22.18 Symplectic Linear Groups

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

Sp( 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

class SymplecticGroup_finite_field

Special Functions: _gap_init_

_gap_init_( self)

Return GAP string that evaluates to this group.

sage: Sp(2,4)._gap_init_()
'Sp(2, 4)'

Class: SymplecticGroup_generic

class SymplecticGroup_generic

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

_latex_( self)

Return LaTeX representation of this group.

sage: latex(Sp(4,5))
\text{Sp}_{4}(\mathbf{F}_{5})

_repr_( 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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