# 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)

Bases: sage.groups.group_homset.GroupHomset_generic

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]
)

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


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