Module special_linear

Special Linear Groups

AUTHOR:
    -- William Stein: initial version
    -- David Joyner (2006-05) - added examples, _latex_, __str__, gens,
                                      as_matrix_group
    -- William Stein (2006-12-09): rewrite                                      
    
EXAMPLES:
        sage: SL(2, ZZ)
        Special Linear Group of degree 2 over Integer Ring
        sage: G = SL(2,GF(3)); G
        Special Linear Group of degree 2 over Finite Field of size 3
        sage: G.is_finite()
        True
        sage: G.conjugacy_class_representatives()
        [
        [1 0]
        [0 1],
        [0 2]
        [1 1],
        [0 1]
        [2 1],
        [2 0]
        [0 2],
        [0 2]
        [1 2],
        [0 1]
        [2 2],
        [0 2]
        [1 0]
        ]
        sage: G = SL(6,GF(5))
        sage: G.gens()
        [
        [2 0 0 0 0 0]
        [0 3 0 0 0 0]
        [0 0 1 0 0 0]
        [0 0 0 1 0 0]
        [0 0 0 0 1 0]
        [0 0 0 0 0 1],
        [4 0 0 0 0 1]
        [4 0 0 0 0 0]
        [0 4 0 0 0 0]
        [0 0 4 0 0 0]
        [0 0 0 4 0 0]
        [0 0 0 0 4 0]
        ]

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

EXAMPLES:
    sage: SL(3,GF(2))
    Special Linear Group of degree 3 over Finite Field of size 2
    sage: G = SL(15,GF(7)); G
    Special Linear Group of degree 15 over Finite Field of size 7
    sage: G.order()
    1956712595698146962015219062429586341124018007182049478916067369638713066737882363393519966343657677430907011270206265834819092046250232049187967718149558134226774650845658791865745408000000
    sage: len(G.gens())
    2
    sage: G = SL(2,ZZ); G
    Special Linear Group of degree 2 over Integer Ring
    sage: G.gens()
    [
    [ 0  1]
    [-1  0],
    [1 1]
    [0 1]
    ]

Next we compute generators for $\SL_3(\ZZ)$.
    sage: G = SL(3,ZZ); G
    Special Linear Group of degree 3 over Integer Ring
    sage: G.gens()
    [
    [0 1 0]
    [0 0 1]
    [1 0 0],
    [ 0  1  0]
    [-1  0  0]
    [ 0  0  1],
    [1 1 0]
    [0 1 0]
    [0 0 1]
    ]