Symplectic Linear Groups with GAP#
- class sage.groups.matrix_gps.symplectic_gap.SymplecticMatrixGroup_gap(degree, base_ring, special, sage_name, latex_string, gap_command_string, category=None)[source]#
Bases:
SymplecticMatrixGroup_generic
,NamedMatrixGroup_gap
,FinitelyGeneratedMatrixGroup_gap
Symplectic group in GAP.
EXAMPLES:
sage: Sp(2,4) # needs sage.rings.finite_rings Symplectic Group of degree 2 over Finite Field in a of size 2^2 sage: latex(Sp(4,5)) \text{Sp}_{4}(\Bold{F}_{5})
>>> from sage.all import * >>> Sp(Integer(2),Integer(4)) # needs sage.rings.finite_rings Symplectic Group of degree 2 over Finite Field in a of size 2^2 >>> latex(Sp(Integer(4),Integer(5))) \text{Sp}_{4}(\Bold{F}_{5})
- invariant_form()[source]#
Return the quadratic form preserved by the symplectic group.
OUTPUT: a matrix
EXAMPLES:
sage: Sp(4, GF(3)).invariant_form() [0 0 0 1] [0 0 1 0] [0 2 0 0] [2 0 0 0]
>>> from sage.all import * >>> Sp(Integer(4), GF(Integer(3))).invariant_form() [0 0 0 1] [0 0 1 0] [0 2 0 0] [2 0 0 0]