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
n, R, [var=a]) |
Return the general linear group of degree
over the ring
.
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_generic
Special Functions: _gap_init_,
_latex_,
_repr_
self) |
sage: G = GL(6,GF(5)) sage: G._gap_init_() 'GL(6, GF(5))'
self) |
sage: G = GL(6,GF(5)) sage: latex(G) ext{GL}_{6}(\mathbf{F}_{5})
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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