| Copyright | (c) Stéphane Laurent 2024 |
|---|---|
| License | GPL-3 |
| Maintainer | laurent_step@outlook.fr |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
Math.Algebra.Jack
Description
Evaluation of Jack polynomials, zonal polynomials, Schur polynomials and skew Schur polynomials. See README for examples and references.
Synopsis
- type Partition = [Int]
- jack :: forall a. (Eq a, C a) => [a] -> Partition -> a -> Char -> a
- jack' :: [Rational] -> Partition -> Rational -> Char -> Rational
- zonal :: (Eq a, C a) => [a] -> Partition -> a
- zonal' :: [Rational] -> Partition -> Rational
- schur :: forall a. C a => [a] -> Partition -> a
- schur' :: [Rational] -> Partition -> Rational
- skewSchur :: forall a. (Eq a, C a) => [a] -> Partition -> Partition -> a
- skewSchur' :: [Rational] -> Partition -> Partition -> Rational
The Partition type
Evaluation of Jack polynomials
Arguments
| :: forall a. (Eq a, C a) | |
| => [a] | values of the variables |
| -> Partition | integer partition |
| -> a | Jack parameter |
| -> Char | which Jack polynomial, |
| -> a |
Evaluation of a Jack polynomial.
Arguments
| :: [Rational] | values of the variables |
| -> Partition | partition of integers |
| -> Rational | Jack parameter |
| -> Char | which Jack polynomial, |
| -> Rational |
Evaluation of a Jack polynomial.
Evaluation of zonal polynomials
Evaluation of a zonal polynomial. The zonal polynomials are the Jack \(C\)-polynomials with Jack parameter \(\alpha=2\).
Evaluation of a zonal polynomial. The zonal polynomials are the Jack \(C\)-polynomials with Jack parameter \(\alpha=2\).
Evaluation of Schur and skew Schur polynomials
Evaluation of a Schur polynomial. The Schur polynomials are the Jack \(P\)-polynomials with Jack parameter \(\alpha=1\).
Evaluation of a Schur polynomial. The Schur polynomials are the Jack \(P\)-polynomials with Jack parameter \(\alpha=1\).