Module general_linear

General Linear Groups

EXAMPLES:
    sage: GL(4,QQ)
    General Linear Group of degree 4 over Rational Field
    sage: GL(1,ZZ)
    General Linear Group of degree 1 over Integer Ring
    sage: GL(100,RR)
    General Linear Group of degree 100 over Real Field with 53 bits of precision
    sage: GL(3,GF(49,'a'))
    General Linear Group of degree 3 over Finite Field in a of size 7^2

AUTHORS:
    -- David Joyner (2006-01)
    -- William Stein (2006-01)
    -- David Joyner (2006-05) - added _latex_, __str__, examples
    -- William Stein (2006-12-09): rewrite

Return the general linear group of degree $n$ over the ring $R$.

EXAMPLES:
    sage: G = GL(6,GF(5))
    sage: G.order()
    11064475422000000000000000
    sage: G.base_ring()
    Finite Field of size 5

    sage: F = GF(3); MS = MatrixSpace(F,2,2)
    sage: gens = [MS([[0,1],[1,0]]),MS([[1,1],[0,1]])]
    sage: G = MatrixGroup(gens)
    sage: G.order()
    48
    sage: H = GL(2,F)
    sage: H.order()
    48
    sage: H == G
    True
    sage: H.as_matrix_group() == G
    True
    sage: H.gens()
    [
    [2 0]
    [0 1],
    [2 1]
    [2 0]
    ]