gave for s =  0.0001953125   minimal norm  26.530142297197827\n",
      "Found minimum norm =  26.398787278846534  for s =  0.0244140625\n",
      "Flow step output with generator type  single_commutator using string  1ZZ111Z  gave for s =  0.0244140625   minimal norm  26.398787278846534\n",
      "Found minimum norm =  26.23581397554724  for s =  0.06894531250000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1111  gave for s =  0.06894531250000001   minimal norm  26.23581397554724\n",
      "Found minimum norm =  26.343516299962857  for s =  0.029882812499999998\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZZ  gave for s =  0.029882812499999998   minimal norm  26.343516299962857\n",
      "Found minimum norm =  26.531652484353508  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZ1  gave for s =  0.0001953125   minimal norm  26.531652484353508\n",
      "Found minimum norm =  26.004188498995795  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ1Z  gave for s =  0.0498046875   minimal norm  26.004188498995795\n",
      "Found minimum norm =  26.525074903843425  for s =  0.0044921875000000005\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ11  gave for s =  0.0044921875000000005   minimal norm  26.525074903843425\n",
      "Found minimum norm =  26.531233964062032  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1ZZ  gave for s =  0.0001953125   minimal norm  26.531233964062032\n",
      "Found minimum norm =  25.943222402980027  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1Z1  gave for s =  0.03886718750000001   minimal norm  25.943222402980027\n",
      "Found minimum norm =  26.529686832896193  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z11Z  gave for s =  0.0001953125   minimal norm  26.529686832896193\n",
      "Found minimum norm =  26.24305892716003  for s =  0.0841796875\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z111  gave for s =  0.0841796875   minimal norm  26.24305892716003\n",
      "Found minimum norm =  26.48226666929979  for s =  0.0373046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZZ  gave for s =  0.0373046875   minimal norm  26.48226666929979\n",
      "Found minimum norm =  26.530142297197827  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZ1  gave for s =  0.0001953125   minimal norm  26.530142297197827\n",
      "Found minimum norm =  26.362833610435  for s =  0.0271484375\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z1Z  gave for s =  0.0271484375   minimal norm  26.362833610435\n",
      "Found minimum norm =  25.924697839797236  for s =  0.07441406250000002\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z11  gave for s =  0.07441406250000002   minimal norm  25.924697839797236\n",
      "Found minimum norm =  26.34623374616906  for s =  0.0283203125\n",
      "Flow step output with generator type  single_commutator using string  1Z111ZZ  gave for s =  0.0283203125   minimal norm  26.34623374616906\n",
      "Found minimum norm =  26.326090107116514  for s =  0.07441406250000002\n",
      "Flow step output with generator type  single_commutator using string  1Z111Z1  gave for s =  0.07441406250000002   minimal norm  26.326090107116514\n",
      "Found minimum norm =  26.215422772175764  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z1111Z  gave for s =  0.0498046875   minimal norm  26.215422772175764\n",
      "Found minimum norm =  26.029430215271137  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  1Z11111  gave for s =  0.0353515625   minimal norm  26.029430215271137\n",
      "Found minimum norm =  26.33375562411597  for s =  0.0240234375\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZZ  gave for s =  0.0240234375   minimal norm  26.33375562411597\n",
      "Found minimum norm =  26.1292542520772  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZ1  gave for s =  0.0498046875   minimal norm  26.1292542520772\n",
      "Found minimum norm =  26.529557416109064  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ1Z  gave for s =  0.0001953125   minimal norm  26.529557416109064\n",
      "Found minimum norm =  26.388990725199278  for s =  0.020117187500000005\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ11  gave for s =  0.020117187500000005   minimal norm  26.388990725199278\n",
      "Found minimum norm =  26.530046856101357  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1ZZ  gave for s =  0.0001953125   minimal norm  26.530046856101357\n",
      "Found minimum norm =  26.525074903843425  for s =  0.0044921875000000005\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1Z1  gave for s =  0.0044921875000000005   minimal norm  26.525074903843425\n",
      "Found minimum norm =  26.38869857929585  for s =  0.022460937500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZ11Z  gave for s =  0.022460937500000003   minimal norm  26.38869857929585\n",
      "Found minimum norm =  26.466408586731614  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11ZZ111  gave for s =  0.0498046875   minimal norm  26.466408586731614\n",
      "Found minimum norm =  26.524486294223955  for s =  0.010351562500000001\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZZ  gave for s =  0.010351562500000001   minimal norm  26.524486294223955\n",
      "Found minimum norm =  26.441535800916892  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZ1  gave for s =  0.018554687500000003   minimal norm  26.441535800916892\n",
      "Found minimum norm =  26.440060744894033  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z1Z  gave for s =  0.019335937500000004   minimal norm  26.440060744894033\n",
      "Found minimum norm =  26.05291453861424  for s =  0.06894531250000001\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z11  gave for s =  0.06894531250000001   minimal norm  26.05291453861424\n",
