# PieriRootCount -- the number of solutions to a generic Pieri problem

## Synopsis

• Usage:
r = PieriRootCount(m,p,q)
• Inputs:
• m, an integer, the dimension of the input planes
• p, an integer, the dimension of the output planes
• q, an integer, the degree of the solution curves producing p-planes
• Optional inputs:
• Verbose => ..., default value false, request verbose feedback
• Outputs:
• r, an integer, the number of curves of the degree $q$ in the Grassmannain $Gr(p,m+p)$ which produce $p$-planes that meet $m\cdot p + q\cdot (m+p)$ generic $m$-planes at given general interpolation points. This is a quantum intersection number

## Description

The example below computes the number of linear curves which produce 2-planes that meet 2*3 + 1*(2 + 3) = eleven generic 3-planes at some eleven distinct interpolation points.

 i1 : r := PieriRootCount(3,2,1); i2 : print r 55

## Ways to use PieriRootCount :

• "PieriRootCount(ZZ,ZZ,ZZ)"

## For the programmer

The object PieriRootCount is .