# regularRep(RingElement,Ideal)

## Synopsis

• Function: regularRep
• Usage:
regularRep(f,I)
• Inputs:
• Outputs:
• , the matrix of the linear map defined by multiplication byfin terms of the standard basis of a finite-dimensional k-vector spaceI

## Description

This command gives the matrix of the linear map defined by multiplication by f in terms of the standard basis of a finite-dimensional k-vector space I

 i1 : R = QQ[x,y] o1 = R o1 : PolynomialRing i2 : F = {y^2-x^2-1,x-y^2+4*y-2} 2 2 2 o2 = {- x + y - 1, - y + x + 4y - 2} o2 : List i3 : I = ideal F 2 2 2 o3 = ideal (- x + y - 1, - y + x + 4y - 2) o3 : Ideal of R i4 : regularRep(y,I) o4 = (| 1 x xy y |, | 0 0 -3 -2 |) | 0 0 -1 1 | | 0 1 4 0 | | 1 0 4 4 | o4 : Sequence i5 : S = R/I o5 = S o5 : QuotientRing i6 : regularRep(y) o6 = (| 1 x xy y |, | 0 0 -3 -2 |) | 0 0 -1 1 | | 0 1 4 0 | | 1 0 4 4 | o6 : Sequence