      "Found minimum norm =  26.421928981075176  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z11ZZ  gave for s =  0.020898437500000002   minimal norm  26.421928981075176\n",
      "Found minimum norm =  25.924697839797204  for s =  0.07441406250000002\n",
      "Flow step output with generator type  single_commutator using string  11Z11Z1  gave for s =  0.07441406250000002   minimal norm  25.924697839797204\n",
      "Found minimum norm =  26.309948309837992  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11Z111Z  gave for s =  0.0498046875   minimal norm  26.309948309837992\n",
      "Found minimum norm =  26.108522270665873  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  11Z1111  gave for s =  0.0322265625   minimal norm  26.108522270665873\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  26.33898109820431  for s =  0.0361328125\n",
      "Flow step output with generator type  single_commutator using string  111ZZZZ  gave for s =  0.0361328125   minimal norm  26.33898109820431\n",
      "Found minimum norm =  26.31950635535973  for s =  0.0244140625\n",
      "Flow step output with generator type  single_commutator using string  111ZZZ1  gave for s =  0.0244140625   minimal norm  26.31950635535973\n",
      "Found minimum norm =  26.449671566758234  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  111ZZ1Z  gave for s =  0.0173828125   minimal norm  26.449671566758234\n",
      "Found minimum norm =  26.46640858673162  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111ZZ11  gave for s =  0.0498046875   minimal norm  26.46640858673162\n",
      "Found minimum norm =  26.482367925052092  for s =  0.013085937500000002\n",
      "Flow step output with generator type  single_commutator using string  111Z1ZZ  gave for s =  0.013085937500000002   minimal norm  26.482367925052092\n",
      "Found minimum norm =  26.243058927160025  for s =  0.0841796875\n",
      "Flow step output with generator type  single_commutator using string  111Z1Z1  gave for s =  0.0841796875   minimal norm  26.243058927160025\n",
      "Found minimum norm =  26.33784042407046  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  111Z11Z  gave for s =  0.0498046875   minimal norm  26.33784042407046\n",
      "Found minimum norm =  26.131863996168352  for s =  0.0306640625\n",
      "Flow step output with generator type  single_commutator using string  111Z111  gave for s =  0.0306640625   minimal norm  26.131863996168352\n",
      "Found minimum norm =  26.21624248729531  for s =  0.0283203125\n",
      "Flow step output with generator type  single_commutator using string  1111ZZZ  gave for s =  0.0283203125   minimal norm  26.21624248729531\n",
      "Found minimum norm =  26.235813975547263  for s =  0.06894531250000001\n",
      "Flow step output with generator type  single_commutator using string  1111ZZ1  gave for s =  0.06894531250000001   minimal norm  26.235813975547263\n",
      "Found minimum norm =  26.15833894592278  for s =  0.0646484375\n",
      "Flow step output with generator type  single_commutator using string  1111Z1Z  gave for s =  0.0646484375   minimal norm  26.15833894592278\n",
      "Found minimum norm =  26.108522270665873  for s =  0.0322265625\n",
      "Flow step output with generator type  single_commutator using string  1111Z11  gave for s =  0.0322265625   minimal norm  26.108522270665873\n",
      "Found minimum norm =  26.094181075568837  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  11111ZZ  gave for s =  0.0498046875   minimal norm  26.094181075568837\n",
      "Found minimum norm =  26.029430215271145  for s =  0.0353515625\n",
      "Flow step output with generator type  single_commutator using string  11111Z1  gave for s =  0.0353515625   minimal norm  26.029430215271145\n",
      "Found minimum norm =  26.034894624060406  for s =  0.03574218750000001\n",
      "Flow step output with generator type  single_commutator using string  111111Z  gave for s =  0.03574218750000001   minimal norm  26.034894624060406\n",
      "Found minimum norm =  26.529486560618874  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1111111  gave for s =  0.0001953125   minimal norm  26.529486560618874\n",
      "Found minimum norm =  25.99533249766773  for s =  0.0021484375\n",
      "Found that canonical is worse because  25.99533249766773 25.924697839797204\n",
      "Found minimum norm =  25.924697839797204  for s =  0.07441406250000002\n",
      "Flowing forwards with type  single_commutator\n",
      "[]\n",
      "Flow step  9\n",
      "Found minimum norm =  25.64753686156869  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZZ  gave for s =  0.024804687500000002   minimal norm  25.64753686156869\n",
      "Found minimum norm =  25.57122518499555  for s =  0.029882812499999998\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZZ1  gave for s =  0.029882812499999998   minimal norm  25.57122518499555\n",
      "Found minimum norm =  25.791581401298735  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ1Z  gave for s =  0.021679687500000003   minimal norm  25.791581401298735\n",
      "Found minimum norm =  25.639620896827733  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZZ11  gave for s =  0.022851562500000002   minimal norm  25.639620896827733\n",
      "Found minimum norm =  25.822654550819795  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1ZZ  gave for s =  0.0166015625   minimal norm  25.822654550819795\n",
      "Found minimum norm =  25.788713735576287  for s =  0.020117187500000005\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ1Z1  gave for s =  0.020117187500000005   minimal norm  25.788713735576287\n",
      "Found minimum norm =  25.746390775075735  for s =  0.020507812500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ11Z  gave for s =  0.020507812500000003   minimal norm  25.746390775075735\n",
