22.15 General Linear Groups

Module: sage.groups.matrix_gps.general_linear

General Linear Groups

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

Author Log:

Module-level Functions

GL( n, R, [var=a])

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

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]
]

Class: GeneralLinearGroup_finite_field

class GeneralLinearGroup_finite_field

Class: GeneralLinearGroup_generic

class GeneralLinearGroup_generic

Special Functions: _gap_init_,$ \,$ _latex_,$ \,$ _repr_

_gap_init_( self)

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

_latex_( self)

sage: G = GL(6,GF(5))
sage: latex(G)
	ext{GL}_{6}(\mathbf{F}_{5})

_repr_( self)

String representation of this linear group.

sage: GL(6,GF(5))
General Linear Group of degree 6 over Finite Field of size 5

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