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# scalarMultiplication -- Add Reduced Ideal Multiple Times

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

## 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

## See also

- add -- Add Reduced Ideals
- double -- Double Reduced Ideal

## Ways to use scalarMultiplication:

- scalarMultiplication(Ideal,ZZ) (missing documentation)

## For the programmer

The object scalarMultiplication is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Miura.m2:200:0.