      "Found minimum norm =  25.72818654891227  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZZ111  gave for s =  0.024804687500000002   minimal norm  25.72818654891227\n",
      "Found minimum norm =  25.873939441179733  for s =  0.0119140625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZZ  gave for s =  0.0119140625   minimal norm  25.873939441179733\n",
      "Found minimum norm =  25.868914226565877  for s =  0.0126953125\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1ZZ1  gave for s =  0.0126953125   minimal norm  25.868914226565877\n",
      "Found minimum norm =  25.81818737133584  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z1Z  gave for s =  0.016992187500000002   minimal norm  25.81818737133584\n",
      "Found minimum norm =  25.88094976964845  for s =  0.0134765625\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1Z11  gave for s =  0.0134765625   minimal norm  25.88094976964845\n",
      "Found minimum norm =  25.889499859731185  for s =  0.009960937500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11ZZ  gave for s =  0.009960937500000003   minimal norm  25.889499859731185\n",
      "Found minimum norm =  25.90636032578277  for s =  0.008398437500000001\n",
      "Flow step output with generator type  single_commutator using string  ZZZ11Z1  gave for s =  0.008398437500000001   minimal norm  25.90636032578277\n",
      "Found minimum norm =  25.862131277635697  for s =  0.0138671875\n",
      "Flow step output with generator type  single_commutator using string  ZZZ111Z  gave for s =  0.0138671875   minimal norm  25.862131277635697\n",
      "Found minimum norm =  25.533344243959966  for s =  0.025585937500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZZ1111  gave for s =  0.025585937500000003   minimal norm  25.533344243959966\n",
      "Found minimum norm =  25.89868379750832  for s =  0.009960937500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZZ  gave for s =  0.009960937500000003   minimal norm  25.89868379750832\n",
      "Found minimum norm =  25.91425369797299  for s =  0.0052734375\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZZ1  gave for s =  0.0052734375   minimal norm  25.91425369797299\n",
      "Found minimum norm =  25.813250829543914  for s =  0.015039062499999999\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ1Z  gave for s =  0.015039062499999999   minimal norm  25.813250829543914\n",
      "Found minimum norm =  25.924923626422228  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1ZZ11  gave for s =  0.0001953125   minimal norm  25.924923626422228\n",
      "Found minimum norm =  25.815392860666652  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1ZZ  gave for s =  0.0173828125   minimal norm  25.815392860666652\n",
      "Found minimum norm =  25.924870011579312  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z1Z1  gave for s =  0.0001953125   minimal norm  25.924870011579312\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  25.861458528178535  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z11Z  gave for s =  0.018554687500000003   minimal norm  25.861458528178535\n",
      "Found minimum norm =  25.804124528456597  for s =  0.015039062499999999\n",
      "Flow step output with generator type  single_commutator using string  ZZ1Z111  gave for s =  0.015039062499999999   minimal norm  25.804124528456597\n",
      "Found minimum norm =  25.8214007834715  for s =  0.0154296875\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZZ  gave for s =  0.0154296875   minimal norm  25.8214007834715\n",
      "Found minimum norm =  25.856692513483626  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  ZZ11ZZ1  gave for s =  0.0166015625   minimal norm  25.856692513483626\n",
      "Found minimum norm =  25.856123060734287  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z1Z  gave for s =  0.019335937500000004   minimal norm  25.856123060734287\n",
      "Found minimum norm =  25.775431254787957  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  ZZ11Z11  gave for s =  0.0166015625   minimal norm  25.775431254787957\n",
      "Found minimum norm =  25.817401448497595  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  ZZ111ZZ  gave for s =  0.019335937500000004   minimal norm  25.817401448497595\n",
      "Found minimum norm =  25.69648905526688  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  ZZ111Z1  gave for s =  0.022851562500000002   minimal norm  25.69648905526688\n",
      "Found minimum norm =  25.75242012238376  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  ZZ1111Z  gave for s =  0.017773437500000003   minimal norm  25.75242012238376\n",
      "Found minimum norm =  25.624006057101102  for s =  0.031835937499999994\n",
      "Flow step output with generator type  single_commutator using string  ZZ11111  gave for s =  0.031835937499999994   minimal norm  25.624006057101102\n",
      "Found minimum norm =  25.763316820929237  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZZ  gave for s =  0.020898437500000002   minimal norm  25.763316820929237\n",
      "Found minimum norm =  25.731664132509614  for s =  0.0236328125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZZ1  gave for s =  0.0236328125   minimal norm  25.731664132509614\n",
      "Found minimum norm =  25.807865127352986  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ1Z  gave for s =  0.017773437500000003   minimal norm  25.807865127352986\n",
      "Found minimum norm =  25.84831019015019  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZZ11  gave for s =  0.019335937500000004   minimal norm  25.84831019015019\n",
      "Found minimum norm =  25.779105771561966  for s =  0.0220703125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1ZZ  gave for s =  0.0220703125   minimal norm  25.779105771561966\n",
