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

## Synopsis

• Usage:
ClassInToricChowRing(Ch,f)
• Inputs:
• Ch, , the Chow ring of a normal toric variety X
• f, , an element of the coordinate ring of the toric variety X
• Outputs:
• , 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 .