Module: sage.groups.matrix_gps.symplectic
Symplectic Linear Groups
Author: David Joyner: initial version (2006-3), modified from special_linear (by W. Stein)
sage: G = Sp(4,GF(7)) sage: G._gap_init_() 'Sp(4, 7)' sage: G Symplectic Group of rank 2 over Finite Field of size 7 sage: G.random_element() [1 6 5 5] [2 1 4 5] [1 2 4 5] [4 0 2 2] sage: G.order() 276595200
Module-level Functions
n, R, [var=a]) |
Return the symplectic group of degree n over R.
sage: Sp(4,5) Symplectic Group of rank 2 over Finite Field of size 5 sage: Sp(3,GF(7)) Traceback (most recent call last): ... ValueError: the degree n (=3) must be even
Class: SymplecticGroup_finite_field
Special Functions: _gap_init_
self) |
Return GAP string that evaluates to this group.
sage: Sp(2,4)._gap_init_() 'Sp(2, 4)'
Class: SymplecticGroup_generic
Special Functions: _gap_init_,
_latex_,
_repr_
self) |
Return LaTeX representation of this group.
sage: latex(Sp(4,5)) \text{Sp}_{4}(\mathbf{F}_{5})
self) |
Return print representation of this group.
sage: Sp(2,4) Symplectic Group of rank 1 over Finite Field in a of size 2^2
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