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

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# 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)

  Bases: `UnitaryMatrixGroup_generic`, `NamedMatrixGroup_gap`, `FinitelyGeneratedMatrixGroup_gap`

  The general or special unitary group in GAP.

  invariant_form()

    Return the hermitian form preserved by the unitary group.

    OUTPUT: a square matrix describing the bilinear form

    EXAMPLES:

    Sage

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

    Python

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