## Synopsis

• Usage:
• Inputs:
• J, an integral ideal
• K, an integral ideal
• Outputs:

## Description

The function add computes the reduced ideal of multiplication of two integral ideals. Each reduced ideal is a representative of its ideal class, and the addition is executed over the ideal class group.

 i1 : setPolynomialRing(GF 13, {x,y}, {2,3}); setQuotientRing(y^2-x^3-7*x) o2 = QR o2 : QuotientRing i3 : J=ideal(x, y); K=ideal(x-2, y-3); add(J, K) o3 : Ideal of QR o4 : Ideal of QR o5 = ideal (x + 3, y + 2) o5 : Ideal of QR i6 : L=J*K; reduced(L) o6 : Ideal of QR o7 = ideal (x + 3, y + 2) o7 : Ideal of QR i8 : setPolynomialRing(GF 5,{x,y,z},{4,6,5}) o8 = PR o8 : PolynomialRing i9 : setQuotientRing({y^2-x^3-1, z^2-x*y-1}) o9 = QR o9 : QuotientRing i10 : J=ideal(x-2,y-2,z) o10 = ideal (x - 2, y - 2, z) o10 : Ideal of QR i11 : K=ideal(x-4,y,z-1) o11 = ideal (x + 1, y, z - 1) o11 : Ideal of QR i12 : add(J, K) 2 o12 = ideal (z + 2x + 1, y + x + 1, x - x - 2) o12 : Ideal of QR