clean-up two files in quadratic forms

Author: fchapoton

src/sage/quadratic_forms/genera/spinor_genus.py

@@ -1,7 +1,8 @@
 r"""
 Spinor genus computations.
 
-This file defines the group of spinor operators used for the computation of spinor genera.
+This file defines the group of spinor operators used
+for the computation of spinor genera.
 It is meant for internal use only.
 
 EXAMPLES::
@@ -24,8 +25,10 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.groups.abelian_gps.abelian_group_gap import AbelianGroupGap, AbelianGroupElement_gap
-from sage.rings.all import ZZ,QQ
+from sage.groups.abelian_gps.abelian_group_gap import (AbelianGroupGap,
+                                                       AbelianGroupElement_gap)
+from sage.rings.all import ZZ, QQ
+
 
 class SpinorOperator(AbelianGroupElement_gap):
     r"""
@@ -42,7 +45,7 @@ class SpinorOperator(AbelianGroupElement_gap):
         [2:7, 3:-1, 7:-1]
     """
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         r"""
         Return the print representation.
 
@@ -64,8 +67,8 @@ def _repr_(self):
             s += "5"
         elif e[0] == 1 and e[1] == 1:
             s += "7"
-        for k in range(1,len(p)):
-            s += ", %s:%s"%(p[k], (-1)**e[k+1])
+        for k in range(1, len(p)):
+            s += ", %s:%s" % (p[k], (-1)**e[k + 1])
         s += "]"
         return s
 
@@ -74,7 +77,8 @@ class SpinorOperators(AbelianGroupGap):
     r"""
     The group of spinor operators of a genus.
 
-    It is a product of `p`-adic unit square classes used for spinor genus computations.
+    It is a product of `p`-adic unit square classes
+    used for spinor genus computations.
 
     INPUT:
 
@@ -88,7 +92,7 @@ class SpinorOperators(AbelianGroupGap):
     """
     def __init__(self, primes):
         r"""
-        Initialize the group of spinor operators
+        Initialize the group of spinor operators.
 
         TESTS::
 
@@ -99,7 +103,7 @@ def __init__(self, primes):
         if primes[0] != 2:
             raise ValueError("first prime must be 2")
         self._primes = tuple(ZZ(p) for p in primes)
-        orders = len(self._primes)*[2] + [2]
+        orders = len(self._primes) * [2] + [2]
         # 3, 5, unit_p1, unit_p2,...
         orders = tuple(orders)
         AbelianGroupGap.__init__(self, orders)
@@ -123,7 +127,7 @@ def __reduce__(self):
 
     Element = SpinorOperator
 
-    def _repr_(self):
+    def _repr_(self) -> str:
         r"""
         Return the print representation of ``self``.
 
@@ -137,7 +141,7 @@ def _repr_(self):
 
     def to_square_class(self, x, p):
         r"""
-        Return `(1, ..., 1, x, 1, ..., 1)` with the square class of `x` at position `p`.
+        Return `(1,...,1,x,1,...,1)` with the square class of `x` at position `p`.
 
         INPUT:
 
@@ -166,7 +170,7 @@ def to_square_class(self, x, p):
         v, u = x.val_unit(p)
         v = v % 2
         if v != 0:
-            raise ValueError("x(=%s) must be a p-adic unit" % x)
+            raise ValueError(f"x(={x}) must be a p-adic unit")
         y = self.one()
         if p == 2:
             u = u % 8
@@ -189,7 +193,8 @@ def delta(self, r, prime=None):
         INPUT:
 
         - ``r`` -- a non zero integer;
-          if ``prime`` is ``None``, ``r`` must not be divisible by the defining primes of ``self``
+          if ``prime`` is ``None``, ``r`` must not be divisible
+          by the defining primes of ``self``
 
         - ``prime`` --(default:``None``) a prime or `-1`
 
@@ -217,17 +222,20 @@ def delta(self, r, prime=None):
         r = ZZ(r)
         if prime is None:
             if any(p.divides(r) for p in self._primes):
-                raise ValueError("r must not be divisible by %s"%(self._primes,))
-            return self.prod([self.to_square_class(r, p) for p in self._primes])
+                raise ValueError(f"r must not be divisible by {self._primes}")
+            return self.prod([self.to_square_class(r, p)
+                              for p in self._primes])
         prime = ZZ(prime)
         if prime == -1:
             r = r.sign()
-            return self.prod([self.to_square_class(r, p) for p in self._primes])
+            return self.prod([self.to_square_class(r, p)
+                              for p in self._primes])
         if prime not in self._primes:
-            raise ValueError("prime must be among %s"%self._primes)
+            raise ValueError("prime must be among %s" % self._primes)
         v, u = r.val_unit(prime)
         pv = prime**v
-        y = self.prod([self.to_square_class(pv,q) for q in self._primes if q!=prime])
+        y = self.prod([self.to_square_class(pv, q)
+                       for q in self._primes if q != prime])
         if prime in self._primes:
             y *= self.to_square_class(u, p=prime)
         return y

