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Jun 22, 2024
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sage.categories: Update # needs, modularization fixes (imports) #38170

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0d1b717
sage.categories: Update # needs, modularization fixes (imports)
mkoeppe Jun 8, 2024
d0e6748
src/sage/categories/finite_dimensional_modules_with_basis.py: Add # n…
mkoeppe Jun 8, 2024
bbc1a6f
src/sage/categories/finite_groups.py: Update # needs
mkoeppe Jun 8, 2024
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12 changes: 6 additions & 6 deletions src/sage/categories/chain_complexes.py
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Expand Up @@ -80,8 +80,8 @@ def homology(self, n=None):
::

sage: # needs sage.combinat sage.modules
sage: A.<x,y,z> = GradedCommutativeAlgebra(QQ, degrees=(2, 2, 3))
sage: C = A.cdg_algebra({z: x*y})
sage: A.<x,y,z> = GradedCommutativeAlgebra(QQ, degrees=(2, 2, 3)) # needs sage.libs.singular
sage: C = A.cdg_algebra({z: x*y}) # needs sage.libs.singular
sage: C.homology(0)
Free module generated by {[1]} over Rational Field
sage: C.homology(1)
Expand Down Expand Up @@ -109,8 +109,8 @@ def differential(self, *args, **kwargs):

::

sage: A.<x,y,z> = GradedCommutativeAlgebra(QQ, degrees=(2, 2, 3)) # needs sage.combinat sage.modules
sage: C = A.cdg_algebra({z: x*y}) # needs sage.combinat sage.modules
sage: A.<x,y,z> = GradedCommutativeAlgebra(QQ, degrees=(2, 2, 3)) # needs sage.combinat sage.libs.singular sage.modules
sage: C = A.cdg_algebra({z: x*y}) # needs sage.combinat sage.libs.singular sage.modules
sage: C.differential() # needs sage.combinat sage.modules
Differential of Commutative Differential Graded Algebra with
generators ('x', 'y', 'z') in degrees (2, 2, 3) over Rational Field
Expand Down Expand Up @@ -182,8 +182,8 @@ class HomologyFunctor(Functor):

::

sage: A.<x,y,z> = GradedCommutativeAlgebra(QQ, degrees=(2, 2, 3)) # needs sage.combinat sage.modules
sage: C = A.cdg_algebra({z: x*y}) # needs sage.combinat sage.modules
sage: A.<x,y,z> = GradedCommutativeAlgebra(QQ, degrees=(2, 2, 3)) # needs sage.combinat sage.libs.singular sage.modules
sage: C = A.cdg_algebra({z: x*y}) # needs sage.combinat sage.libs.singular sage.modules
sage: H = HomologyFunctor(ChainComplexes(QQ), 2)
sage: H(C) # needs sage.combinat sage.modules
Free module generated by {[x], [y]} over Rational Field
Expand Down
6 changes: 3 additions & 3 deletions src/sage/categories/examples/lie_algebras.py
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Expand Up @@ -70,7 +70,7 @@ def __classcall_private__(cls, gens):

EXAMPLES::

sage: # needs sage.combinat
sage: # needs sage.combinat sage.groups
sage: S3 = SymmetricGroupAlgebra(QQ, 3)
sage: L1 = LieAlgebras(QQ).example()
sage: gens = list(S3.algebra_generators())
Expand All @@ -84,8 +84,8 @@ def __init__(self, gens):
"""
EXAMPLES::

sage: L = LieAlgebras(QQ).example() # needs sage.combinat
sage: TestSuite(L).run() # needs sage.combinat
sage: L = LieAlgebras(QQ).example() # needs sage.combinat sage.groups
sage: TestSuite(L).run() # needs sage.combinat sage.groups
"""
if not gens:
raise ValueError("need at least one generator")
Expand Down
34 changes: 20 additions & 14 deletions src/sage/categories/fields.py
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Expand Up @@ -98,25 +98,31 @@ def __contains__(self, x):
in other doctests, we introduced a strong reference to all previously created
uncollected objects in :issue:`19244`. ::

sage: # needs sage.libs.pari
sage: import gc
sage: _ = gc.collect()
sage: permstore = [X for X in gc.get_objects() if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]
sage: permstore = [X for X in gc.get_objects()
....: if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]
sage: n = len(permstore)
sage: for i in prime_range(100): # needs sage.libs.pari
sage: for i in prime_range(100):
....: R = ZZ.quotient(i)
....: t = R in Fields()

