def _Hom_(self, G, cat=None):
"""
Construct a homset.
INPUT:
- ``G`` -- group. The codomain.
- ``cat`` -- a category. Must be unset.
OUTPUT:
The set of homomorphisms from ``self`` to ``G``.
EXAMPLES::
sage: MS = MatrixSpace(SR, 2, 2)
sage: G = MatrixGroup([MS(1), MS([1,2,3,4])])
sage: G.Hom(G)
Set of Homomorphisms from Matrix group over Symbolic Ring with 2 generators (
[1 0] [1 2]
[0 1], [3 4]
) to Matrix group over Symbolic Ring with 2 generators (
[1 0] [1 2]
[0 1], [3 4]
)
"""
if not (cat is None or (cat is G.category() and cat is self.category())):
raise TypeError
if not is_MatrixGroup(G):
raise TypeError, "G (=%s) must be a matrix group."%G
import homset
return homset.MatrixGroupHomset(self, G)
def _Hom_(self, G, cat=None):
if not (cat is None or
(cat is G.category() and cat is self.category())):
raise TypeError
if not is_MatrixGroup(G):
raise TypeError, "G (=%s) must be a matrix group." % G
import homset
return homset.MatrixGroupHomset(self, G)
def _Hom_(self, G, cat=None):
"""
Construct a homset.
INPUT:
- ``G`` -- group; the codomain
- ``cat`` -- category; must be unset
OUTPUT:
The set of homomorphisms from ``self`` to ``G``.
EXAMPLES::
sage: MS = MatrixSpace(SR, 2, 2)
sage: G = MatrixGroup([MS(1), MS([1,2,3,4])])
sage: G.Hom(G)
Set of Homomorphisms from Matrix group over Symbolic Ring with 2 generators (
[1 0] [1 2]
[0 1], [3 4]
) to Matrix group over Symbolic Ring with 2 generators (
[1 0] [1 2]
[0 1], [3 4]
)
TESTS:
Check that :trac:`19407` is fixed::
sage: G = GL(2, GF(2))
sage: H = GL(3, ZZ)
sage: Hom(G, H)
Set of Homomorphisms from General Linear Group of degree 2
over Finite Field of size 2 to General Linear Group of degree 3
over Integer Ring
"""
if not is_MatrixGroup(G):
raise TypeError("G (=%s) must be a matrix group." % G)
import homset
return homset.MatrixGroupHomset(self, G, cat)