204 lines
12 KiB
Diff
204 lines
12 KiB
Diff
diff --git a/src/sage/algebras/fusion_rings/fusion_double.py b/src/sage/algebras/fusion_rings/fusion_double.py
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index 7ce086f70d0..954513572c3 100644
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--- a/src/sage/algebras/fusion_rings/fusion_double.py
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+++ b/src/sage/algebras/fusion_rings/fusion_double.py
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@@ -133,7 +133,7 @@ class FusionDouble(CombinatorialFreeModule):
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sage: G = SmallPermutationGroup(16,9)
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sage: F = FusionDouble(G, prefix="b",inject_variables=True)
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sage: b13^2 # long time (4s)
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- b0 + b2 + b4 + b15 + b16 + b17 + b18 + b24 + b26 + b27
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+ b0 + b3 + b4
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"""
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@staticmethod
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diff --git a/src/sage/categories/simplicial_sets.py b/src/sage/categories/simplicial_sets.py
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index e714a4571c4..a2b87a729d1 100644
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--- a/src/sage/categories/simplicial_sets.py
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+++ b/src/sage/categories/simplicial_sets.py
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@@ -593,9 +593,9 @@ def _canonical_twisting_operator(self):
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sage: X = simplicial_sets.Torus()
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sage: d = X._canonical_twisting_operator()
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sage: d
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- {(s_0 v_0, sigma_1): f3, (sigma_1, s_0 v_0): f2*f3^-1, (sigma_1, sigma_1): f2}
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+ {(s_0 v_0, sigma_1): f2, (sigma_1, s_0 v_0): f1*f2^-1, (sigma_1, sigma_1): f1}
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sage: list(d.values())[0].parent()
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- Multivariate Laurent Polynomial Ring in f2, f3 over Integer Ring
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+ Multivariate Laurent Polynomial Ring in f1, f2 over Integer Ring
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sage: Y = simplicial_sets.RealProjectiveSpace(2)
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sage: d2 = Y._canonical_twisting_operator()
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sage: d2
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@@ -677,10 +677,10 @@ def twisted_chain_complex(self, twisting_operator=None, dimensions=None, augment
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sage: X = simplicial_sets.Torus()
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sage: C = X.twisted_chain_complex()
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sage: C.differential(1)
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- [ f3 - 1 f2*f3^-1 - 1 f2 - 1]
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+ [ f2 - 1 f1*f2^-1 - 1 f1 - 1]
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sage: C.differential(2)
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- [ 1 f2*f3^-1]
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- [ f3 1]
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+ [ 1 f1*f2^-1]
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+ [ f2 1]
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[ -1 -1]
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sage: C.differential(3)
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[]
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@@ -848,29 +848,29 @@ def twisted_homology(self, n, reduced=False):
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sage: # needs sage.graphs
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sage: Y = simplicial_sets.Torus()
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sage: Y.twisted_homology(1)
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- Quotient module by Submodule of Ambient free module of rank 5 over the integral domain Multivariate Polynomial Ring in f2, f2inv, f3, f3inv over Integer Ring
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+ Quotient module by Submodule of Ambient free module of rank 5 over the integral domain Multivariate Polynomial Ring in f1, f1inv, f2, f2inv over Integer Ring
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Generated by the rows of the matrix:
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[ 1 0 0 0 0]
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[ 0 1 0 0 0]
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[ 0 0 1 0 0]
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[ 0 0 0 1 0]
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[ 0 0 0 0 1]
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+ [f1*f1inv - 1 0 0 0 0]
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+ [ 0 f1*f1inv - 1 0 0 0]
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+ [ 0 0 f1*f1inv - 1 0 0]
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+ [ 0 0 0 f1*f1inv - 1 0]
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+ [ 0 0 0 0 f1*f1inv - 1]
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[f2*f2inv - 1 0 0 0 0]
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[ 0 f2*f2inv - 1 0 0 0]
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[ 0 0 f2*f2inv - 1 0 0]
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[ 0 0 0 f2*f2inv - 1 0]
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[ 0 0 0 0 f2*f2inv - 1]
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- [f3*f3inv - 1 0 0 0 0]
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- [ 0 f3*f3inv - 1 0 0 0]
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- [ 0 0 f3*f3inv - 1 0 0]
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- [ 0 0 0 f3*f3inv - 1 0]
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- [ 0 0 0 0 f3*f3inv - 1]
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sage: Y.twisted_homology(2)
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- Quotient module by Submodule of Ambient free module of rank 0 over the integral domain Multivariate Polynomial Ring in f2, f2inv, f3, f3inv over Integer Ring
