GAP Manual: 19.7. Degree

Degree( f )

Degree returns the degree d_f of f (see Polynomials).

Note that this is only equal to the Euclidean degree in the polynomial ring P(R). It is not equal in the Laurent polynomial ring L(R).

    gap> x := Indeterminate(Rationals);; x.name := "x";;
    gap> Degree( x^10 + x^2 + 1 );
    10
    gap> EuclideanDegree( x^10 + x^2 + 1 );
    10      # the default ring is the polynomial ring
    gap> Degree( x^-10 + x^-11 );
    -10
    gap> EuclideanDegree( x^-10 + x^-11 );
    1       # the default ring is the Laurent polynomial ring