fix typo in ladder_idempotent

src/sage/combinat/symmetric_group_algebra.py

@@ -14,10 +14,13 @@
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.categories.algebras_with_basis import AlgebrasWithBasis
 from sage.combinat.free_module import CombinatorialFreeModule
-from sage.combinat.permutation import Permutation, Permutations, from_permutation_group_element
-from sage.combinat.permutation_cython import (left_action_same_n, right_action_same_n)
+from sage.combinat.permutation import (Permutation, Permutations,
+                                       from_permutation_group_element)
+from sage.combinat.permutation_cython import (left_action_same_n,
+                                              right_action_same_n)
 from sage.combinat.partition import _Partitions, Partitions, Partitions_n
-from sage.combinat.tableau import Tableau, StandardTableaux_size, StandardTableaux_shape, StandardTableaux
+from sage.combinat.tableau import (Tableau, StandardTableaux_size,
+                                   StandardTableaux_shape, StandardTableaux)
 from sage.combinat.skew_tableau import SkewTableau
 from sage.algebras.group_algebra import GroupAlgebra_class
 from sage.algebras.cellular_basis import CellularBasis
@@ -30,7 +33,8 @@
 from sage.misc.lazy_import import lazy_import
 from sage.misc.persist import register_unpickle_override
 
-lazy_import('sage.groups.perm_gps.permgroup_element', 'PermutationGroupElement')
+lazy_import('sage.groups.perm_gps.permgroup_element',
+            'PermutationGroupElement')
 
 
 # TODO: Remove this function and replace it with the class
@@ -74,7 +78,8 @@
         sage: a = sum(basis); a
         [1, 2, 3] + [1, 3, 2] + [2, 1, 3] + [2, 3, 1] + [3, 1, 2] + [3, 2, 1]
         sage: a^2
-        6*[1, 2, 3] + 6*[1, 3, 2] + 6*[2, 1, 3] + 6*[2, 3, 1] + 6*[3, 1, 2] + 6*[3, 2, 1]
+        6*[1, 2, 3] + 6*[1, 3, 2] + 6*[2, 1, 3] + 6*[2, 3, 1]
+        + 6*[3, 1, 2] + 6*[3, 2, 1]
         sage: a^2 == 6*a
         True
         sage: b = QS3([3, 1, 2])
@@ -105,7 +110,8 @@
         sage: SGA = SymmetricGroupAlgebra(QQ, WeylGroup(["A",3], prefix='s')); SGA
         Symmetric group algebra of order 4 over Rational Field
         sage: SGA.group()
-        Weyl Group of type ['A', 3] (as a matrix group acting on the ambient space)
+        Weyl Group of type ['A', 3] (as a matrix group acting
+        on the ambient space)
         sage: SGA.an_element()
         s1*s2*s3 + 3*s2*s3*s1*s2 + 2*s3*s1 + 1
 
@@ -184,7 +190,8 @@
 
         sage: QS3 = SymmetricGroupAlgebra(QQ, 3, category=Monoids())
         sage: QS3.category()
-        Category of finite dimensional cellular monoid algebras over Rational Field
+        Category of finite dimensional cellular monoid algebras
+        over Rational Field
         sage: TestSuite(QS3).run(skip=['_test_construction'])
 
 
@@ -1247,17 +1254,17 @@
                 blocks[c] = [la]
         return blocks
 
-    def ladder_idemponent(self, la):
+    def ladder_idempotent(self, la):
         r"""
-        Return the ladder idempontent of ``self``.
+        Return the ladder idempotent of ``self``.
 
         Let `F` be a field of characteristic `p`. The *ladder idempotent*
         of shape `\lambda` is the idempotent of `F[S_n]` defined as follows.
         Let `T` be the :meth:`ladder tableau
         <sage.combinat.partition.Partition.ladder_tableau>` of shape `\lambda`.
         Let `[T]` be the set of standard tableaux whose residue sequence
         is the same as for `T`. Let `\alpha` be the sizes of the ladders
-        of `\lambda`. Then the ladder idempontent is constructed as
+        of `\lambda`. Then the ladder idempotent is constructed as
 
         .. MATH::
 