src/sage/quadratic_forms/random_quadraticform.py

@@ -1,13 +1,16 @@
 """
-Creating A Random Quadratic Form
+Random Quadratic Forms
+
+This file contains a set of routines to create a random quadratic form.
 """
 from sage.quadratic_forms.quadratic_form import QuadraticForm
 from sage.quadratic_forms.ternary_qf import TernaryQF
 from sage.rings.ring import is_Ring
 from sage.rings.integer_ring import ZZ
 
+
 ################################################
-## Routines to create a random quadratic form ##
+# Routines to create a random quadratic form ##
 ################################################
 
 def random_quadraticform(R, n, rand_arg_list=[]):
@@ -31,51 +34,47 @@ def random_quadraticform(R, n, rand_arg_list=[]):
 
     EXAMPLES::
 
-        sage: random_quadraticform(ZZ, 3, [1,5])    ## RANDOM
+        sage: random_quadraticform(ZZ, 3, [1,5])    # random
         Quadratic form in 3 variables over Integer Ring with coefficients:
         [ 3 2 3 ]
         [ * 1 4 ]
         [ * * 3 ]
 
-    ::
-
-        sage: random_quadraticform(ZZ, 3, [-5,5])    ## RANDOM
+        sage: random_quadraticform(ZZ, 3, [-5,5])    # random
         Quadratic form in 3 variables over Integer Ring with coefficients:
         [ 3 2 -5 ]
         [ * 2 -2 ]
         [ * * -5 ]
 
-    ::
-
-        sage: random_quadraticform(ZZ, 3, [-50,50])    ## RANDOM
+        sage: random_quadraticform(ZZ, 3, [-50,50])    # random
         Quadratic form in 3 variables over Integer Ring with coefficients:
         [ 1 8 -23 ]
         [ * 0 0 ]
         [ * * 6 ]
+
+    TESTS::
+
+        sage: random_quadraticform(ZZ, 3, [1,2,3,4])
+        Traceback (most recent call last):
+        ...
+        TypeError: the list of randomness arguments can have at most 3 elements
     """
-    ## Sanity Checks: We have a ring and there are at most 3 parameters for randomness!
     if len(rand_arg_list) > 3:
-        raise TypeError("Oops!  The list of randomness arguments can have at most 3 elements.")
+        raise TypeError("the list of randomness arguments can have "
+                        "at most 3 elements")
     if not is_Ring(R):
-        raise TypeError("Oops!  The first argument must be a ring.")
-
-    ## Create a list of upper-triangular entries for the quadratic form
-    L = len(rand_arg_list)
-    nn = int(n*(n+1)/2)
-    if L == 0:
-        rand_list = [R.random_element()  for _ in range(nn)]
-    elif L == 1:
-        rand_list = [R.random_element(rand_arg_list[0])  for _ in range(nn)]
-    elif L == 2:
-        rand_list = [R.random_element(rand_arg_list[0], rand_arg_list[1])  for _ in range(nn)]
-    elif L == 3:
-        rand_list = [R.random_element(rand_arg_list[0], rand_arg_list[1], rand_arg_list[2])  for _ in range(nn)]
-
-    ## Return  the Quadratic Form
+        raise TypeError("the first argument must be a ring")
+    # Create a list of upper-triangular entries for the quadratic form
+    n2 = (n * (n + 1)) // 2
+    if not rand_arg_list:
+        rand_list = [R.random_element() for _ in range(n2)]
+    else:
+        rand_list = [R.random_element(*rand_arg_list) for _ in range(n2)]
     return QuadraticForm(R, n, rand_list)
 
 
-def random_quadraticform_with_conditions(R, n, condition_list=[], rand_arg_list=[]):
+def random_quadraticform_with_conditions(R, n, condition_list=[],
+                                         rand_arg_list=[]):
     """
     Create a random quadratic form in `n` variables defined over the ring `R`
     satisfying a list of boolean (i.e. True/False) conditions.
@@ -90,38 +89,39 @@ def random_quadraticform_with_conditions(R, n, condition_list=[], rand_arg_list=
 
     EXAMPLES::
 
