Is there a good software package for doing computations in the cohomology ring of Grassmannians? Things like, I can write down a polynomial in, in fact, special Schubert classes, but it's one where doing the multiplication out is too tedious for me to have any chance at accuracy in the final answer, and want an efficient way to tell a computer to do it (things that will just multiply pairs, and then you input the next set of pairs don't count).



Is there a software package that does Schubert Calculus computations?
There's a Littlewood-Richardson calculator here:
<http://math.rutgers.edu/~asbuch/lrcalc/>


I usually use the "SchurRings" package in Macaulay 2 ( <http://www.math.uiuc.edu/Macaulay2/> ) though. No particular reason why, just that Macaulay 2 is something I am used to using. It's very easy to use, here's an example (it doesn't print correctly on this page) where the 4 in the first command means use 4 variables (so we're working in Gr(4, infinity)). 


i1 : S = schurRing(s,4)


o1 = S


o1 : SchurRing


i2 : s\_{2,2} \* s\_{3,1}


o2 = s + s + s + s + s + s + s



```
  5,3    5,2,1    4,3,1    4,2,2    4,2,1,1    3,3,2    3,2,2,1

```

o2 : S


