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()
[5 4 6 0]
[1 1 6 2]
[5 5 0 6]
[5 4 5 1]
sage: G.order()
276595200
sage.groups.matrix_gps.symplectic.Sp(n, R, var='a')

Return the symplectic group of degree n over R.

Note

This group is also available via groups.matrix.Sp().

EXAMPLES:

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

TESTS:

sage: groups.matrix.Sp(2, 3)
Symplectic Group of rank 1 over Finite Field of size 3
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

INPUT:

  • n - the degree
  • R - the base ring
  • var - variable used to define field of definition of actual matrices in this group.
class sage.groups.matrix_gps.symplectic.SymplecticGroup_generic(n, R, var='a', category=None)

Bases: sage.groups.matrix_gps.matrix_group.MatrixGroup_gap

INPUT:

  • n - the degree
  • R - the base ring
  • var - variable used to define field of definition of actual matrices in this group.

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