-        sage: Q = random_quadraticform_with_conditions(ZZ, 3, [QuadraticForm.is_positive_definite], [-5, 5])
-        sage: Q    ## RANDOM
+        sage: check = QuadraticForm.is_positive_definite
+        sage: Q = random_quadraticform_with_conditions(ZZ, 3, [check], [-5, 5])
+        sage: Q    # random
         Quadratic form in 3 variables over Integer Ring with coefficients:
         [ 3 -2 -5 ]
         [ * 2 2 ]
         [ * * 3 ]
-
     """
     Q = random_quadraticform(R, n, rand_arg_list)
-    Done_Flag = True
+    done_flag = True
 
-    ## Check that all conditions are satisfied
-    while Done_Flag:
-        Done_Flag = False
+    # Check that all conditions are satisfied
+    while done_flag:
+        done_flag = False
         for c in condition_list:
 
-            ## Check if condition c is satisfied
+            # Check if condition c is satisfied
             try:
                 bool_ans = Q.c()
             except Exception:
                 bool_ans = c(Q)
 
-            ## Create a new quadratic form if a condition fails
+            # Create a new quadratic form if a condition fails
             if not bool_ans:
                 Q = random_quadraticform(R, n, rand_arg_list)
-                Done_Flag = True
+                done_flag = True
                 break
 
-    ## Return the quadratic form
+    # Return the quadratic form
     return Q
 
-def random_ternaryqf(rand_arg_list = []):
+
+def random_ternaryqf(rand_arg_list=[]):
     """
     Create a random ternary quadratic form.
 
@@ -140,37 +140,27 @@ def random_ternaryqf(rand_arg_list = []):
 
     EXAMPLES::
 
-        sage: random_ternaryqf()  ##RANDOM
+        sage: random_ternaryqf()  # random
         Ternary quadratic form with integer coefficients:
         [1 1 4]
         [-1 1 -1]
-        sage: random_ternaryqf([-1, 2])  ##RANDOM
+        sage: random_ternaryqf([-1, 2])  # random
         Ternary quadratic form with integer coefficients:
         [1 0 1]
         [-1 -1 -1]
-        sage: random_ternaryqf([-10, 10, "uniform"])  ##RANDOM
+        sage: random_ternaryqf([-10, 10, "uniform"])  # random
         Ternary quadratic form with integer coefficients:
         [7 -8 2]
         [0 3 -6]
     """
-
-
     R = ZZ
-    n = 6
-    L = len(rand_arg_list)
-    if L == 0:
-        rand_list = [ R.random_element() for _ in range(n)]
-    elif L == 1:
-        rand_list = [ R.random_element(rand_arg_list[0]) for _ in range(6)]
-    elif L == 2:
-        rand_list = [ R.random_element(rand_arg_list[0], rand_arg_list[1]) for _ in range(6)]
-    elif L == 3:
-        rand_list = [ R.random_element(rand_arg_list[0], rand_arg_list[1], rand_arg_list[2]) for _ in range(6)]
-
+    if not rand_arg_list:
+        rand_list = [R.random_element() for _ in range(6)]
+    else:
+        rand_list = [R.random_element(*rand_arg_list) for _ in range(6)]
     return TernaryQF(rand_list)
 
 
-
 def random_ternaryqf_with_conditions(condition_list=[], rand_arg_list=[]):
     """
     Create a random ternary quadratic form satisfying a list of boolean
@@ -186,30 +176,29 @@ def random_ternaryqf_with_conditions(condition_list=[], rand_arg_list=[]):
 
     EXAMPLES::
 
-        sage: Q = random_ternaryqf_with_conditions([TernaryQF.is_positive_definite], [-5, 5])
-        sage: Q    ## RANDOM
+        sage: check = TernaryQF.is_positive_definite
+        sage: Q = random_ternaryqf_with_conditions([check], [-5, 5])
+        sage: Q    # random
         Ternary quadratic form with integer coefficients:
         [3 4 2]
         [2 -2 -1]
     """
-
     Q = random_ternaryqf(rand_arg_list)
-    Done_Flag = True
+    done_flag = True
 
-    ## Check that all conditions are satisfied
-    while Done_Flag:
-        Done_Flag = False
+    # Check that all conditions are satisfied
+    while done_flag:
+        done_flag = False
         for c in condition_list:
-
-            ## Check if condition c is satisfied
+            # Check if condition c is satisfied
             try:
                 bool_ans = Q.c()
             except Exception:
                 bool_ans = c(Q)
 
-            ## Create a new quadratic form if a condition fails
+            # Create a new quadratic form if a condition fails
             if not bool_ans:
                 Q = random_ternaryqf(rand_arg_list)
-                Done_Flag = True
+                done_flag = True
                 break
     return Q