First, we show that there are now more quotient rings in cache than before::

sage: len([X for X in gc.get_objects() if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]) > n
sage: # needs sage.libs.pari
sage: len([X for X in gc.get_objects()
....: if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]) > n
True

When we delete the last quotient ring created in the loop and then do a garbage
collection, all newly created rings vanish::

sage: # needs sage.libs.pari
sage: del R
sage: _ = gc.collect()
sage: len([X for X in gc.get_objects() if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]) - n
sage: len([X for X in gc.get_objects()
....: if isinstance(X, sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic)]) - n
0

"""
Expand Down Expand Up @@ -623,15 +629,15 @@ def gcd(self,other):
For field of characteristic zero, the gcd of integers is considered
as if they were elements of the integer ring::

sage: gcd(15.0,12.0)
sage: gcd(15.0,12.0) # needs sage.rings.real_mpfr
3.00000000000000

But for other floating point numbers, the gcd is just `0.0` or `1.0`::

sage: gcd(3.2, 2.18)
sage: gcd(3.2, 2.18) # needs sage.rings.real_mpfr
1.00000000000000

sage: gcd(0.0, 0.0)
sage: gcd(0.0, 0.0) # needs sage.rings.real_mpfr
0.000000000000000

AUTHOR:
Expand Down Expand Up @@ -677,15 +683,15 @@ def lcm(self, other):
For field of characteristic zero, the lcm of integers is considered
as if they were elements of the integer ring::

sage: lcm(15.0,12.0)
sage: lcm(15.0, 12.0) # needs sage.rings.real_mpfr
60.0000000000000

But for others floating point numbers, it is just `0.0` or `1.0`::

sage: lcm(3.2, 2.18)
sage: lcm(3.2, 2.18) # needs sage.rings.real_mpfr
1.00000000000000

sage: lcm(0.0, 0.0)
sage: lcm(0.0, 0.0) # needs sage.rings.real_mpfr
0.000000000000000

AUTHOR:
Expand Down Expand Up @@ -747,13 +753,13 @@ def xgcd(self, other):
the result is a floating point version of the standard gcd on
`\ZZ`::

sage: xgcd(12.0, 8.0)
sage: xgcd(12.0, 8.0) # needs sage.rings.real_mpfr
(4.00000000000000, 1.00000000000000, -1.00000000000000)

sage: xgcd(3.1, 2.98714)
sage: xgcd(3.1, 2.98714) # needs sage.rings.real_mpfr
(1.00000000000000, 0.322580645161290, 0.000000000000000)

sage: xgcd(0.0, 1.1)
sage: xgcd(0.0, 1.1) # needs sage.rings.real_mpfr
(1.00000000000000, 0.000000000000000, 0.909090909090909)
"""
P = self.parent()
Expand Down Expand Up @@ -786,7 +792,7 @@ def factor(self):
sage: x = GF(7)(5)
sage: x.factor()
5
sage: RR(0).factor()
sage: RR(0).factor() # needs sage.rings.real_mpfr
Traceback (most recent call last):
...
ArithmeticError: factorization of 0.000000000000000 is not defined
Expand Down
14 changes: 9 additions & 5 deletions src/sage/categories/finite_dimensional_modules_with_basis.py
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Expand Up @@ -685,6 +685,7 @@ def _repr_matrix(self):

EXAMPLES::

sage: # needs sage.modules
sage: M = matrix(ZZ, [[1, 0, 0], [0, 1, 0]],
....: column_keys=['a', 'b', 'c'],
....: row_keys=['v', 'w']); M
Expand Down Expand Up @@ -713,6 +714,7 @@ def _ascii_art_matrix(self):

