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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/groups/matrix_gps/homset.py
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"""

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Matrix Group Homsets

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AUTHORS:

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

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"""

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

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#       Copyright (C) 2006 David Joyner and William Stein <[email protected]>

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#

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

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#

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#  The full text of the GPL is available at:

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#

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#                  http://www.gnu.org/licenses/

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

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from sage.groups.group_homset import GroupHomset_generic

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from sage.categories.homset import HomsetWithBase

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from sage.categories.all import Groups

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GROUPS = Groups()

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import matrix_group_morphism

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def is_MatrixGroupHomset(x):

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    r"""

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    EXAMPLES::

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

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        sage: is_MatrixGroupHomset(4)

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        False

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    ::

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        sage: F = GF(5)

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

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        sage: G = MatrixGroup(gens)

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

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        sage: M = MatrixGroupHomset(G, G)

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        sage: is_MatrixGroupHomset(M)

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        True

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    """

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    return isinstance(x, MatrixGroupHomset)

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class MatrixGroupHomset(GroupHomset_generic):

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    r"""

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    Return the homset of two matrix groups.

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    INPUT:

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    - ``G`` - a matrix group

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    - ``H`` - a matrix group

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    OUTPUT:

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    The homset of two matrix groups.

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    EXAMPLES::

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        sage: F = GF(5)

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

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        sage: G = MatrixGroup(gens)

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

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        sage: MatrixGroupHomset(G, G)

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        Set of Homomorphisms from Matrix group over Finite Field of size 5 with 2 generators: 

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         [[[1, 2], [4, 1]], [[1, 1], [0, 1]]] to Matrix group over Finite Field of size 5 with 2 generators: 

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         [[[1, 2], [4, 1]], [[1, 1], [0, 1]]]

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    """

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    def __init__(self, G, H):

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        r"""

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        See ``MatrixGroupHomset`` for full documentation.

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        EXAMPLES::

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            sage: F = GF(5)

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

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            sage: G = MatrixGroup(gens)

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

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            sage: MatrixGroupHomset(G, G)

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            Set of Homomorphisms from Matrix group over Finite Field of size 5 with 2 generators: 

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             [[[1, 2], [4, 1]], [[1, 1], [0, 1]]] to Matrix group over Finite Field of size 5 with 2 generators: 

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             [[[1, 2], [4, 1]], [[1, 1], [0, 1]]]

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        """

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

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

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        """

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        Return the homomorphism defined by images of generators.

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        INPUT:

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

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          the domain

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

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          if images define a valid homomorphism

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        EXAMPLES::

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            sage: F = GF(5)

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

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            sage: G = MatrixGroup(gens)

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

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            sage: M = MatrixGroupHomset(G, G)

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            sage: M(gens) 

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

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             [[[1, 2], [4, 1]], [[1, 1], [0, 1]]] --> Matrix group over Finite Field of size 5 with 2 generators: 

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             [[[1, 2], [4, 1]], [[1, 1], [0, 1]]]

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        """

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        try:

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            return matrix_group_morphism.MatrixGroupMorphism_im_gens(self,

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                                                            im_gens, check=check)

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        except (NotImplementedError, ValueError), err:

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            raise TypeError, "images (=%s) do not define a valid homomorphism"%im_gens

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