Unitary Groups \(GU(n,q)\) and \(SU(n,q)\) with GAP#

class sage.groups.matrix_gps.unitary_gap.UnitaryMatrixGroup_gap(degree, base_ring, special, sage_name, latex_string, gap_command_string, category=None)[source]#

Bases: UnitaryMatrixGroup_generic, NamedMatrixGroup_gap, FinitelyGeneratedMatrixGroup_gap

The general or special unitary group in GAP.

invariant_form()[source]#

Return the hermitian form preserved by the unitary group.

OUTPUT: a square matrix describing the bilinear form

EXAMPLES:

sage: G32 = GU(3,2)
sage: G32.invariant_form()
[0 0 1]
[0 1 0]
[1 0 0]

>>> from sage.all import *
>>> G32 = GU(Integer(3),Integer(2))
>>> G32.invariant_form()
[0 0 1]
[0 1 0]
[1 0 0]