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]