      "Found minimum norm =  25.60058672629026  for s =  0.0330078125\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ1Z1  gave for s =  0.0330078125   minimal norm  25.60058672629026\n",
      "Found minimum norm =  25.80001100567794  for s =  0.0244140625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ11Z  gave for s =  0.0244140625   minimal norm  25.80001100567794\n",
      "Found minimum norm =  25.797584794736295  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  Z1ZZ111  gave for s =  0.0166015625   minimal norm  25.797584794736295\n",
      "Found minimum norm =  25.823167410144467  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZZ  gave for s =  0.018554687500000003   minimal norm  25.823167410144467\n",
      "Found minimum norm =  25.81315328275439  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1ZZ1  gave for s =  0.019726562500000003   minimal norm  25.81315328275439\n",
      "Found minimum norm =  25.78314978677538  for s =  0.0232421875\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z1Z  gave for s =  0.0232421875   minimal norm  25.78314978677538\n",
      "Found minimum norm =  25.78458567828688  for s =  0.017773437500000003\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1Z11  gave for s =  0.017773437500000003   minimal norm  25.78458567828688\n",
      "Found minimum norm =  25.87816412876084  for s =  0.013085937500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11ZZ  gave for s =  0.013085937500000002   minimal norm  25.87816412876084\n",
      "Found minimum norm =  25.831610145508016  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z11Z1  gave for s =  0.016992187500000002   minimal norm  25.831610145508016\n",
      "Found minimum norm =  25.81348895060722  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1Z111Z  gave for s =  0.016992187500000002   minimal norm  25.81348895060722\n",
      "Found minimum norm =  25.693258684297213  for s =  0.032617187500000006\n",
      "Flow step output with generator type  single_commutator using string  Z1Z1111  gave for s =  0.032617187500000006   minimal norm  25.693258684297213\n",
      "Found minimum norm =  25.80642186204509  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZZ  gave for s =  0.016992187500000002   minimal norm  25.80642186204509\n",
      "Found minimum norm =  25.858963311221615  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZZ1  gave for s =  0.0166015625   minimal norm  25.858963311221615\n",
      "Found minimum norm =  25.820275189588134  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ1Z  gave for s =  0.024804687500000002   minimal norm  25.820275189588134\n",
      "Found minimum norm =  25.75265699978215  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  Z11ZZ11  gave for s =  0.0181640625   minimal norm  25.75265699978215\n",
      "Found minimum norm =  25.80922282257439  for s =  0.0220703125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1ZZ  gave for s =  0.0220703125   minimal norm  25.80922282257439\n",
      "Found minimum norm =  25.881103684622524  for s =  0.011132812500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11Z1Z1  gave for s =  0.011132812500000002   minimal norm  25.881103684622524\n",
      "Found minimum norm =  25.767159971452244  for s =  0.0173828125\n",
      "Flow step output with generator type  single_commutator using string  Z11Z11Z  gave for s =  0.0173828125   minimal norm  25.767159971452244\n",
      "Found minimum norm =  25.836000929285007  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  Z11Z111  gave for s =  0.022851562500000002   minimal norm  25.836000929285007\n",
      "Found minimum norm =  25.879858417899513  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZZ  gave for s =  0.012304687500000001   minimal norm  25.879858417899513\n",
      "Found minimum norm =  25.782053811775224  for s =  0.018945312500000002\n",
      "Flow step output with generator type  single_commutator using string  Z111ZZ1  gave for s =  0.018945312500000002   minimal norm  25.782053811775224\n",
      "Found minimum norm =  25.751458440380134  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  Z111Z1Z  gave for s =  0.019726562500000003   minimal norm  25.751458440380134\n",
      "Found minimum norm =  25.79034964607325  for s =  0.0279296875\n",
      "Flow step output with generator type  single_commutator using string  Z111Z11  gave for s =  0.0279296875   minimal norm  25.79034964607325\n",
      "Found minimum norm =  25.74281428466682  for s =  0.020117187500000005\n",
      "Flow step output with generator type  single_commutator using string  Z1111ZZ  gave for s =  0.020117187500000005   minimal norm  25.74281428466682\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  25.771655653994582  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  Z1111Z1  gave for s =  0.024804687500000002   minimal norm  25.771655653994582\n",
      "Found minimum norm =  25.81915958114934  for s =  0.022460937500000003\n",
      "Flow step output with generator type  single_commutator using string  Z11111Z  gave for s =  0.022460937500000003   minimal norm  25.81915958114934\n",
      "Found minimum norm =  25.32424487306821  for s =  0.0306640625\n",
      "Flow step output with generator type  single_commutator using string  Z111111  gave for s =  0.0306640625   minimal norm  25.32424487306821\n",
      "Found minimum norm =  25.561077600020926  for s =  0.028710937500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZZ  gave for s =  0.028710937500000002   minimal norm  25.561077600020926\n",
      "Found minimum norm =  25.63925099038835  for s =  0.0283203125\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZZ1  gave for s =  0.0283203125   minimal norm  25.63925099038835\n",
