19.1 Multivariate Polynomials

As explained above, each ring R has exactly one indeterminate associated with R. In order to construct a polynomial ring with two indeterminates over R you must first construct the polynomial ring P(R) and then the polynomial ring over P(R).

    gap> x  := Indeterminate(Integers);; x.name := "x";;
    gap> Rx := PolynomialRing(Integers);;
    gap> y  := Indeterminate(Rx);; y.name := "y";;
    gap> x  := y^0 * x;
    x*y^0
    gap> f := x^2*y^2 + 3*x*y + x + 4*y;
    (x^2)*y^2 + (3*x + 4)*y + (x)
    gap> Value( f, 4 );
    16*x^2 + 13*x + 16
    gap> Value( last, -2 );
    54
    gap> (-2)^2 * 4^2 + 3*(-2)*4 + (-2) + 4*4;
    54 

We plan to add support for (proper) multivariate polynomials in one of the next releases of GAP.

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