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RealRoots :: regularRepresentation

regularRepresentation -- the regular representation of a rational polynomial

Synopsis

Description

This command gives the matrix of the linear map defined by multiplication by f (resp. g) in terms of the standard basis of the finite-dimensional vector space ring f (resp. (ring g)/I).

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing
i2 : I = ideal(y^2 - x^2 - 1,x - y^2 + 4*y - 2)

               2    2         2
o2 = ideal (- x  + y  - 1, - y  + x + 4y - 2)

o2 : Ideal of R
i3 : regularRepresentation(y,I)

o3 = (| 1 x xy y |, | 0 0 -3 -2 |)
                    | 0 0 -1 1  |
                    | 0 1 4  0  |
                    | 1 0 4  4  |

o3 : Sequence
i4 : S = R/I

o4 = S

o4 : QuotientRing
i5 : regularRepresentation(y)

o5 = (| 1 x xy y |, | 0 0 -3 -2 |)
                    | 0 0 -1 1  |
                    | 0 1 4  0  |
                    | 1 0 4  4  |

o5 : Sequence

Ways to use regularRepresentation :

For the programmer

The object regularRepresentation is a method function.