      "Found minimum norm =  25.796092976062585  for s =  0.019726562500000003\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ1Z  gave for s =  0.019726562500000003   minimal norm  25.796092976062585\n",
      "Found minimum norm =  25.678828745274494  for s =  0.026757812500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZZ11  gave for s =  0.026757812500000002   minimal norm  25.678828745274494\n",
      "Found minimum norm =  25.80989739485318  for s =  0.020117187500000005\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1ZZ  gave for s =  0.020117187500000005   minimal norm  25.80989739485318\n",
      "Found minimum norm =  25.919910242404388  for s =  0.004882812500000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ1Z1  gave for s =  0.004882812500000001   minimal norm  25.919910242404388\n",
      "Found minimum norm =  25.736619944731903  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ11Z  gave for s =  0.024804687500000002   minimal norm  25.736619944731903\n",
      "Found minimum norm =  25.6283746638399  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZZ111  gave for s =  0.024804687500000002   minimal norm  25.6283746638399\n",
      "Found minimum norm =  25.905846091621072  for s =  0.008398437500000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZZ  gave for s =  0.008398437500000001   minimal norm  25.905846091621072\n",
      "Found minimum norm =  25.908799901552435  for s =  0.0072265625\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1ZZ1  gave for s =  0.0072265625   minimal norm  25.908799901552435\n",
      "Found minimum norm =  25.887150815836804  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z1Z  gave for s =  0.012304687500000001   minimal norm  25.887150815836804\n",
      "Found minimum norm =  25.85667963898248  for s =  0.013085937500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1Z11  gave for s =  0.013085937500000002   minimal norm  25.85667963898248\n",
      "Found minimum norm =  25.833460536872604  for s =  0.016992187500000002\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11ZZ  gave for s =  0.016992187500000002   minimal norm  25.833460536872604\n",
      "Found minimum norm =  25.92527180411145  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ11Z1  gave for s =  0.0001953125   minimal norm  25.92527180411145\n",
      "Found minimum norm =  25.828757229187215  for s =  0.0158203125\n",
      "Flow step output with generator type  single_commutator using string  1ZZ111Z  gave for s =  0.0158203125   minimal norm  25.828757229187215\n",
      "Found minimum norm =  25.620798130885223  for s =  0.0306640625\n",
      "Flow step output with generator type  single_commutator using string  1ZZ1111  gave for s =  0.0306640625   minimal norm  25.620798130885223\n",
      "Found minimum norm =  25.700294063887434  for s =  0.022460937500000003\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZZ  gave for s =  0.022460937500000003   minimal norm  25.700294063887434\n",
      "Found minimum norm =  25.925976554713976  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZZ1  gave for s =  0.0001953125   minimal norm  25.925976554713976\n",
      "Found minimum norm =  25.7221993246501  for s =  0.03886718750000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ1Z  gave for s =  0.03886718750000001   minimal norm  25.7221993246501\n",
      "Found minimum norm =  25.773130910119203  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  1Z1ZZ11  gave for s =  0.0166015625   minimal norm  25.773130910119203\n",
      "Found minimum norm =  25.925183143965246  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1ZZ  gave for s =  0.0001953125   minimal norm  25.925183143965246\n",
      "Found minimum norm =  25.650743710254137  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z1Z1  gave for s =  0.022851562500000002   minimal norm  25.650743710254137\n",
      "Found minimum norm =  25.84906087612354  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z11Z  gave for s =  0.012304687500000001   minimal norm  25.84906087612354\n",
      "Found minimum norm =  25.919781584352734  for s =  0.020117187500000005\n",
      "Flow step output with generator type  single_commutator using string  1Z1Z111  gave for s =  0.020117187500000005   minimal norm  25.919781584352734\n",
      "Found minimum norm =  25.913218852226848  for s =  0.009179687500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZZ  gave for s =  0.009179687500000002   minimal norm  25.913218852226848\n",
      "Found minimum norm =  25.84292673252889  for s =  0.0134765625\n",
      "Flow step output with generator type  single_commutator using string  1Z11ZZ1  gave for s =  0.0134765625   minimal norm  25.84292673252889\n",
      "Found minimum norm =  25.687596111361355  for s =  0.0212890625\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z1Z  gave for s =  0.0212890625   minimal norm  25.687596111361355\n",
      "Found minimum norm =  25.690498859449384  for s =  0.0498046875\n",
      "Flow step output with generator type  single_commutator using string  1Z11Z11  gave for s =  0.0498046875   minimal norm  25.690498859449384\n",
      "Found minimum norm =  25.72746300929977  for s =  0.020898437500000002\n",
      "Flow step output with generator type  single_commutator using string  1Z111ZZ  gave for s =  0.020898437500000002   minimal norm  25.72746300929977\n",
      "Found minimum norm =  25.924501944242888  for s =  0.0021484375\n",
      "Flow step output with generator type  single_commutator using string  1Z111Z1  gave for s =  0.0021484375   minimal norm  25.924501944242888\n",
      "Found minimum norm =  25.810872900564853  for s =  0.032617187500000006\n",
