10.13 General Linear Groups

Module: sage.groups.matrix_gps.general_linear

sage: GL(4,Q)
General Linear Group of degree 4 over Rational Field
sage: GL(1,Z)
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))
General Linear Group of degree 3 over Finite Field in a of size 7^2

Author Log:

TODO: Write a method to coerce GL into a MatrixGroup...

Module-level Functions

GL( n, R)

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

sage: G = GL(6,GF(5))
sage: G.order()
11064475422000000000000000L
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
False
sage: H.as_matrix_group() == G
False
sage: H.gens()
[[2 0]
 [0 1], [2 1]
        [2 0]]

Class: GeneralLinearGroup_finite_field

class GeneralLinearGroup_finite_field

Class: GeneralLinearGroup_generic

class GeneralLinearGroup_generic

Functions: as_matrix_group,$  $ gens

gens( self)

sage: G = GL(6,GF(5))
sage: G.gens()
[[2 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 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 = GL(6,GF(5))
sage: print G
GL(6, GF(5))

_gap_init_( self)

sage: G = GL(6,GF(5))
sage: G._gap_init_()
'GL(6, 5)'

_latex_( self)

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

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