Module: sage.groups.matrix_gps.special_linear
Special Linear Groups
Author Log:
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] ]
Module-level Functions
n, R, [var=a]) |
Return the special linear group of degree
over the ring
.
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() 195671259569814696201521906242958634112401800718204947891606736963871306673 788236339351996634365767743090701127020626583481909204625023204918796771814 9558134226774650845658791865745408000000 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
.
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] ]
Class: SpecialLinearGroup_finite_field
Class: SpecialLinearGroup_generic
Special Functions: _gap_init_,
_latex_,
_repr_
self) |
String to create this grop in GAP.
sage: G = SL(6,GF(5)); G Special Linear Group of degree 6 over Finite Field of size 5 sage: G._gap_init_() 'SL(6, GF(5))'
self) |
sage: G = SL(6,GF(5)) sage: latex(G) \text{SL}_{6}(\mathbf{F}_{5})
self) |
Text representation of self.
sage: SL(6,GF(5)) Special Linear Group of degree 6 over Finite Field of size 5
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