      "Flow step output with generator type  single_commutator using string  1Z1111Z  gave for s =  0.032617187500000006   minimal norm  25.810872900564853\n",
      "Found minimum norm =  25.370135027836483  for s =  0.0279296875\n",
      "Flow step output with generator type  single_commutator using string  1Z11111  gave for s =  0.0279296875   minimal norm  25.370135027836483\n",
      "Found minimum norm =  25.77680246810241  for s =  0.018945312500000002\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZZ  gave for s =  0.018945312500000002   minimal norm  25.77680246810241\n",
      "Found minimum norm =  25.840271198123762  for s =  0.0146484375\n",
      "Flow step output with generator type  single_commutator using string  11ZZZZ1  gave for s =  0.0146484375   minimal norm  25.840271198123762\n",
      "Found minimum norm =  25.88444093380275  for s =  0.0115234375\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ1Z  gave for s =  0.0115234375   minimal norm  25.88444093380275\n",
      "Found minimum norm =  25.791241610179966  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  11ZZZ11  gave for s =  0.0166015625   minimal norm  25.791241610179966\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found minimum norm =  25.86774614242938  for s =  0.012304687500000001\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1ZZ  gave for s =  0.012304687500000001   minimal norm  25.86774614242938\n",
      "Found minimum norm =  25.925177769100767  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11ZZ1Z1  gave for s =  0.0001953125   minimal norm  25.925177769100767\n",
      "Found minimum norm =  25.71399839800094  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZ11Z  gave for s =  0.021679687500000003   minimal norm  25.71399839800094\n",
      "Found minimum norm =  25.783444004220833  for s =  0.021679687500000003\n",
      "Flow step output with generator type  single_commutator using string  11ZZ111  gave for s =  0.021679687500000003   minimal norm  25.783444004220833\n",
      "Found minimum norm =  25.851553089085122  for s =  0.0134765625\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZZ  gave for s =  0.0134765625   minimal norm  25.851553089085122\n",
      "Found minimum norm =  25.924872783059683  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  11Z1ZZ1  gave for s =  0.0001953125   minimal norm  25.924872783059683\n",
      "Found minimum norm =  25.773698108564016  for s =  0.018945312500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z1Z  gave for s =  0.018945312500000002   minimal norm  25.773698108564016\n",
      "Found minimum norm =  25.83262435803524  for s =  0.019335937500000004\n",
      "Flow step output with generator type  single_commutator using string  11Z1Z11  gave for s =  0.019335937500000004   minimal norm  25.83262435803524\n",
      "Found minimum norm =  25.923085450091406  for s =  0.0021484375\n",
      "Flow step output with generator type  single_commutator using string  11Z11ZZ  gave for s =  0.0021484375   minimal norm  25.923085450091406\n",
      "Found minimum norm =  25.861657630279066  for s =  0.013085937500000002\n",
      "Flow step output with generator type  single_commutator using string  11Z11Z1  gave for s =  0.013085937500000002   minimal norm  25.861657630279066\n",
      "Found minimum norm =  25.865022368614994  for s =  0.0138671875\n",
      "Flow step output with generator type  single_commutator using string  11Z111Z  gave for s =  0.0138671875   minimal norm  25.865022368614994\n",
      "Found minimum norm =  25.44893082640924  for s =  0.0291015625\n",
      "Flow step output with generator type  single_commutator using string  11Z1111  gave for s =  0.0291015625   minimal norm  25.44893082640924\n",
      "Found minimum norm =  25.74280951021812  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  111ZZZZ  gave for s =  0.024804687500000002   minimal norm  25.74280951021812\n",
      "Found minimum norm =  25.7255805539483  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  111ZZZ1  gave for s =  0.018554687500000003   minimal norm  25.7255805539483\n",
      "Found minimum norm =  25.714655827665585  for s =  0.018554687500000003\n",
      "Flow step output with generator type  single_commutator using string  111ZZ1Z  gave for s =  0.018554687500000003   minimal norm  25.714655827665585\n",
      "Found minimum norm =  25.723221239308643  for s =  0.0427734375\n",
      "Flow step output with generator type  single_commutator using string  111ZZ11  gave for s =  0.0427734375   minimal norm  25.723221239308643\n",
      "Found minimum norm =  25.761441433771793  for s =  0.0181640625\n",
      "Flow step output with generator type  single_commutator using string  111Z1ZZ  gave for s =  0.0181640625   minimal norm  25.761441433771793\n",
      "Found minimum norm =  25.90068650433818  for s =  0.0166015625\n",
      "Flow step output with generator type  single_commutator using string  111Z1Z1  gave for s =  0.0166015625   minimal norm  25.90068650433818\n",
      "Found minimum norm =  25.846685920901262  for s =  0.024804687500000002\n",
      "Flow step output with generator type  single_commutator using string  111Z11Z  gave for s =  0.024804687500000002   minimal norm  25.846685920901262\n",
      "Found minimum norm =  25.501237439106514  for s =  0.0244140625\n",
      "Flow step output with generator type  single_commutator using string  111Z111  gave for s =  0.0244140625   minimal norm  25.501237439106514\n",
      "Found minimum norm =  25.601357693548646  for s =  0.022851562500000002\n",
      "Flow step output with generator type  single_commutator using string  1111ZZZ  gave for s =  0.022851562500000002   minimal norm  25.601357693548646\n",
      "Found minimum norm =  25.781511070201685  for s =  0.026367187500000003\n",
