Îõ³h*&$Þ(      !"#$%&'1.4.1.0 Safe-InferredÝÞ()*+,-./01234Evaluation of Jack polynomials.(c) Stéphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-InferredÝŠjackpolynomialsEvaluation 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)  Symbolic Jack polynomials.(c) Stéphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-InferredÝc jackpolynomialsSymbolic Jack polynomial jackpolynomialsSymbolic Jack polynomial jackpolynomialsSymbolic zonal polynomial jackpolynomialsSymbolic zonal polynomialjackpolynomialsSymbolic Schur polynomialjackpolynomialsSymbolic Schur polynomialjackpolynomialsSymbolic skew Schur polynomialjackpolynomialsSymbolic skew Schur polynomial jackpolynomialsnumber of variablesjackpolynomialspartition of integersjackpolynomialsJack parameterjackpolynomialswhich Jack polynomial, J, C, P or Q jackpolynomialsnumber of variablesjackpolynomialspartition of integersjackpolynomialsJack parameterjackpolynomialswhich Jack polynomial, J, C, P or Q jackpolynomialsnumber of variablesjackpolynomialspartition of integers jackpolynomialsnumber 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-InferredÝãjackpolynomials,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$Some utilities for Jack polynomials.(c) Stéphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-InferredÃÝ$²jackpolynomialsMonomial symmetric polynomial/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.x3^2jackpolynomialsëChecks 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 contextjackpolynomialsÎSymmetric polynomial as a linear combination of monomial symmetric polynomialsjackpolynomialsÒPrints 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 5 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]jackpolynomialsúLaplace-Beltrami operator on the space of homogeneous symmetric polynomials; neither symmetry and homogeneity are checkedjackpolynomialsýCalogero-Sutherland operator on the space of homogeneous symmetric polynomials; neither symmetry and homogeneity are checkedjackpolynomialsPower sum polynomial/putStrLn $ prettyQSpray (psPolynomial 3 [2, 1])?x^3 + x^2.y + x^2.z + x.y^2 + x.z^2 + y^3 + y^2.z + y.z^2 + z^36jackpolynomialsÐmonomial symmetric polynomial as a linear combination of power sum polynomials7jackpolynomials$the factor in the Hall inner product8jackpolynomialsÅsymmetric polynomial as a linear combination of power sum polynomialsjackpolynomialsáSymmetric polynomial as a linear combination of power sum polynomials. Symmetry is not checked.jackpolynomialsÑSymmetric polynomial as a linear combination of power sum polynomials. Same as  psCombination: but with other constraints on the base ring of the spray.9jackpolynomials%the Hall inner product with parameter jackpolynomialsïHall inner product with parameter. It makes sense only for symmetric sprays, and the symmetry is not checked. !jackpolynomials+Hall inner product with parameter. Same as hallInnerProduct= but with other constraints on the base ring of the sprays."jackpolynomials+Hall inner product with parameter. Same as hallInnerProductÔ but with other constraints on the base ring of the sprays. It is applicable to  Spray Int sprays.#jackpolynomialsßHall inner product with parameter for parametric sprays, because the type of the parameter in hallInnerProduct is strange. For example, a ParametricQSpray spray is a Spray RatioOfQSpraysÄ spray, and it makes more sense to compute the Hall product with a Rational5 parameter then to compute the Hall product with a RatioOfQSprays parameter.-import Math.Algebra.Jack.SymmetricPolynomials#import Math.Algebra.JackSymbolicPolimport Math.Algebra.Hspray!jp = jackSymbolicPol 3 [2, 1] 'P'ÏhallInnerProduct''' jp jp 5 == hallInnerProduct jp jp (constantRatioOfSprays 5)$jackpolynomialsÃHall inner product with parameter for parametric sprays. Same as hallInnerProduct'''À but with other constraints on the types. It is applicable to SimpleParametricQSpray sprays, while hallInnerProduct''' is not.:jackpolynomials.the Hall inner product with symbolic parameter%jackpolynomialsÉHall inner product with symbolic parameter. See README for some examples.&jackpolynomials4Hall inner product with symbolic parameter. Same as symbolicHallInnerProduct# but with other type constraints.'jackpolynomials4Hall inner product with symbolic parameter. Same as symbolicHallInnerProduct8 but with other type constraints. It is applicable to  Spray Int sprays.jackpolynomialsnumber of variablesjackpolynomialsinteger partitionjackpolynomialsnumber of variablesjackpolynomialsinteger partition9jackpolynomialssprayjackpolynomialssprayjackpolynomials parameter jackpolynomialssprayjackpolynomialssprayjackpolynomials parameter!jackpolynomialssprayjackpolynomialssprayjackpolynomials parameter"jackpolynomialssprayjackpolynomialssprayjackpolynomials parameter#jackpolynomialsparametric sprayjackpolynomialsparametric sprayjackpolynomials parameter$jackpolynomialsparametric sprayjackpolynomialsparametric sprayjackpolynomials parameter !"#$%&' !"#$%&';      !"#$%&'()*+,-./0123456789:;<=>?@ABCDÅ.jackpolynomials-1.4.1.0-KVoEozHY29D9zAsO5gfWleMath.Algebra.JackMath.Algebra.Jack.HypergeoPQMath.Algebra.JackPolMath.Algebra.JackSymbolicPol!Math.Algebra.SymmetricPolynomialsjackpolynomialsMath.Algebra.Jack.Internal Partitionjack'jackzonal'zonalschur'schur skewSchur' skewSchur hypergeoPQjackPol'jackPol zonalPol'zonalPol schurPol'schurPol skewSchurPol' skewSchurPoljackSymbolicPol'jackSymbolicPol msPolynomialisSymmetricSpray msCombinationprettySymmetricNumSprayprettySymmetricQSprayprettySymmetricQSpray'prettySymmetricParametricQSpraylaplaceBeltramicalogeroSutherland psPolynomial psCombinationpsCombination'hallInnerProducthallInnerProduct'hallInnerProduct''hallInnerProduct'''hallInnerProduct''''symbolicHallInnerProductsymbolicHallInnerProduct'symbolicHallInnerProduct'' jackCoeffP jackCoeffQ jackCoeffCjackSymbolicCoeffCjackSymbolicCoeffPinvjackSymbolicCoeffQinv _betaratio_betaRatioOfSprays _isPartition_N_fromIntskewSchurLRCoefficientsisSkewPartition%hspray-0.5.2.0-1E9VAR3DXwPFTQIGvv3h5zMath.Algebra.HsprayQSpray' mspInPSbasiszlambda_psCombination_hallInnerProduct_symbolicHallInnerProduct