# scalarMultiplication -- Add Reduced Ideal Multiple Times

## Synopsis

• Usage:
K=scalarMultiplication(J,m)
• Inputs:
• J, an integral ideal
• m, a nonnegative integer
• Outputs:

## Description

The function scalarMultiplication computes the reduced ideal of an integral ideal scalarMultiplicationplied by a nonnegative integer

 ```i1 : setPolynomialRing(GF 13,{x,y},{2,3}); setQuotientRing(y^2-x^3-7*x) o2 = QR o2 : QuotientRing``` ```i3 : J=ideal(x,y) o3 = ideal (x, y) o3 : Ideal of QR``` ```i4 : scalarMultiplication(J,5) o4 = ideal (x, y) o4 : Ideal of QR``` ```i5 : setPolynomialRing({x,y}, {2,3}) o5 = PR o5 : PolynomialRing``` ```i6 : setQuotientRing(y^2-x^3-7*x) o6 = QR o6 : QuotientRing``` ```i7 : J=ideal(x,y) o7 = ideal (x, y) o7 : Ideal of QR``` ```i8 : K=ideal(x-2,y-3) o8 = ideal (x - 2, y - 3) o8 : Ideal of QR``` ```i9 : add(J,K) o9 = ideal (x, y) o9 : Ideal of QR``` ```i10 : scalarMultiplication(K,5) o10 = ideal 1 o10 : Ideal of QR```

• double -- Double Reduced Ideal

## Ways to use scalarMultiplication :

• scalarMultiplication(Ideal,ZZ) (missing documentation)