# Implement intersection products

I am doing a counting problem, and it comes to compute intersection products ( Chow ring ) on some varieties. Is there any computer algebra that deals with this?

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If not, then see here: mathoverflow.net/questions/18440 –  Steve Huntsman Mar 18 '10 at 3:12
Also, many enumeration problems deal with toric varieties, for which see here: portal.acm.org/citation.cfm?id=1243161 –  Steve Huntsman Mar 18 '10 at 3:14

Schubert2 in Macaulay2 and the original maple package schubert let you build enough of the chow rings of parameter spaces to tackle some enumerative geometry problems like those of "Kalkül der abzählenden Geometrie" by H. Schubert (1879):

### Count the number of space conics intersecting 8 given lines

> with(schubert):

> grass(3,4,d,all):

> Proj(f,dual(symm(2,Qd)),e):

> integral(Gd,lowerstar(f,(2*d1+e)^8));

                                  92


(Example 3.2.22 of "Intersection Theory" by W. Fulton (1984))

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