Matrix Group Homsets¶
AUTHORS:
- William Stein (2006-05-07): initial version
- Volker Braun (2013-1) port to new Parent, libGAP
-
class
sage.groups.matrix_gps.homset.
MatrixGroupHomset
(G, H, category=None)¶ Bases:
sage.groups.group_homset.GroupHomset_generic
Return the homset of two matrix groups.
INPUT:
G
– a matrix groupH
– 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] )
-
sage.groups.matrix_gps.homset.
is_MatrixGroupHomset
(x)¶ 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