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+ Quotient module by Submodule of Ambient free module of rank 0 over the integral domain Multivariate Polynomial Ring in f1, f1inv, f2, f2inv over Integer Ring
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Generated by the rows of the matrix:
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[]
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sage: Y.twisted_homology(1, reduced=True)
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- Quotient module by Submodule of Ambient free module of rank 5 over the integral domain Multivariate Polynomial Ring in f2, f2inv, f3, f3inv over Integer Ring
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+ Quotient module by Submodule of Ambient free module of rank 5 over the integral domain Multivariate Polynomial Ring in f1, f1inv, f2, f2inv over Integer Ring
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Generated by the rows of the matrix:
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[1 0 0 0 0]
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[0 1 0 0 0]
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diff --git a/src/sage/combinat/matrices/latin.py b/src/sage/combinat/matrices/latin.py
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index 936edcc6ea4..c06a53d9afd 100644
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--- a/src/sage/combinat/matrices/latin.py
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+++ b/src/sage/combinat/matrices/latin.py
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@@ -2453,7 +2453,7 @@ def p3_group_bitrade_generators(p):
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EXAMPLES::
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sage: from sage.combinat.matrices.latin import *
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- sage: p3_group_bitrade_generators(3)
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+ sage: p3_group_bitrade_generators(3) # random output
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((2,6,7)(3,8,9),
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(1,2,3)(4,7,8)(5,6,9),
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(1,9,2)(3,7,4)(5,8,6),
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diff --git a/src/sage/groups/cubic_braid.py b/src/sage/groups/cubic_braid.py
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index 257b400f1c7..36423c756aa 100644
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--- a/src/sage/groups/cubic_braid.py
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+++ b/src/sage/groups/cubic_braid.py
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@@ -282,7 +282,7 @@ def _richcmp_(self, other, op):
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EXAMPLES::
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sage: CBG3 = CubicBraidGroup(3)
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- sage: sorted(CBG3) # indirect doctest
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+ sage: sorted(CBG3) # indirect doctest, random output
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[(c0*c1^-1)^2, c0*c1^-1*c0, c0^-1*c1*c0^-1, c0^-1*c1^-1*c0,
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c1*c0^-1*c1, c0^-1*c1^-1*c0^-1, c0^-1*c1^-1, c1^-1*c0*c1^-1,
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c0*c1^-1*c0^-1, c0^-1*c1, c0^-1*c1*c0, c0*c1^-1, c1*c0^-1,
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diff --git a/src/sage/groups/finitely_presented.py b/src/sage/groups/finitely_presented.py
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index 4bb52ee4efb..85f572fac6c 100644
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--- a/src/sage/groups/finitely_presented.py
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+++ b/src/sage/groups/finitely_presented.py
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@@ -1344,8 +1344,8 @@ def abelianization_map(self):
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sage: H = G.quotient([g1^2, g2*g1*g2^(-1)*g1^(-1), g1*g3^(-2), g0^4])
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sage: H.abelianization_map()
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Group morphism:
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- From: Finitely presented group < g0, g1, g2, g3 | g1^2, g2*g1*g2^-1*g1^-1, g1*g3^-2, g0^4 >
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- To: Finitely presented group < f2, f3, f4 | f2^-1*f3^-1*f2*f3, f2^-1*f4^-1*f2*f4, f3^-1*f4^-1*f3*f4, f2^4, f3^4 >
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+ From: Finitely presented group < g0, g1, g2, g3 | g1^2, g2*g1*g2^-1*g1^-1, g1*g3^-2, g0^4 >
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+ To: Finitely presented group < f1, f2, f3 | f1^4, f2^-1*f1^-1*f2*f1, f2^4, f3^-1*f1^-1*f3*f1, f3^-1*f2^-1*f3*f2 >
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sage: g = FreeGroup(0) / []
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sage: g.abelianization_map()
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Group endomorphism of Finitely presented group < | >
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@@ -1394,10 +1394,10 @@ def abelianization_to_algebra(self, ring=QQ):
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Defining g0, g1, g2, g3
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sage: H = G.quotient([g1^2, g2*g1*g2^(-1)*g1^(-1), g1*g3^(-2), g0^4])
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sage: H.abelianization_to_algebra()
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- (Finitely presented group < f2, f3, f4 | f2^-1*f3^-1*f2*f3, f2^-1*f4^-1*f2*f4,
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- f3^-1*f4^-1*f3*f4, f2^4, f3^4 >,
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- Multivariate Laurent Polynomial Ring in f2, f3, f4 over Rational Field,
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- [f2^4 - 1, f3^4 - 1], [f2^-1*f3^-2, f3^-2, f4, f3])
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+ (Finitely presented group < f1, f2, f3 | f1^4, f2^-1*f1^-1*f2*f1, f2^4, f3^-1*f1^-1*f3*f1, f3^-1*f2^-1*f3*f2 >,
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+ Multivariate Laurent Polynomial Ring in f1, f2, f3 over Rational Field,
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+ [f1^4 - 1, f2^4 - 1],
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+ [f1^3*f2^2, f2^2, f3, f2])
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sage: g=FreeGroup(0) / []
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sage: g.abelianization_to_algebra()