      "Flow step output with generator type  single_commutator using string  1111ZZ1  gave for s =  0.026367187500000003   minimal norm  25.781511070201685\n",
      "Found minimum norm =  25.70902857682333  for s =  0.040429687500000006\n",
      "Flow step output with generator type  single_commutator using string  1111Z1Z  gave for s =  0.040429687500000006   minimal norm  25.70902857682333\n",
      "Found minimum norm =  25.267041784523297  for s =  0.0294921875\n",
      "Flow step output with generator type  single_commutator using string  1111Z11  gave for s =  0.0294921875   minimal norm  25.267041784523297\n",
      "Found minimum norm =  25.41111432618843  for s =  0.0392578125\n",
      "Flow step output with generator type  single_commutator using string  11111ZZ  gave for s =  0.0392578125   minimal norm  25.41111432618843\n",
      "Found minimum norm =  25.37420122800835  for s =  0.0302734375\n",
      "Flow step output with generator type  single_commutator using string  11111Z1  gave for s =  0.0302734375   minimal norm  25.37420122800835\n",
      "Found minimum norm =  25.342701056029377  for s =  0.0291015625\n",
      "Flow step output with generator type  single_commutator using string  111111Z  gave for s =  0.0291015625   minimal norm  25.342701056029377\n",
      "Found minimum norm =  25.924697839797204  for s =  0.0001953125\n",
      "Flow step output with generator type  single_commutator using string  1111111  gave for s =  0.0001953125   minimal norm  25.924697839797204\n",
      "Found minimum norm =  25.261673515467788  for s =  0.0021484375\n",
      "Found that canonical is better because  25.261673515467788 25.267041784523297\n",
      "Found minimum norm =  25.261673515467788  for s =  0.0021484375\n",
      "Flowing forwards with type  canonical\n",
      "[]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from class_double_bracket_flow import *\n",
    "\n",
    "\n",
    "flow = double_bracket_flow( H_TLFIM )\n",
    "\n",
    "flow.please_be_exhaustively_verbose = False\n",
    "flow.please_be_verbose = True\n",
    "\n",
    "flow.nmb_search_points_minimizing_s_search = 10\n",
    "flow.flow_step_max = 0.2\n",
    "flow.nmb_flow_steps = 10\n",
    "flow.please_use_binary_search =  True\n",
    "flow.please_compute_observables = False\n",
    "\n",
    "#flow.flow_forwards( )\n",
    "flow.flow_via_best_Z_search( please_also_check_canonical_bracket = True )\n",
    "\n",
    "flow.show_flow_forwards_results()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/ipykernel_launcher.py:66: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "/usr/lib/python3/dist-packages/ipykernel_launcher.py:107: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "/usr/lib/python3/dist-packages/ipykernel_launcher.py:111: UserWarning: FixedFormatter should only be used together with FixedLocator\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x504 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "\n",
    "def plot_iteration_results(  ):\n",
    "    flow.run_param_rc(fontsize=18)\n",
    "    flow_results = flow.flow_outputs\n",
    "\n",
    "    f=plt.figure(figsize = ( 8,7 ))\n",
    "    n=1\n",
    "    ax_a = f.add_subplot(1,n,1)\n",
    "    norms = flow_results['minimal_norm_sigma_H_s']\n",
    "    x_axis = [sum(flow_results['minimizing_flow_step'][:k])for k in range( 1, len(flow_results['minimizing_flow_step'])+1)]\n",
    "\n",
    "    plt.plot( x_axis, norms, '-o')   \n",
    "    N = 10\n",
    "    k=0\n",
    "    for xy in zip([x+.01 for x in x_axis[0:N]], \n",
    "                  [n - 0.03 for n in norms[0:N]]):  \n",
    "        if k == 0 or k == 9 or k == 8 or k== 7 or k ==6:\n",
    "            a=1\n",
    "        else:\n",
    "            plt.annotate('k = ' + str(k) + ': ' + flow_results['strs_of_minimizer_Z'][k-1], xy=xy, textcoords='data', fontsize=16)\n",
    "        k=k+1\n",
    "    #10\n",
    "    plt.annotate('k = ' + str(k) + ': ' + flow_results['strs_of_minimizer_Z'][k-1], \n",
    "                 xy=(x_axis[-1]-.062,norms[-1]-1.5), textcoords='data', fontsize=16)\n",
    "#8\n",
    "    plt.annotate('k = ' + str(k-2) + ': ' + flow_results['strs_of_minimizer_Z'][k-3], \n",
    "                 xy=(x_axis[k-2]-.071,norms[k-2]-1.66), textcoords='data', fontsize=17)\n",
    "#9\n",
    "    plt.annotate('k = ' + str(k-1) + ': ' + flow_results['strs_of_minimizer_Z'][k-2], \n",
    "                  xy=(x_axis[k-1]-.03,norms[k-1]+0.5), textcoords='data', fontsize=17)\n",
    "#7\n",
    "    plt.annotate('k = ' + str(k-3) + ': ' + flow_results['strs_of_minimizer_Z'][k-4], \n",
    "                  xy=(x_axis[k-3]-.072,norms[k-3]-.7), textcoords='data', fontsize=17)\n",
    "    plt.annotate('k = ' + str(k-4) + ': ' + flow_results['strs_of_minimizer_Z'][k-5], \n",
    "                  xy=(x_axis[k-4]+.0051,norms[k-4]-.7), textcoords='data', fontsize=17)\n",
    "    plt.annotate('a)', xy = (-.1,1.02),\n",
    "                 xycoords='axes fraction')\n",
    "    x_labels_rounded = [ round(x, 2 ) for x in x_axis ]\n",
    "    x_labels_rounded = [0] + x_labels_rounded[1:9]  + [max(x_labels_rounded)]\n",
    "    x_labels_rounded.pop(2)\n",
    "    x_labels_rounded.pop(2)\n",
    "    x_labels_rounded.pop(4)\n",
    "\n",
    "    x_labels_rounded.pop(-2)\n",
    "#     x_labels_rounded.pop(4)\n",
    "    \n",
    "    plt.xticks(x_labels_rounded)\n",
    "    y_labels_rounded = [ round(y, 1 ) for y in norms ]\n",
    "    y_labels_rounded = y_labels_rounded[0:5] + [min(y_labels_rounded)]\n",
    "    plt.yticks(y_labels_rounded)\n",
    "    plt.grid()\n",
    "    plt.xlabel(r'Total flow duration $\\ell$')\n",
    "    plt.title(r'Norm off-diagonal $\\vert\\vert\\sigma(\\hat H_k)\\vert\\vert$')\n",
    "    a =-.1\n",
    "    b = 1.05\n",
    " \n",
