Coverage for local/lib/python2.7/site-packages/sage/groups/old.pyx : 49%
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""" Base class for groups """
#***************************************************************************** # Copyright (C) 2005 William Stein <wstein@gmail.com> # # Distributed under the terms of the GNU General Public License (GPL) # # This code is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU # General Public License for more details. # # The full text of the GPL is available at: # # http://www.gnu.org/licenses/ #***************************************************************************** from __future__ import absolute_import
doc=""" Base class for all groups """
import random
from sage.rings.infinity import infinity import sage.rings.integer_ring
cdef class Group(sage.structure.parent_gens.ParentWithGens): """ Generic group class """ def __init__(self, category = None): """
TESTS::
sage: from sage.groups.old import Group sage: G = Group() sage: G.category() Category of groups sage: G = Group(category = Groups()) # todo: do the same test with some subcategory of Groups when there will exist one sage: G.category() Category of groups sage: G = Group(category = CommutativeAdditiveGroups()) Traceback (most recent call last): ... AssertionError: Category of commutative additive groups is not a subcategory of Category of groups
Check for :trac:`8119`::
sage: G = SymmetricGroup(2) sage: h = hash(G) sage: G.rename('S2') sage: h == hash(G) True """ else:
#def __call__(self, x): # this gets in the way of the coercion mechanism # """ # Coerce x into this group. # """ # raise NotImplementedError
def __contains__(self, x): r""" True if coercion of `x` into self is defined.
EXAMPLES::
sage: from sage.groups.old import Group sage: G = Group() sage: 4 in G #indirect doctest Traceback (most recent call last): ... NotImplementedError: cannot construct elements of <sage.groups.old.Group object at ...> """ return False return True
# def category(self): # """ # The category of all groups # """ # import sage.categories.all # return sage.categories.all.Groups()
def is_abelian(self): """ Return True if this group is abelian.
EXAMPLES::
sage: from sage.groups.old import Group sage: G = Group() sage: G.is_abelian() Traceback (most recent call last): ... NotImplementedError """
def is_commutative(self): r""" Return True if this group is commutative. This is an alias for is_abelian, largely to make groups work well with the Factorization class.
(Note for developers: Derived classes should override is_abelian, not is_commutative.)
EXAMPLES::
sage: SL(2, 7).is_commutative() False """ return self.is_abelian()
def order(self): """ Returns the number of elements of this group, which is either a positive integer or infinity.
EXAMPLES::
sage: from sage.groups.old import Group sage: G = Group() sage: G.order() Traceback (most recent call last): ... NotImplementedError """
def is_finite(self): """ Returns True if this group is finite.
EXAMPLES::
sage: from sage.groups.old import Group sage: G = Group() sage: G.is_finite() Traceback (most recent call last): ... NotImplementedError """
def is_multiplicative(self): """ Returns True if the group operation is given by \* (rather than +).
Override for additive groups.
EXAMPLES::
sage: from sage.groups.old import Group sage: G = Group() sage: G.is_multiplicative() True """
def random_element(self, bound=None): """ Return a random element of this group.
EXAMPLES::
sage: from sage.groups.old import Group sage: G = Group() sage: G.random_element() Traceback (most recent call last): ... NotImplementedError """
def quotient(self, H): """ Return the quotient of this group by the normal subgroup `H`.
EXAMPLES::
sage: from sage.groups.old import Group sage: G = Group() sage: G.quotient(G) Traceback (most recent call last): ... NotImplementedError """
cdef class AbelianGroup(Group): """ Generic abelian group. """ def is_abelian(self): """ Return True.
EXAMPLES::
sage: from sage.groups.old import AbelianGroup sage: G = AbelianGroup() sage: G.is_abelian() True """
cdef class FiniteGroup(Group): """ Generic finite group. """ def is_finite(self): """ Return True.
EXAMPLES::
sage: from sage.groups.old import FiniteGroup sage: G = FiniteGroup() sage: G.is_finite() True """
cdef class AlgebraicGroup(Group): """ Generic algebraic group. """ |