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# NSC2phc -- dictionary between different notations for Schubert problems.

- Usage:
    `M = NSC2phc(conds,k,n)`
- Inputs:
  - conds, a list, of Schubert conditions, either partitions or brackets, that constitutes a Schubert problem on the Grassmannian $Gr(k,n)$
  - k, an integer,
  - n, an integer, $k$ and $n$ represent the Grassmannian $Gr(k,n)$
- Outputs:
  - a matrix, the corresponding Schubert problem in notation for PHCPack implementation of Littlewood-Richardson rule and homotopies. Its rows encode Schubert conditions with multiplicities. Each row is a $k+1$-tuple, {m,b}, where $m$ is a nonegative integer and $b$ a bracket (see bracket2partition for details). The bracket $b$ represents a Schubert condition and $m$ is its multiplicity in this Schubert intersection problem.

## Description

A Schubert problem in the Grassmannian $Gr(k,n)$ is encoded by either a list of partitions or brackets whose codimensions sum to $k(n-k)$. (see bracket2partition for details on brackets and partitions)

The PHCPack implementations of the geometric Littlewood-Richardson rule encode the brackets in a matrix, where each row has the form ${m, b}$ with $m$ the multiplicity of the bracket $b$, which is a strictly increasing sequence of $k$ integers between $1$ and $n$.

    i1 : k=4;

    i2 : n = 8;

    i3 : SchubProbP = {{2,2},{2,2},{2,2},{1},{1},{1},{1}}

    o3 = {{2, 2}, {2, 2}, {2, 2}, {1}, {1}, {1}, {1}}

    o3 : List

    i4 : NSC2phc(SchubProbP,k,n)

    o4 = | 3 3 4 7 8 |
         | 4 4 6 7 8 |

                  2       5
    o4 : Matrix ZZ  <-- ZZ

    i5 : k=4;

    i6 : n = 8;

    i7 : SchubProbB = {{3,4,7,8},{3,4,7,8},{3,4,7,8},{4,6,7,8},{4,6,7,8},{4,6,7,8},{4,6,7,8}}

    o7 = {{3, 4, 7, 8}, {3, 4, 7, 8}, {3, 4, 7, 8}, {4, 6, 7, 8}, {4, 6, 7, 8},
         ------------------------------------------------------------------------
         {4, 6, 7, 8}, {4, 6, 7, 8}}

    o7 : List

    i8 : NSC2phc(SchubProbB,4,8)

    o8 = | 3 3 4 7 8 |
         | 4 4 6 7 8 |

                  2       5
    o8 : Matrix ZZ  <-- ZZ

## See also

- LRrule -- computes the product of Schubert classes using geometric Littlewood-Richardson rule

## Ways to use NSC2phc:

- `NSC2phc(List,ZZ,ZZ)`

## For the programmer

The object NSC2phc is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NumericalSchubertCalculus/doc.m2:415:0.