EXAMPLES::

sage: # needs sage.modules
sage: M = matrix(ZZ, [[1, 0, 0], [0, 1, 0]],
....: column_keys=['a', 'b', 'c'],
....: row_keys=['v', 'w']); M
Expand Down Expand Up @@ -744,6 +746,7 @@ def _unicode_art_matrix(self):

EXAMPLES::

sage: # needs sage.modules
sage: M = matrix(ZZ, [[1, 0, 0], [0, 1, 0]],
....: column_keys=['a', 'b', 'c'],
....: row_keys=['v', 'w']); M
Expand Down Expand Up @@ -909,6 +912,7 @@ def characteristic_polynomial(self):

EXAMPLES::

sage: # needs sage.modules
sage: V = ZZ^2; phi = V.hom([V.0 + V.1, 2*V.1])
sage: phi.characteristic_polynomial()
x^2 - 3*x + 2
Expand All @@ -918,7 +922,6 @@ def characteristic_polynomial(self):
x^2 - 3*x + 2
sage: phi.charpoly('T')
T^2 - 3*T + 2

sage: W = CombinatorialFreeModule(ZZ, ['x', 'y'])
sage: M = matrix(ZZ, [[1, 0], [1, 2]])
sage: psi = W.module_morphism(matrix=M, codomain=W)
Expand All @@ -938,12 +941,12 @@ def determinant(self):

EXAMPLES::

sage: # needs sage.modules
sage: V = ZZ^2; phi = V.hom([V.0 + V.1, 2*V.1])
sage: phi.determinant()
2
sage: phi.det()
2

sage: W = CombinatorialFreeModule(ZZ, ['x', 'y'])
sage: M = matrix(ZZ, [[1, 0], [1, 2]])
sage: psi = W.module_morphism(matrix=M, codomain=W)
Expand All @@ -965,12 +968,12 @@ def fcp(self):

EXAMPLES::

sage: # needs sage.modules
sage: V = ZZ^2; phi = V.hom([V.0 + V.1, 2*V.1])
sage: phi.fcp() # needs sage.libs.pari
(x - 2) * (x - 1)
sage: phi.fcp('T') # needs sage.libs.pari
(T - 2) * (T - 1)

sage: W = CombinatorialFreeModule(ZZ, ['x', 'y'])
sage: M = matrix(ZZ, [[1, 0], [1, 2]])
sage: psi = W.module_morphism(matrix=M, codomain=W)
Expand All @@ -994,6 +997,7 @@ def minimal_polynomial(self):

Compute the minimal polynomial, and check it. ::

sage: # needs sage.modules
sage: V = GF(7)^3
sage: H = V.Hom(V)([[0,1,2], [-1,0,3], [2,4,1]]); H
Vector space morphism represented by the matrix:
Expand All @@ -1014,7 +1018,7 @@ def minimal_polynomial(self):
Domain: Vector space of dimension 3 over Finite Field of size 7
Codomain: Vector space of dimension 3 over Finite Field of size 7

sage: # needs sage.rings.finite_rings
sage: # needs sage.modules sage.rings.finite_rings
sage: k = GF(9, 'c')
sage: V = CombinatorialFreeModule(k, ['x', 'y', 'z', 'w'])
sage: A = matrix(k, 4, [1,1,0,0, 0,1,0,0, 0,0,5,0, 0,0,0,5])
Expand All @@ -1037,10 +1041,10 @@ def trace(self):

EXAMPLES::

sage: # needs sage.modules
sage: V = ZZ^2; phi = V.hom([V.0 + V.1, 2*V.1])
sage: phi.trace()
3

sage: W = CombinatorialFreeModule(ZZ, ['x', 'y'])
sage: M = matrix(ZZ, [[1, 0], [1, 2]])
sage: psi = W.module_morphism(matrix=M, codomain=W)
Expand Down
10 changes: 5 additions & 5 deletions src/sage/categories/finite_groups.py
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Expand Up @@ -94,11 +94,11 @@ def cardinality(self):
We need to use a finite group which uses this default
implementation of cardinality::

