Symplectic Linear Groups

AUTHORS:

• David Joyner (2006-03): initial version, modified from special_linear (by W. Stein)

EXAMPLES:

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

sage.groups.matrix_gps.symplectic.Sp(n, R, var='a')

Return the symplectic group of degree n over R.

EXAMPLES:

sage: Sp(4,5)
Symplectic Group of rank 2 over Finite Field of size 5
sage: Sp(3,GF(7))
...
ValueError: the degree n (=3) must be even

class sage.groups.matrix_gps.symplectic.SymplecticGroup_finite_field(n, R, var='a', category=None)

Bases: sage.groups.matrix_gps.symplectic.SymplecticGroup_generic, sage.groups.matrix_gps.matrix_group.MatrixGroup_gap_finite_field

class sage.groups.matrix_gps.symplectic.SymplecticGroup_generic(n, R, var='a', category=None)

Bases: sage.groups.matrix_gps.matrix_group.MatrixGroup_gap