    "    axin1 = ax_a.inset_axes([0.2,.7, 0.31, 0.27])\n",
    "    inset1 = axin1.imshow( H_TLFIM, cmap='RdBu' )\n",
    "    divider1 = make_axes_locatable(axin1)\n",
    "    div_ax = divider1.append_axes(\"right\", size=\"10%\", pad=0.05)\n",
    "    cbar1 = plt.colorbar(inset1, cax = div_ax )\n",
    "    range_plot = np.max( np.abs( H_TLFIM ) )\n",
    "#     cbar1.set_clim( -range_plot, range_plot )\n",
    "    axin1.set_yticks(range(2**L))  \n",
    "    axin1.set_xticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin1.set_yticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin1.set_xticks(range(2**L))\n",
    "    ax_a.annotate(' ',\n",
    "            xy=(x_axis[0]+.01, norms[0]),  # theta, radius\n",
    "            xytext=(0.24, 0.81),    # fraction, fraction\n",
    "            textcoords='figure fraction',\n",
    "            arrowprops=dict(facecolor='gray', shrink=0.01),\n",
    "            horizontalalignment='left',\n",
    "            verticalalignment='bottom')\n",
    "#     axin1.set_xlabel(r'$j$')\n",
    "#     axin1.set_title(r'$k$')\n",
    "#     axin1.grid()\n",
    "    axin2 = ax_a.inset_axes([0.65,.32, 0.31, 0.27])\n",
    "    inset2 = axin2.imshow(flow_results['optimally_flowed_H'][-1], cmap='RdBu')\n",
    "\n",
    "    divider2 = make_axes_locatable(axin2)\n",
    "    div_ax2 = divider2.append_axes(\"right\", size=\"10%\", pad=0.05)\n",
    "    cbar2 = plt.colorbar(inset2, cax = div_ax2 )\n",
    "    ax_a.annotate(' ',\n",
    "        xy=(x_axis[-1], 11.4),  # theta, radius\n",
    "        xytext=(.95, .3),    # fraction, fraction\n",
    "        textcoords='axes fraction',\n",
    "        arrowprops=dict(facecolor='gray', shrink=0.05),\n",
    "        horizontalalignment='left',\n",
    "        verticalalignment='bottom')\n",
    "    \n",
    "    axin3 = ax_a.inset_axes([0.65,.7, 0.31, 0.27])\n",
    "    inset3 = axin3.imshow(flow_results['optimally_flowed_H'][2], cmap='RdBu')\n",
    "\n",
    "    divider3 = make_axes_locatable(axin3)\n",
    "    div_ax3 = divider3.append_axes(\"right\", size=\"10%\", pad=0.05)\n",
    "    cbar2 = plt.colorbar(inset3, cax = div_ax3 )\n",
    "    ax_a.annotate(' ',\n",
    "        xy=(x_axis[2]+.01, norms[2]+.6),  # theta, radius\n",
    "        xytext=(0.65, 0.67),    # fraction, fraction\n",
    "        textcoords='axes fraction',\n",
    "        arrowprops=dict(facecolor='gray', shrink=0.05),\n",
    "        horizontalalignment='left',\n",
    "        verticalalignment='bottom')\n",
    "    axin2.set_yticks(range(2**L))  \n",
    "    axin2.set_xticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin2.set_yticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin2.set_xticks(range(2**L))    \n",
    "    axin3.set_yticks(range(2**L))  \n",
    "    axin3.set_xticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin3.set_yticklabels([1]+['']*(2**L-2)+[2**L])\n",
    "    axin3.set_xticks(range(2**L))\n",
    "    chosen_steps = [1,2]\n",
    "    plt.savefig( 'figs/variational_norm_'+hamiltonian_name+'.pdf')\n",
    "    \n",
    "plot_iteration_results()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Simple plot for debugging"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "H = flow.flow_outputs['final_flowed_H'][-1]\n",
    "\n",
    "plt.figure()\n",
    "plt.subplot(121)\n",
    "plt.imshow(abs(H_TLFIM), cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.subplot(122)\n",
    "plt.imshow(abs(H), cmap='RdBu')\n",
    "plt.colorbar()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This variable stores or strings that have been tested in each step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['ZZZZZZZ', 'ZZZZZZ1', 'ZZZZZ1Z', 'ZZZZZ11', 'ZZZZ1ZZ', 'ZZZZ1Z1', 'ZZZZ11Z', 'ZZZZ111', 'ZZZ1ZZZ', 'ZZZ1ZZ1', 'ZZZ1Z1Z', 'ZZZ1Z11', 'ZZZ11ZZ', 'ZZZ11Z1', 'ZZZ111Z', 'ZZZ1111', 'ZZ1ZZZZ', 'ZZ1ZZZ1', 'ZZ1ZZ1Z', 'ZZ1ZZ11', 'ZZ1Z1ZZ', 'ZZ1Z1Z1', 'ZZ1Z11Z', 'ZZ1Z111', 'ZZ11ZZZ', 'ZZ11ZZ1', 'ZZ11Z1Z', 'ZZ11Z11', 'ZZ111ZZ', 'ZZ111Z1', 'ZZ1111Z', 'ZZ11111', 'Z1ZZZZZ', 'Z1ZZZZ1', 'Z1ZZZ1Z', 'Z1ZZZ11', 'Z1ZZ1ZZ', 'Z1ZZ1Z1', 'Z1ZZ11Z', 'Z1ZZ111', 'Z1Z1ZZZ', 'Z1Z1ZZ1', 'Z1Z1Z1Z', 'Z1Z1Z11', 'Z1Z11ZZ', 'Z1Z11Z1', 'Z1Z111Z', 'Z1Z1111', 'Z11ZZZZ', 'Z11ZZZ1', 'Z11ZZ1Z', 'Z11ZZ11', 'Z11Z1ZZ', 'Z11Z1Z1', 'Z11Z11Z', 'Z11Z111', 'Z111ZZZ', 'Z111ZZ1', 'Z111Z1Z', 'Z111Z11', 'Z1111ZZ', 'Z1111Z1', 'Z11111Z', 'Z111111', '1ZZZZZZ', '1ZZZZZ1', '1ZZZZ1Z', '1ZZZZ11', '1ZZZ1ZZ', '1ZZZ1Z1', '1ZZZ11Z', '1ZZZ111', '1ZZ1ZZZ', '1ZZ1ZZ1', '1ZZ1Z1Z', '1ZZ1Z11', '1ZZ11ZZ', '1ZZ11Z1', '1ZZ111Z', '1ZZ1111', '1Z1ZZZZ', '1Z1ZZZ1', '1Z1ZZ1Z', '1Z1ZZ11', '1Z1Z1ZZ', '1Z1Z1Z1', '1Z1Z11Z', '1Z1Z111', '1Z11ZZZ', '1Z11ZZ1', '1Z11Z1Z', '1Z11Z11', '1Z111ZZ', '1Z111Z1', '1Z1111Z', '1Z11111', '11ZZZZZ', '11ZZZZ1', '11ZZZ1Z', '11ZZZ11', '11ZZ1ZZ', '11ZZ1Z1', '11ZZ11Z', '11ZZ111', '11Z1ZZZ', '11Z1ZZ1', '11Z1Z1Z', '11Z1Z11', '11Z11ZZ', '11Z11Z1', '11Z111Z', '11Z1111', '111ZZZZ', '111ZZZ1', '111ZZ1Z', '111ZZ11', '111Z1ZZ', '111Z1Z1', '111Z11Z', '111Z111', '1111ZZZ', '1111ZZ1', '1111Z1Z', '1111Z11', '11111ZZ', '11111Z1', '111111Z', '1111111']\n"
     ]
    }
   ],
   "source": [
    "print(flow.flow_outputs['all_Z_names'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and these are the strings that gave the optimal generator to decrease the norm of the off-diagonal restriction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Canonical',\n",
       " 'Canonical',\n",
       " 'Canonical',\n",
       " 'Canonical',\n",
       " 'Canonical',\n",
       " '1Z1Z1Z1',\n",
       " 'Canonical',\n",
       " '111Z111',\n",
       " '11Z11Z1',\n",
       " 'Canonical']"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flow.flow_outputs['strs_of_minimizer_Z']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
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}