sage: G = groups.misc.SemimonomialTransformation(GF(5), 3); G
sage: G = groups.misc.SemimonomialTransformation(GF(5), 3); G # needs sage.rings.number_field
Semimonomial transformation group over Finite Field of size 5 of degree 3
sage: G.cardinality.__module__
sage: G.cardinality.__module__ # needs sage.rings.number_field
'sage.categories.finite_groups'
sage: G.cardinality()
sage: G.cardinality() # needs sage.rings.number_field
384
"""
if hasattr(self, 'order'):
Expand Down Expand Up @@ -172,7 +172,7 @@ def conjugacy_classes_representatives(self):
EXAMPLES::

sage: G = SymmetricGroup(3)
sage: G.conjugacy_classes_representatives()
sage: G.conjugacy_classes_representatives() # needs sage.combinat
[(), (1,2), (1,2,3)]
"""
return [C.representative() for C in self.conjugacy_classes()]
Expand Down Expand Up @@ -231,7 +231,7 @@ def __init_extra__(self):
sage: A in Algebras.Semisimple
False

sage: G = groups.misc.AdditiveCyclic(4)
sage: G = groups.misc.AdditiveCyclic(4) # needs sage.rings.number_field
sage: Cat = CommutativeAdditiveGroups().Finite()
sage: A = G.algebra(GF(5), category=Cat)
sage: A in Algebras.Semisimple
Expand Down
14 changes: 7 additions & 7 deletions src/sage/categories/group_algebras.py
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Expand Up @@ -128,7 +128,7 @@ def __init_extra__(self):

EXAMPLES::

sage: # needs sage.groups sage.modules
sage: # needs sage.combinat sage.groups sage.modules
sage: A = GroupAlgebra(SymmetricGroup(4), QQ)
sage: B = GroupAlgebra(SymmetricGroup(3), ZZ)
sage: A.has_coerce_map_from(B)
Expand Down Expand Up @@ -172,7 +172,7 @@ def group(self):

sage: GroupAlgebras(QQ).example(GL(3, GF(11))).group() # needs sage.groups sage.modules
General Linear Group of degree 3 over Finite Field of size 11
sage: SymmetricGroup(10).algebra(QQ).group() # needs sage.groups sage.modules
sage: SymmetricGroup(10).algebra(QQ).group() # needs sage.combinat sage.groups sage.modules
Symmetric group of order 10! as a permutation group
"""
return self.basis().keys()
Expand Down Expand Up @@ -200,7 +200,7 @@ def center_basis(self):

EXAMPLES::

sage: SymmetricGroup(3).algebra(QQ).center_basis() # needs sage.groups sage.modules
sage: SymmetricGroup(3).algebra(QQ).center_basis() # needs sage.combinat sage.groups sage.modules
((), (2,3) + (1,2) + (1,3), (1,2,3) + (1,3,2))

.. SEEALSO::
Expand Down Expand Up @@ -318,12 +318,12 @@ def is_integral_domain(self, proof=True):

sage: # needs sage.groups sage.modules
sage: S2 = SymmetricGroup(2)
sage: GroupAlgebra(S2).is_integral_domain()
sage: GroupAlgebra(S2).is_integral_domain() # needs sage.combinat
False
sage: S1 = SymmetricGroup(1)
sage: GroupAlgebra(S1).is_integral_domain()
sage: GroupAlgebra(S1).is_integral_domain() # needs sage.combinat
True
sage: GroupAlgebra(S1, IntegerModRing(4)).is_integral_domain()
sage: GroupAlgebra(S1, IntegerModRing(4)).is_integral_domain() # needs sage.combinat
False
sage: GroupAlgebra(AbelianGroup(1)).is_integral_domain()
True
Expand Down Expand Up @@ -399,7 +399,7 @@ def central_form(self):

EXAMPLES::

sage: # needs sage.groups sage.modules
sage: # needs sage.combinat sage.groups sage.modules
sage: QS3 = SymmetricGroup(3).algebra(QQ)
sage: A = QS3([2,3,1]) + QS3([3,1,2])
sage: A.central_form()
Expand Down
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