10.14 Special Linear Groups

Module: sage.groups.matrix_gps.special_linear

Author Log:

sage: SL(2, ZZ)
Modular Group SL(2,Z)
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]]

Module-level Functions

SL( n, R)

Class: SpecialLinearGroup_finite_field

class SpecialLinearGroup_finite_field

Class: SpecialLinearGroup_generic

class SpecialLinearGroup_generic

Functions: as_matrix_group,$  $ gens

as_matrix_group( self)

sage: G = SL(6,GF(5))
sage: G.as_matrix_group()
Matrix group over Finite Field of size 5 with 2 generators:
[[[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]]]

gens( self)

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]]

Special Functions: __repr__,$  $ __str__,$  $ _gap_init_,$  $ _latex_

__str__( self)

sage: G = SL(6,GF(5))
sage: print G
SL(6, GF(5))

_gap_init_( self)

sage: G = SL(6,GF(5))
sage: print G
SL(6, GF(5))

_latex_( self)

sage: G = SL(6,GF(5))
sage: G._latex_()
'SL$(6, GF(5))$'

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