next | previous | forward | backward | up | top | index | toc | Macaulay2 website
NumericalSchubertCalculus :: LRnumber

LRnumber -- returns the number of solutions to the given Schubert problem

Synopsis

Description

This first verifies that the conditions are either all partitions or all brackets, and that they form a Schubert problem on $Gr(k,n)$.

Then it computes the intersection number of the prodiuct of Schubert classes in the cohomology ring of the Grassmannnian

For instance, the problem of four lines is given by 4 partitions {1}$^4$ in $Gr(2,4)$

i1 : LRnumber({{1},{1},{1},{1}},2,4)

o1 = 2

the same problem but using brackets instead of partitions

i2 : LRnumber({{2,4},{2,4},{2,4},{2,4}},2,4)

o2 = 2

the same problem but using phc implementation of Littlewood-Richardson rule

i3 : LRnumber({{1},{1},{1},{1}},2,4,Strategy => "phc")

o3 = 2

Caveat

This uses the package Schubert2 and the Strategy "phc" requires the string parsing capabilities of Macaulay2 version 1.17 or later

See also

Ways to use LRnumber :

For the programmer

The object LRnumber is a method function with options.