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Fixed a bug in AbelianGroup.Subgroup.gens_orders(), which returns the reduced order of the subgroup #36986

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merged 8 commits into from
Jan 22, 2024
Merged

Fixed a bug in AbelianGroup.Subgroup.gens_orders(), which returns the reduced order of the subgroup #36986

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a31de1b
resolved the bug in abelian_group of gens_orders not being equal to gens
amanmoon Jan 1, 2024
b390e75
commit cleaned the abelian_group.py code
amanmoon Jan 1, 2024
28427c4
g.Order().sage() is only added to the list if it is finite
amanmoon Jan 1, 2024
2605463
added a test for gens_orders() method
amanmoon Jan 1, 2024
9613cb9
removed ges_order form init that was creating redundent information a…
amanmoon Jan 9, 2024
356645f
made the code readable
amanmoon Jan 10, 2024
adaeec9
resolved merge conflicts
amanmoon Jan 12, 2024
300c530
Merge branch 'develop' into bug/AbelianGroup.Subgroup
amanmoon Jan 16, 2024
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42 changes: 24 additions & 18 deletions src/sage/groups/abelian_gps/abelian_group.py
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Original file line number Diff line number Diff line change
Expand Up @@ -380,6 +380,7 @@ def _normalize(n, gens_orders=None, names="f"):
names = tuple(names)
return (gens_orders, names)


def AbelianGroup(n, gens_orders=None, names="f"):
r"""
Create the multiplicative abelian group in `n` generators
Expand Down Expand Up @@ -444,6 +445,7 @@ def AbelianGroup(n, gens_orders=None, names="f"):
M = AbelianGroup_class(gens_orders, names)
return M


def is_AbelianGroup(x):
"""
Return True if ``x`` is an Abelian group.
Expand Down Expand Up @@ -514,7 +516,7 @@ class AbelianGroup_class(UniqueRepresentation, AbelianGroupBase):
"""
Element = AbelianGroupElement

def __init__(self, generator_orders, names, category=None):
def __init__(self, generator_orders, names, gens_orders=None, category=None):
"""
The Python constructor

Expand All @@ -535,8 +537,8 @@ def __init__(self, generator_orders, names, category=None):
"""
assert isinstance(names, (str, tuple))
assert isinstance(generator_orders, tuple)
assert all(isinstance(order,Integer) for order in generator_orders)
self._gens_orders = generator_orders
assert all(isinstance(order, Integer) for order in generator_orders)
self._gens_orders = generator_orders if gens_orders is None else gens_orders
n = len(generator_orders)
names = normalize_names(n, names)
self._assign_names(names)
Expand Down Expand Up @@ -943,7 +945,7 @@ def gens(self):
sage: [g.order() for g in F.gens()]
[+Infinity, +Infinity, +Infinity, 3, 2]
"""
return tuple( self.gen(i) for i in range(self.ngens()) )
return tuple(self.gen(i) for i in range(self.ngens()))

def gens_orders(self):
"""
Expand Down Expand Up @@ -976,13 +978,15 @@ def gens_orders(self):
sage: Z2xZ3 is Z6
False

TESTS::

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TESTS::
sage: G, (g0, g1) = AbelianGroup(2, [48, 0]).objgens()
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sage: G0 = G.subgroup([g0])
sage: len(G0.gens()) == len(G0.gens_orders())
True
sage: F = AbelianGroup(3, [2], names='abc')
sage: list(map(type, F.gens_orders()))
[<class 'sage.rings.integer.Integer'>,
<class 'sage.rings.integer.Integer'>,
<class 'sage.rings.integer.Integer'>]
[<class 'sage.rings.integer.Integer'>, <class 'sage.rings.integer.Integer'>, <class 'sage.rings.integer.Integer'>]
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"""
return self._gens_orders

