Îõ³h*”Á     1.3.0.0 Safe-InferredÝÙjackpolynomialsaddition of a term to a spray !"#$%&'(Evaluation of Jack polynomials.(c) Stéphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-InferredÝ…jackpolynomialsEvaluation of Jack polynomialjackpolynomialsEvaluation of Jack polynomialjackpolynomialsEvaluation of zonal polynomialjackpolynomialsEvaluation of zonal polynomialjackpolynomialsEvaluation of Schur polynomialjackpolynomialsEvaluation of Schur polynomialjackpolynomials%Evaluation of a skew Schur polynomialjackpolynomials%Evaluation of a skew Schur polynomialjackpolynomialsvalues of the variablesjackpolynomialspartition of integersjackpolynomialsJack parameterjackpolynomialswhich Jack polynomial, J, C, P or Qjackpolynomialsvalues of the variablesjackpolynomialspartition of integersjackpolynomialsJack parameterjackpolynomialswhich Jack polynomial, J, C, P or Qjackpolynomialsvalues of the variablesjackpolynomialspartition of integersjackpolynomialsvalues of the variablesjackpolynomialspartition of integersjackpolynomialsvalues of the variablesjackpolynomialspartition of integers jackpolynomialsvalues of the variablesjackpolynomialspartition of integers jackpolynomialsvalues of the variablesjackpolynomials)the outer partition of the skew partitionjackpolynomials)the inner partition of the skew partitionjackpolynomialsvalues of the variablesjackpolynomials)the outer partition of the skew partitionjackpolynomials)the inner partition of the skew partition Safe-Inferred jackpolynomialsÎInefficient hypergeometric function of a matrix argument (for testing purpose)$Some utilities for Jack polynomials.(c) Stéphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-Inferred ñ jackpolynomialsMonomial symmetric polynomials/putStrLn $ prettySpray' (msPolynomial 3 [2, 1])Ñ(1) x1^2.x2 + (1) x1^2.x3 + (1) x1.x2^2 + (1) x1.x3^2 + (1) x2^2.x3 + (1) x2.x3^2 jackpolynomialsëChecks whether a spray defines a symmetric polynomial; this is useless for Jack polynomials because they always are symmetric, but this module contains everything needed to build this function which can be useful in another context jackpolynomialsÎSymmetric polynomial as a linear combination of monomial symmetric polynomials jackpolynomialsÒPrints a symmetric spray as a linear combination of monomial symmetric polynomials:putStrLn $ prettySymmetricNumSpray $ schurPol' 3 [3, 1, 1]M[3,1,1] + M[2,2,1] jackpolynomialsÒPrints a symmetric spray as a linear combination of monomial symmetric polynomials=putStrLn $ prettySymmetricQSpray $ jackPol' 3 [3, 1, 1] 2 'J'42*M[3,1,1] + 28*M[2,2,1]jackpolynomialsSame as   but for a ) symmetric sprayjackpolynomialsßPrints a symmetric parametric spray as a linear combination of monomial symmetric polynomialsÓputStrLn $ prettySymmetricParametricQSpray ["a"] $ jackSymbolicPol' 3 [3, 1, 1] 'J'={ [ 4*a^2 + 10*a + 6 ] }*M[3,1,1] + { [ 8*a + 12 ] }*M[2,2,1] jackpolynomialsnumber of variablesjackpolynomialsinteger partition  Symbolic Jack polynomials.(c) Stéphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-InferredÝ9jackpolynomialsSymbolic Jack polynomialjackpolynomialsSymbolic Jack polynomialjackpolynomialsSymbolic zonal polynomialjackpolynomialsSymbolic zonal polynomialjackpolynomialsSymbolic Schur polynomialjackpolynomialsSymbolic Schur polynomialjackpolynomialsSymbolic skew Schur polynomialjackpolynomialsSymbolic skew Schur polynomialjackpolynomialsnumber of variablesjackpolynomialspartition of integersjackpolynomialsJack parameterjackpolynomialswhich Jack polynomial, J, C, P or Qjackpolynomialsnumber of variablesjackpolynomialspartition of integersjackpolynomialsJack parameterjackpolynomialswhich Jack polynomial, J, C, P or Qjackpolynomialsnumber of variablesjackpolynomialspartition of integersjackpolynomialsnumber of variablesjackpolynomialspartition of integersjackpolynomialsnumber of variablesjackpolynomialspartition of integersjackpolynomialsnumber of variablesjackpolynomialspartition of integersjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partition.Jack polynomials with symbolic Jack parameter.(c) Stéphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-Inferredݹjackpolynomials,Jack polynomial with symbolic Jack parameterjackpolynomials,Jack polynomial with symbolic Jack parameterjackpolynomialsnumber of variablesjackpolynomialspartition of integersjackpolynomialswhich Jack polynomial, J, C, P or Qjackpolynomialsnumber of variablesjackpolynomialspartition of integersjackpolynomialswhich Jack polynomial, J, C, P or Q*      !"#$%&'()*+,-./01234-jackpolynomials-1.3.0.0-Fps5PhZ3acVxg1NwG1ccoMath.Algebra.JackMath.Algebra.Jack.HypergeoPQ&Math.Algebra.Jack.SymmetricPolynomialsMath.Algebra.JackPolMath.Algebra.JackSymbolicPoljackpolynomialsMath.Algebra.Jack.Internaljack'jackzonal'zonalschur'schur skewSchur' skewSchur hypergeoPQ msPolynomialisSymmetricSpray msCombinationprettySymmetricNumSprayprettySymmetricQSprayprettySymmetricQSpray'prettySymmetricParametricQSprayjackPol'jackPol zonalPol'zonalPol schurPol'schurPol skewSchurPol' skewSchurPoljackSymbolicPol'jackSymbolicPoladdTerm Partition jackCoeffP jackCoeffQ jackCoeffCjackSymbolicCoeffCjackSymbolicCoeffPinvjackSymbolicCoeffQinv _betaratio_betaRatioOfSprays _isPartition_N_fromIntskewSchurLRCoefficientsisSkewPartition$hspray-0.4.0.0-WyxFWMJoceDFdFfsHDrjMMath.Algebra.HsprayQSpray'