diff --git a/CHANGELOG.md b/CHANGELOG.md --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -10,3 +10,8 @@ ------- * replaced the 'mpolynomials' dependency with 'hspray' * unit tests + +1.1.0.1 +------- +* unexported some useless functions +* one more unit test diff --git a/README.md b/README.md --- a/README.md +++ b/README.md @@ -5,6 +5,8 @@ [Jack polynomials](https://en.wikipedia.org/wiki/Jack_function). This package allows to evaluate these polynomials. It can also compute their symbolic form. +___ + ```haskell import Math.Algebra.Jack import Data.Ratio @@ -22,3 +24,12 @@ evalSpray jp [1, 1] -- 48 % 1 ``` + + +## References + +* I.G. Macdonald. *Symmetric Functions and Hall Polynomials*. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, second edition, 1995. + +* J. Demmel and P. Koev. *Accurate and efficient evaluation of Schur and Jack functions*. Mathematics of computations, vol. 75, n. 253, 223-229, 2005. + +* Jack polynomials. . diff --git a/jackpolynomials.cabal b/jackpolynomials.cabal --- a/jackpolynomials.cabal +++ b/jackpolynomials.cabal @@ -1,53 +1,47 @@ -cabal-version: >=1.10 -name: jackpolynomials -version: 1.1.0.0 -license: GPL-3 -license-file: LICENSE -copyright: 2022 Stéphane Laurent -maintainer: laurent_step@outlook.fr -author: Stéphane Laurent -homepage: https://github.com/stla/jackpolynomials#readme -synopsis: Jack, zonal, and Schur polynomials -description: - This library can evaluate Jack polynomials, zonal polynomials and Schur polynomials. It is also able to compute them in symbolic form. - -category: Math, Algebra -build-type: Simple -extra-source-files: - README.md - CHANGELOG.md - -source-repository head - type: git - location: https://github.com/stla/jackpolynomials +name: jackpolynomials +version: 1.1.0.1 +synopsis: Jack, zonal, and Schur polynomials +description: This library can evaluate Jack polynomials, zonal polynomials and Schur polynomials. It is also able to compute them in symbolic form. +homepage: https://github.com/stla/jackpolynomials#readme +license: GPL-3 +license-file: LICENSE +author: Stéphane Laurent +maintainer: laurent_step@outlook.fr +copyright: 2022 Stéphane Laurent +category: Math, Algebra +build-type: Simple +extra-source-files: README.md + CHANGELOG.md +cabal-version: >=1.10 library - exposed-modules: - Math.Algebra.Jack.GPochhammer - Math.Algebra.Jack - Math.Algebra.JackPol - - hs-source-dirs: src - other-modules: Math.Algebra.Jack.Internal - default-language: Haskell2010 - ghc-options: -Wall - build-depends: - base >=4.7 && <5, - ilist >=0.4.0.1, - array >=0.5.4.0, - lens >=5.0.1, - math-functions >=0.3.4.2, - hspray >=0.1.0.0, - numeric-prelude >=0.4.4 + hs-source-dirs: src + exposed-modules: Math.Algebra.Jack.HypergeoPQ + , Math.Algebra.Jack + , Math.Algebra.JackPol + other-modules: Math.Algebra.Jack.Internal + build-depends: base >= 4.7 && < 5 + , ilist >= 0.4.0.1 + , array >= 0.5.4.0 + , lens >= 5.0.1 + , math-functions >= 0.3.4.2 + , hspray >= 0.1.0.0 + , numeric-prelude >= 0.4.4 + default-language: Haskell2010 + ghc-options: -Wall test-suite unit-tests - type: exitcode-stdio-1.0 - main-is: Main.hs - hs-source-dirs: tests/ - default-language: Haskell2010 - build-depends: - base >=4.7 && <5, - tasty, - tasty-hunit, - jackpolynomials, - hspray + type: exitcode-stdio-1.0 + main-is: Main.hs + hs-source-dirs: tests/ + Build-Depends: base >= 4.7 && < 5 + , tasty + , tasty-hunit + , jackpolynomials + , hspray + , hypergeomatrix + Default-Language: Haskell2010 + +source-repository head + type: git + location: https://github.com/stla/jackpolynomials diff --git a/src/Math/Algebra/Jack/GPochhammer.hs b/src/Math/Algebra/Jack/GPochhammer.hs deleted file mode 100644 --- a/src/Math/Algebra/Jack/GPochhammer.hs +++ /dev/null @@ -1,40 +0,0 @@ -module Math.Algebra.Jack.GPochhammer where -import Math.Algebra.Jack (zonal) - -gpochhammer :: Fractional a => a -> [Int] -> a -> a -gpochhammer a kappa alpha = - product $ - map (\i -> product $ - map (\j -> a - (fromIntegral i - 1)/alpha + fromIntegral j -1) - [1 .. kappa !! (i-1)]) - [1 .. length kappa] - -hcoeff :: Fractional a => [a] -> [a] -> [Int] -> a -> a -hcoeff a b kappa alpha = - numerator / denominator / fromIntegral (factorial (sum kappa)) - where - factorial n = product [1 .. n] - numerator = product $ map (\x -> gpochhammer x kappa alpha) a - denominator = product $ map (\x -> gpochhammer x kappa alpha) b - -testHypergeo :: Double -testHypergeo = - let a = [2,3] in - let b = [4] in - let coeff kappa = hcoeff a b kappa 2 in - let kappas = [[], [1], [1,1], [2]] in - let x = [5,6] in - sum $ map (\kappa -> coeff kappa * zonal x kappa) kappas - -_allPartitions :: Int -> [[Int]] -_allPartitions m = last ps - where - ps = [] : map parts [1..m] - parts n = [n] : [x : p | x <- [1..n], p <- ps !! (n - x), x <= head p] - -hypergeoPQ :: (Fractional a, Ord a) => Int -> [a] -> [a] -> [a] -> a -hypergeoPQ m a b x = - sum $ map (\kappa -> coeff kappa * zonal x kappa) kappas - where - kappas = filter (\kap -> length kap <= length x) (_allPartitions m) - coeff kappa = hcoeff a b kappa 2 diff --git a/src/Math/Algebra/Jack/HypergeoPQ.hs b/src/Math/Algebra/Jack/HypergeoPQ.hs new file mode 100644 --- /dev/null +++ b/src/Math/Algebra/Jack/HypergeoPQ.hs @@ -0,0 +1,33 @@ +module Math.Algebra.Jack.HypergeoPQ + ( hypergeoPQ, _allPartitions + ) where +import Math.Algebra.Jack ( zonal ) + +gpochhammer :: Fractional a => a -> [Int] -> a -> a +gpochhammer a kappa alpha = product $ map + (\i -> product $ map + (\j -> a - (fromIntegral i - 1) / alpha + fromIntegral j - 1) + [1 .. kappa !! (i - 1)] + ) + [1 .. length kappa] + +hcoeff :: Fractional a => [a] -> [a] -> [Int] -> a -> a +hcoeff a b kappa alpha = numerator / denominator / + fromIntegral (factorial (sum kappa)) + where + factorial n = product [1 .. n] + numerator = product $ map (\x -> gpochhammer x kappa alpha) a + denominator = product $ map (\x -> gpochhammer x kappa alpha) b + +_allPartitions :: Int -> [[Int]] +_allPartitions m = [[]] ++ (map reverse (concat ps)) + where + ps = [] : map parts [1 .. m] + parts n = [n] : [ x : p | x <- [1 .. n], p <- ps !! (n - x), x <= head p ] + +-- | Inefficient hypergeometric function of a matrix argument +hypergeoPQ :: (Fractional a, Ord a) => Int -> [a] -> [a] -> [a] -> a +hypergeoPQ m a b x = sum $ map (\kappa -> coeff kappa * zonal x kappa) kappas + where + kappas = filter (\kap -> length kap <= length x) (_allPartitions m) + coeff kappa = hcoeff a b kappa 2 diff --git a/tests/Main.hs b/tests/Main.hs --- a/tests/Main.hs +++ b/tests/Main.hs @@ -1,61 +1,65 @@ module Main where -import Math.Algebra.JackPol -import Math.Algebra.Jack -import Data.Ratio -import Math.Algebra.Hspray -import Test.Tasty (defaultMain, testGroup) -import Test.Tasty.HUnit (assertEqual, testCase) +import Data.Ratio +import Math.Algebra.Hspray +import Math.Algebra.Jack +import Math.Algebra.Jack.HypergeoPQ +import Math.Algebra.JackPol +import Math.HypergeoMatrix +import Test.Tasty ( defaultMain + , testGroup + ) +import Test.Tasty.HUnit ( assertEqual + , testCase + ) main :: IO () -main = defaultMain $ - testGroup "Tests" +main = defaultMain $ testGroup + + "Tests" + [ testCase "jackPol" $ do - let jp = jackPol 2 [3, 1] (2%1) - let v = evalSpray jp [1, 1] - assertEqual "" - v - (48%1), + let jp = jackPol 2 [3, 1] (2 % 1) + v = evalSpray jp [1, 1] + assertEqual "" v (48 % 1) - testCase "jack" $ do - assertEqual "" - (jack [1, 1] [3, 1] (2%1)) - (48%1), + , testCase "jack" $ do + assertEqual "" (jack [1, 1] [3, 1] (2 % 1)) (48 % 1) - testCase "schurPol" $ do - let sp1 = schurPol 4 [4] - let sp2 = schurPol 4 [3, 1] - let sp3 = schurPol 4 [2, 2] - let sp4 = schurPol 4 [2, 1, 1] - let sp5 = schurPol 4 [1, 1, 1, 1] - let v = evalSpray (sp1 ^+^ 3 *^ sp2 ^+^ 2*^ sp3 ^+^ 3*^ sp4 ^+^ sp5) [2, 2, 2, 2] - assertEqual "" - v - 4096, + , testCase "schurPol" $ do + let sp1 = schurPol 4 [4] + sp2 = schurPol 4 [3, 1] + sp3 = schurPol 4 [2, 2] + sp4 = schurPol 4 [2, 1, 1] + sp5 = schurPol 4 [1, 1, 1, 1] + v = evalSpray (sp1 ^+^ 3 *^ sp2 ^+^ 2 *^ sp3 ^+^ 3 *^ sp4 ^+^ sp5) [2, 2, 2, 2] + assertEqual "" v 4096 - testCase "schur" $ do - let sp1 = schur [1, 1, 1, 1] [4] - let sp2 = schur [1, 1, 1, 1] [3, 1] - let sp3 = schur [1, 1, 1, 1] [2, 2] - let sp4 = schur [1, 1, 1, 1] [2, 1, 1] - let sp5 = schur [1, 1, 1, 1] [1, 1, 1, 1] - assertEqual "" - (sp1 + 3*sp2 + 2*sp3 + 3*sp4 + sp5) - 256, + , testCase "schur" $ do + let sp1 = schur [1, 1, 1, 1] [4] + sp2 = schur [1, 1, 1, 1] [3, 1] + sp3 = schur [1, 1, 1, 1] [2, 2] + sp4 = schur [1, 1, 1, 1] [2, 1, 1] + sp5 = schur [1, 1, 1, 1] [1, 1, 1, 1] + assertEqual "" (sp1 + 3 * sp2 + 2 * sp3 + 3 * sp4 + sp5) 256 - testCase "zonalPol" $ do - let zp1 = zonalPol 4 [3] :: Spray Rational - let zp2 = zonalPol 4 [2, 1] :: Spray Rational - let zp3 = zonalPol 4 [1, 1, 1] :: Spray Rational - let v = evalSpray (zp1 ^+^ zp2 ^+^ zp3) [2, 2, 2, 2] - assertEqual "" - v - 512, + , testCase "zonalPol" $ do + let zp1 = zonalPol 4 [3] :: Spray Rational + zp2 = zonalPol 4 [2, 1] :: Spray Rational + zp3 = zonalPol 4 [1, 1, 1] :: Spray Rational + v = evalSpray (zp1 ^+^ zp2 ^+^ zp3) [2, 2, 2, 2] + assertEqual "" v 512 - testCase "zonal" $ do - let zp1 = zonal [2%1, 2%1, 2%1, 2%1] [3] - let zp2 = zonal [2%1, 2%1, 2%1, 2%1] [2, 1] - let zp3 = zonal [2%1, 2%1, 2%1, 2%1] [1, 1, 1] - assertEqual "" - (zp1 + zp2 + zp3) - 512 + , testCase "zonal" $ do + let zp1 = zonal [2 % 1, 2 % 1, 2 % 1, 2 % 1] [3] + zp2 = zonal [2 % 1, 2 % 1, 2 % 1, 2 % 1] [2, 1] + zp3 = zonal [2 % 1, 2 % 1, 2 % 1, 2 % 1] [1, 1, 1] + assertEqual "" (zp1 + zp2 + zp3) 512 + + , testCase "hypergeometric function" $ do + let a = [1 % 1, 2 % 1] + b = [3 % 1] + x = [1 % 5, 1 % 2] + h1 = hypergeoPQ 10 a b x + h2 <- hypergeomat 10 2 a b x + assertEqual "" h1 h2 ]