Expand Down Expand Up @@ -1175,7 +1179,7 @@ def random_element(self):
order = g.order()
if order is infinity:
order = 42 # infinite order; randomly chosen maximum
result *= g**(randint(0,order))
result *= g**(randint(0, order))
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return result

def _repr_(self):
Expand Down Expand Up @@ -1553,8 +1557,8 @@ def subgroup_reduced(self, elts, verbose=False):
rel_lattice = X.span([X.gen(i) * self.gens_orders()[i] for i in range(d)])
isect = elt_lattice.intersection(rel_lattice)
mat = matrix([elt_lattice.coordinate_vector(x) for x in isect.gens()]).change_ring(ZZ)
D,U,V = mat.smith_form()
new_basis = [(elt_lattice.linear_combination_of_basis((~V).row(i)).list(), D[i,i]) for i in range(U.ncols())]
D, U, V = mat.smith_form()
new_basis = [(elt_lattice.linear_combination_of_basis((~V).row(i)).list(), D[i, i]) for i in range(U.ncols())]
return self.subgroup([self([x[0][i] % self.gens_orders()[i]
for i in range(d)]) for x in new_basis if x[1] != 1])

Expand Down Expand Up @@ -1627,7 +1631,7 @@ def __init__(self, ambient, gens, names="f", category=None):
Multiplicative Abelian subgroup isomorphic to Z x Z generated by {a^3, b}
sage: F.subgroup([c])
Multiplicative Abelian subgroup isomorphic to C2 x C3 x C5 generated by {c}
sage: F.subgroup([a, c])
sage: S = F.subgroup([a, c]); S
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Multiplicative Abelian subgroup isomorphic to C2 x C3 x C5 x Z generated by {a, c}
sage: F.subgroup([a, b*c])
Multiplicative Abelian subgroup isomorphic to Z x Z generated by {a, b*c}
Expand Down Expand Up @@ -1657,7 +1661,7 @@ def __init__(self, ambient, gens, names="f", category=None):
sage: B = A.subgroup([a^3, b, c, d, e^2]); B
Multiplicative Abelian subgroup isomorphic to C4 x C5 x C5 x C7 generated by {b, c, d, e^2}
sage: B.gens_orders()
(4, 5, 5, 7)
(5, 5, 7, 4)
sage: A = AbelianGroup(4,[1009, 2003, 3001, 4001], names="abcd")
sage: a,b,c,d = A.gens()
sage: B = A.subgroup([a^3,b,c,d])
Expand All @@ -1682,7 +1686,7 @@ def __init__(self, ambient, gens, names="f", category=None):
Multiplicative Abelian subgroup isomorphic to C2 x C3 x Z
generated by {a, b^2, c}
sage: F.gens_orders()
(2, 3, 0)
(3, 2, 0)
sage: F.gens()
(a, b^2, c)
sage: F.order()
Expand All @@ -1708,16 +1712,19 @@ def __init__(self, ambient, gens, names="f", category=None):
H = libgap(ambient).Subgroup(H_gens)

invs = H.TorsionSubgroup().AbelianInvariants().sage()
gens_orders = [order_sage for g in H.GeneratorsOfGroup() if (order_sage := g.Order().sage()) is not infinity]
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rank = len([1 for g in H.GeneratorsOfGroup()
if g.Order().sage() is infinity])
invs += [0] * rank

gens_orders += [0] * rank
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self._abinvs = invs
invs = tuple(ZZ(i) for i in invs)
gens_orders = tuple(ZZ(i) for i in gens_orders)
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if category is None:
category = Groups().Commutative().Subobjects()
AbelianGroup_class.__init__(self, invs, names, category=category)
AbelianGroup_class.__init__(self, invs, names, category=category, gens_orders=gens_orders)

def __contains__(self, x):
"""
Expand Down Expand Up @@ -1770,8 +1777,7 @@ def __contains__(self, x):
ZZ, len(self._gens), len(amb_inv),
[g.list() for g in self._gens]
)
return (vector(ZZ, x.list())
in inv_basis.stack(gens_basis).row_module())
return (vector(ZZ, x.list()) in inv_basis.stack(gens_basis).row_module())
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return False

def ambient_group(self):
Expand Down
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