ClassInToricChowRing -- Gives the class of a hypersurface in the associated Chow ring of a toric variety

Synopsis

Usage:

ClassInToricChowRing(Ch,f)
Inputs:
- Ch, a quotient ring, the Chow ring of a normal toric variety X
- f, a ring element, an element of the coordinate ring of the toric variety X
Outputs:
- a ring element, the class of V(f), [V(f)] in the Chow ring of X

Description

This method finds the class [V(f)] of the hypersurface V(f) where f is a polynomial in the graded coordinate ring of a toric variety X. The class [V(f)] is an element of the Chow ring of X.

i1 : needsPackage "NormalToricVarieties"

o1 = NormalToricVarieties

o1 : Package

i2 : Rho = {{1,0,0},{0,1,0},{0,0,1},{-1,-1,0},{0,0,-1}}

o2 = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {-1, -1, 0}, {0, 0, -1}}

o2 : List

i3 : Sigma = {{0,1,2},{1,2,3},{0,2,3},{0,1,4},{1,3,4},{0,3,4}}

o3 = {{0, 1, 2}, {1, 2, 3}, {0, 2, 3}, {0, 1, 4}, {1, 3, 4}, {0, 3, 4}}

o3 : List

i4 : X = normalToricVariety(Rho,Sigma,CoefficientRing =>ZZ/32749)

o4 = X

o4 : NormalToricVariety

i5 : R=ring X

o5 = R

o5 : PolynomialRing

i6 : Ch=ToricChowRing(X)

o6 = Ch

o6 : QuotientRing

i7 : f=random({1,0},R)

o7 = 107x  + 4376x  - 6316x
         0        1        3

o7 : R

i8 : ClassInToricChowRing(Ch,f)

o8 = -1833x
           3

o8 : Ch

Ways to use ClassInToricChowRing :

ClassInToricChowRing(QuotientRing,RingElement)

For the programmer

The object ClassInToricChowRing is a method function.