@@ -1273,7 +1280,7 @@
 
             sage: SGA = SymmetricGroupAlgebra(GF(3), 4)
             sage: for la in Partitions(SGA.n):
-            ....:     idem = SGA.ladder_idemponent(la)
+            ....:     idem = SGA.ladder_idempotent(la)
             ....:     print(la)
             ....:     print(idem)
             ....:     assert idem^2 == idem
@@ -1301,8 +1308,8 @@
         and also projective modules)::
 
             sage: SGA = SymmetricGroupAlgebra(QQ, 5)
             sage: for la in Partitions(SGA.n):
-            ....:     idem = SGA.ladder_idemponent(la)
+            ....:     idem = SGA.ladder_idempotent(la)
             ....:     assert idem^2 == idem
             ....:     print(la, SGA.principal_ideal(idem).dimension())
             [5] 1
@@ -1324,15 +1331,14 @@
         n = self.n
         if not p:
             p = n + 1
-        la = _Partitions(la)
-        if sum(la) != n:
-            raise ValueError(f"{la} is not a partition of {n}")
+        la = Partitions_n(n)(la)
         Tlad, alpha = la.ladder_tableau(p, ladder_lengths=True)
         if not all(val < p for val in alpha):
             raise ValueError(f"{la} is not {p}-ladder restricted")
         Tclass = Tlad.residue_sequence(p).standard_tableaux()
         Elad = sum(epsilon_ik(T, T) for T in Tclass)
-        Elad = self.element_class(self, {sigma: R(c) for sigma, c in Elad._monomial_coefficients.items()})
+        Elad = self.element_class(self, {sigma: R(c)
+                                         for sigma, c in Elad._monomial_coefficients.items()})
         from sage.groups.perm_gps.permgroup_named import SymmetricGroup
         YG = SymmetricGroup(n).young_subgroup(alpha)
         coeff = ~R.prod(factorial(val) for val in alpha)
@@ -2066,7 +2072,7 @@
             return self._dft_seminormal(mult=mult)
         if form == "modular":
             return self._dft_modular()
-        raise ValueError("invalid form (= %s)" % form)
+        raise ValueError(f"invalid form (= {form})")
 
     def _dft_seminormal(self, mult='l2r'):
         """
@@ -2382,7 +2388,7 @@
             [1, 1, 1] [1, 2, 3] - [1, 3, 2] - [2, 1, 3] + [2, 3, 1] + [3, 1, 2] - [3, 2, 1]
         """
         T = []
-        total = 1 # make it 1-based
+        total = 1  # make it 1-based
         for r in la:
             T.append(list(range(total, total+r)))
             total += r
@@ -3454,7 +3460,7 @@
             T[1, 2, 3]
         """
         if i not in range(1, self.n):
-            raise ValueError("i (= %(i)d) must be between 1 and n (= %(n)d)" % {'i': i, 'n': self.n})
+            raise ValueError(f"i (= {i}) must be between 1 and n (={self.n})")
 
         t_i = Permutation((i, i + 1))
         perm_i = t_i.right_action_product(perm)
@@ -3496,7 +3502,8 @@
             sage: H3 = HeckeAlgebraSymmetricGroupT(QQ, 3, 1)
             sage: a = H3([2,1,3])+2*H3([1,2,3])-H3([3,2,1])
             sage: a^2 #indirect doctest
-            6*T[1, 2, 3] + 4*T[2, 1, 3] - T[2, 3, 1] - T[3, 1, 2] - 4*T[3, 2, 1]
+            6*T[1, 2, 3] + 4*T[2, 1, 3] - T[2, 3, 1]
+            - T[3, 1, 2] - 4*T[3, 2, 1]
 
         ::
 
@@ -3527,7 +3534,7 @@
             ValueError: i (= 0) must be between 1 and n-1 (= 2)
         """
         if i not in range(1, self.n):
-            raise ValueError("i (= %(i)d) must be between 1 and n-1 (= %(nm)d)" % {'i': i, 'nm': self.n - 1})
+            raise ValueError(f"i (= {i}) must be between 1 and n-1 (= {self.n - 1})")
 
         P = self.basis().keys()
         return self.monomial(P(list(range(1, i)) + [i + 1, i] +
@@ -3591,7 +3598,7 @@
         if k not in range(2, self.n + 1):
             if k == 1:
                 return self.one()
-            raise ValueError("k (= %(k)d) must be between 1 and n (= %(n)d)" % {'k': k, 'n': self.n})
+            raise ValueError(f"k (= {k}) must be between 1 and n (= {self.n})")
 
         q = self.q()
         P = self._indices