regularRep(RingElement,Ideal)

Synopsis

• Function: regularRep

• Usage:

  regularRep(f,I)

• Inputs:
  • f, a ring element
  • I, an ideal
• Outputs:
  • a matrix, 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