67.47 OrderMat -- enhanced

OrderMat(g)

This function works as described in the GAP manual but uses the algorithm of [2] for matrices over finite fields.

    gap> OrderMat( [ [ Z(17)^4, Z(17)^12, Z(17)^4, Z(17)^7 ],
    >   [ Z(17)^10, Z(17), Z(17)^11, 0*Z(17) ],
    >   [ Z(17)^8, Z(17)^13, Z(17)^0, Z(17)^14 ],
    >   [ Z(17)^14, Z(17)^10, Z(17), Z(17)^10 ] ] );
    5220 

ProjectiveOrderMat(g)

This function computes the least positive integer n such that g^n is scalar; it returns, as a list, n and z, where g^n is scalar in z.

    gap> ProjectiveOrderMat( [ [ Z(17)^4, Z(17)^12, Z(17)^4, Z(17)^7 ], 
    >   [ Z(17)^10, Z(17), Z(17)^11, 0*Z(17) ],
    >   [ Z(17)^8, Z(17)^13, Z(17)^0, Z(17)^14 ],
    >   [ Z(17)^14, Z(17)^10, Z(17), Z(17)^10 ] ] );
    [ 1305, Z(17)^12 ] 

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