Coverage for local/lib/python2.7/site-packages/sage/groups/matrix_gps/homset.py : 100%

""" 

Matrix Group Homsets 

AUTHORS: 

- William Stein (2006-05-07): initial version 

- Volker Braun (2013-1) port to new Parent, libGAP 

""" 

############################################################################## 

# Copyright (C) 2006 David Joyner and William Stein <wstein@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# 

# The full text of the GPL is available at: 

# 

# http://www.gnu.org/licenses/ 

############################################################################## 

from sage.groups.group_homset import GroupHomset_generic 

def is_MatrixGroupHomset(x): 

r""" 

Test whether ``x`` is a homset. 

EXAMPLES:: 

sage: from sage.groups.matrix_gps.homset import is_MatrixGroupHomset 

sage: is_MatrixGroupHomset(4) 

False 

sage: F = GF(5) 

sage: gens = [matrix(F,2,[1,2, -1, 1]), matrix(F,2, [1,1, 0,1])] 

sage: G = MatrixGroup(gens) 

sage: from sage.groups.matrix_gps.homset import MatrixGroupHomset 

sage: M = MatrixGroupHomset(G, G) 

sage: is_MatrixGroupHomset(M) 

True 

""" 

return isinstance(x, MatrixGroupHomset) 

class MatrixGroupHomset(GroupHomset_generic): 

def __init__(self, G, H, category=None): 

r""" 

Return the homset of two matrix groups. 

INPUT: 

- ``G`` -- a matrix group 

- ``H`` -- a matrix group 

OUTPUT: 

The homset of two matrix groups. 

EXAMPLES:: 

sage: F = GF(5) 

sage: gens = [matrix(F,2,[1,2, -1, 1]), matrix(F,2, [1,1, 0,1])] 

sage: G = MatrixGroup(gens) 

sage: from sage.groups.matrix_gps.homset import MatrixGroupHomset 

sage: MatrixGroupHomset(G, G) 

Set of Homomorphisms from 

Matrix group over Finite Field of size 5 with 2 generators ( 

[1 2] [1 1] 

[4 1], [0 1] 

) to Matrix group over Finite Field of size 5 with 2 generators ( 

[1 2] [1 1] 

[4 1], [0 1] 

) 

""" 

from sage.categories.homset import HomsetWithBase 

HomsetWithBase.__init__(self, G, H, category, G.base_ring()) 

def __call__(self, im_gens, check=True): 

""" 

Return the homomorphism defined by images of generators. 

INPUT: 

- ``im_gens`` -- iterable, the list of images of the 

generators of the domain 

- ``check`` -- bool (optional, default: ``True``), whether to 

check if images define a valid homomorphism 

OUTPUT: 

Group homomorphism. 

EXAMPLES:: 

sage: F = GF(5) 

sage: gens = [matrix(F,2,[1,2, -1, 1]), matrix(F,2, [1,1, 0,1])] 

sage: G = MatrixGroup(gens) 

sage: from sage.groups.matrix_gps.homset import MatrixGroupHomset 

sage: M = MatrixGroupHomset(G, G) 

sage: M(gens) 

Homomorphism : Matrix group over Finite Field of size 5 with 2 generators ( 

[1 2] [1 1] 

[4 1], [0 1] 

) --> Matrix group over Finite Field of size 5 with 2 generators ( 

[1 2] [1 1] 

[4 1], [0 1] 

) 

""" 

from sage.groups.matrix_gps.morphism import MatrixGroupMorphism_im_gens 

try: 

return MatrixGroupMorphism_im_gens(self, im_gens, check=check) 

except (NotImplementedError, ValueError) as err: 

raise TypeError('images do not define a group homomorphism')