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(Finitely presented group < | >, Rational Field, [], [])
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@@ -1673,7 +1673,7 @@ def abelian_alexander_matrix(self, ring=QQ, simplified=True):
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[]
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sage: G = FreeGroup(3)/[(2, 1, 1), (1, 2, 2, 3, 3)]
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sage: A, ideal = G.abelian_alexander_matrix(simplified=True); A
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- [-f3^2 - f3^4 - f3^6 f3^3 + f3^6]
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+ [-f1^2 - f1^4 - f1^6 f1^3 + f1^6]
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sage: g = FreeGroup(1) / []
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sage: g.abelian_alexander_matrix()
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([], [])
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@@ -1773,11 +1773,11 @@ def characteristic_varieties(self, ring=QQ, matrix_ideal=None, groebner=False):
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3: Ideal (1) of Multivariate Laurent Polynomial Ring in f1, f2 over Integer Ring}
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sage: G = FreeGroup(2)/[(1,2,1,-2,-1,-2)]
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sage: G.characteristic_varieties()
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- {0: Ideal (0) of Univariate Laurent Polynomial Ring in f2 over Rational Field,
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- 1: Ideal (-1 + 2*f2 - 2*f2^2 + f2^3) of Univariate Laurent Polynomial Ring in f2 over Rational Field,
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- 2: Ideal (1) of Univariate Laurent Polynomial Ring in f2 over Rational Field}
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+ {0: Ideal (0) of Univariate Laurent Polynomial Ring in f1 over Rational Field,
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+ 1: Ideal (-1 + 2*f1 - 2*f1^2 + f1^3) of Univariate Laurent Polynomial Ring in f1 over Rational Field,
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+ 2: Ideal (1) of Univariate Laurent Polynomial Ring in f1 over Rational Field}
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sage: G.characteristic_varieties(groebner=True)
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- {0: [0], 1: [-1 + f2, 1 - f2 + f2^2], 2: []}
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+ {0: [0], 1: [-1 + f1, 1 - f1 + f1^2], 2: []}
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sage: G = FreeGroup(2)/[3 * (1, ), 2 * (2, )]
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sage: G.characteristic_varieties(groebner=True)
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{0: [-1 + F1, 1 + F1, 1 - F1 + F1^2, 1 + F1 + F1^2], 1: [1 - F1 + F1^2], 2: []}
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diff --git a/src/sage/groups/perm_gps/permgroup_named.py b/src/sage/groups/perm_gps/permgroup_named.py
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index c1f2683907b..d219e104a2c 100644
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--- a/src/sage/groups/perm_gps/permgroup_named.py
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+++ b/src/sage/groups/perm_gps/permgroup_named.py
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@@ -3468,16 +3468,14 @@ class SmallPermutationGroup(PermutationGroup_generic):
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sage: G = SmallPermutationGroup(12,4); G
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Group of order 12 and GAP Id 4 as a permutation group
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sage: G.gens()
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- ((1,2)(3,5)(4,10)(6,8)(7,12)(9,11),
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- (1,3)(2,5)(4,7)(6,9)(8,11)(10,12),
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- (1,4,8)(2,6,10)(3,7,11)(5,9,12))
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+ ((4,5), (1,2), (3,4,5))
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sage: G.character_table() # needs sage.rings.number_field
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[ 1 1 1 1 1 1]
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- [ 1 -1 -1 1 1 -1]
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+ [ 1 -1 1 -1 1 -1]
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[ 1 -1 1 1 -1 1]
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- [ 1 1 -1 1 -1 -1]
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- [ 2 0 -2 -1 0 1]
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- [ 2 0 2 -1 0 -1]
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+ [ 1 1 1 -1 -1 -1]
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+ [ 2 0 -1 -2 0 1]
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+ [ 2 0 -1 2 0 -1]
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sage: def numgps(n): return ZZ(libgap.NumberSmallGroups(n))
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sage: all(SmallPermutationGroup(n,k).id() == [n,k]
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....: for n in [1..64] for k in [1..numgps(n)])
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@@ -3486,11 +3484,11 @@ class SmallPermutationGroup(PermutationGroup_generic):
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sage: H.is_abelian()
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False
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sage: [H.centralizer(g) for g in H.conjugacy_classes_representatives()]
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- [Subgroup generated by [(1,2)(3,6)(4,5), (1,3,5)(2,4,6)] of
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+ [Subgroup generated by [(1,3), (2,3)] of
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(Group of order 6 and GAP Id 1 as a permutation group),
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- Subgroup generated by [(1,2)(3,6)(4,5)] of
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+ Subgroup generated by [(2,3)] of
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(Group of order 6 and GAP Id 1 as a permutation group),
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- Subgroup generated by [(1,3,5)(2,4,6), (1,5,3)(2,6,4)] of
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+ Subgroup generated by [(1,2,3)] of
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(Group of order 6 and GAP Id 1 as a permutation group)]
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"""
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