h*G      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefgh1.4.7.0  Safe-Inferredijackpolynomialsmonomial symmetric polynomialjjackpolynomials elementary symmetric polynomial.kjackpolynomialsJack polynomial for alpha=0.ljackpolynomials9monomial symmetric polynomials in Schur polynomials basismjackpolynomialsmonomial symmetric polynomial in Hall-Littlewood P-polynomials basisijackpolynomialsnumber of variablesjackpolynomialsinteger partitionjjackpolynomialsnumber of variablesjackpolynomialsinteger partitionkjackpolynomialsnumber of variablesjackpolynomialsinteger partition3ijknopqrstuvwxyz{|}~mEvaluation of Jack polynomials.(c) Stphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-Inferred jackpolynomials Evaluation of a Jack polynomial.jackpolynomials Evaluation of a Jack polynomial.jackpolynomialsEvaluation of a zonal polynomial. The zonal polynomials are the Jack C!-polynomials with Jack parameter \alpha=2.jackpolynomialsEvaluation of a zonal polynomial. The zonal polynomials are the Jack C!-polynomials with Jack parameter \alpha=2.jackpolynomialsEvaluation of a Schur polynomial. The Schur polynomials are the Jack P!-polynomials with Jack parameter \alpha=1.jackpolynomialsEvaluation of a Schur polynomial. The Schur polynomials are the Jack P!-polynomials with Jack parameter \alpha=1.jackpolynomials%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 variablesjackpolynomialsinteger partition jackpolynomialsJack parameterjackpolynomialswhich Jack polynomial, J, C, P or Qjackpolynomialsvalues of the variablesjackpolynomialsinteger partition jackpolynomialsvalues of the variablesjackpolynomialspartition of integersjackpolynomialsvalues of the variablesjackpolynomialsinteger partition jackpolynomialsvalues of the variablesjackpolynomialsinteger partition 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 $ jackpolynomialsInefficient hypergeometric function of a matrix argument (for testing purpose)  Symbolic Jack polynomials.(c) Stphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-Inferred jackpolynomialsJack polynomial. jackpolynomialsJack polynomial. jackpolynomialsSkew Jack polynomial. jackpolynomialsSkew Jack polynomial.jackpolynomials7Zonal polynomial. The zonal polynomials are the Jack C!-polynomials with Jack parameter \alpha=2.jackpolynomials7Zonal polynomial. The zonal polynomials are the Jack C!-polynomials with Jack parameter \alpha=2.jackpolynomialsSkew zonal polynomial.jackpolynomialsSkew zonal polynomial.jackpolynomials7Schur polynomial. The Schur polynomials are the Jack P!-polynomials with Jack parameter \alpha=1.jackpolynomials7Schur polynomial. The Schur polynomials are the Jack P!-polynomials with Jack parameter \alpha=1.jackpolynomialsSkew Schur polynomialjackpolynomialsSkew Schur polynomial jackpolynomialsnumber of variablesjackpolynomialsinteger partition jackpolynomialsJack parameterjackpolynomialswhich Jack polynomial, J, C, P or Q jackpolynomialsnumber of variablesjackpolynomialsinteger partition jackpolynomialsJack parameterjackpolynomialswhich Jack polynomial, J, C, P or Q jackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomialsJack parameterjackpolynomialswhich skew Jack polynomial, J, C, P or Q jackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomialsJack parameterjackpolynomialswhich skew Jack polynomial, J, C, P or Qjackpolynomialsnumber 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 partitionjackpolynomialsnumber 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) Stphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-Inferredjackpolynomials/Jack polynomial with a symbolic Jack parameter.jackpolynomials/Jack polynomial with a symbolic Jack parameter.jackpolynomials4Skew Jack polynomial with a symbolic Jack parameter.jackpolynomials4Skew Jack polynomial with a symbolic Jack parameter.jackpolynomialsnumber of variablesjackpolynomialsinteger partition jackpolynomialswhich Jack polynomial, J, C, P or Qjackpolynomialsnumber of variablesjackpolynomialsinteger partition jackpolynomialswhich Jack polynomial, J, C, P or Qjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomialswhich skew Jack polynomial, J, C, P or Qjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomialswhich skew Jack polynomial, J, C, P or QMore symmetric polynomials.(c) Stphane Laurent, 2024GPL-3laurent_step@outlook.fr Safe-InferredjackpolynomialsMonomial symmetric polynomial/putStrLn $ prettySpray' (msPolynomial 3 [2, 1])(1) x1^2.x2 + (1) x1^2.x3 + (1) x1.x2^2 + (1) x1.x3^2 + (1) x2^2.x3 + (1) x2.x3^2jackpolynomials6Checks whether a spray defines a symmetric polynomial.-- note that the sum of two symmetric polynomials is not symmetric/-- if they have different numbers of variables:1spray = schurPol' 4 [2, 2] ^+^ schurPol' 3 [2, 1]isSymmetricSpray sprayjackpolynomialsSymmetric polynomial as a linear combination of monomial symmetric polynomials.jackpolynomialsPrints 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]jackpolynomialsPrints 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 spray jackpolynomialsPrints a symmetric parametric spray as a linear combination of monomial symmetric polynomials.putStrLn $ 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]!jackpolynomialsPrints a symmetric simple parametric spray as a linear combination of monomial symmetric polynomials."jackpolynomialsLaplace-Beltrami operator on the space of homogeneous symmetric polynomials; neither symmetry and homogeneity are checked.#jackpolynomialsCalogero-Sutherland operator on the space of homogeneous symmetric polynomials; neither symmetry and homogeneity are checked$jackpolynomialsPower 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^3jackpolynomialsmonomial symmetric polynomial as a linear combination of power sum polynomialsjackpolynomials$the factor in the Hall inner productjackpolynomialssymmetric polynomial as a linear combination of power sum polynomials%jackpolynomialsSymmetric polynomial as a linear combination of power sum polynomials. Symmetry is not checked.&jackpolynomialsSymmetric polynomial as a linear combination of power sum polynomials. Same as  psCombination: but with other constraints on the base ring of the spray.'jackpolynomialsSymmetric parametric spray as a linear combination of power sum polynomials. jackpolynomials%the Hall inner product with parameter(jackpolynomialsHall inner product with Jack parameter, aka Jack scalar product. It makes sense only for symmetric sprays, and the symmetry is not checked. )jackpolynomials0Hall inner product with Jack parameter. Same as hallInnerProduct= but with other constraints on the base ring of the sprays.*jackpolynomials0Hall inner product with Jack parameter. Same as hallInnerProduct but with other constraints on the base ring of the sprays. It is applicable to  Spray Int sprays.+jackpolynomialsHall inner product with Jack parameter for parametric sprays, because the type of the parameter in hallInnerProduct is strange. For example, a ParametricQSpray spray is a Spray RatioOfQSprays 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'hallInnerProduct''' jp jp 5 == hallInnerProduct jp jp (constantRatioOfSprays 5),jackpolynomialsHall inner product with Jack parameter for parametric sprays. Same as hallInnerProduct''' 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-jackpolynomialsHall inner product with symbolic Jack parameter. See README for some examples..jackpolynomials9Hall inner product with symbolic Jack parameter. Same as symbolicHallInnerProduct# but with other type constraints./jackpolynomials9Hall inner product with symbolic Jack parameter. Same as symbolicHallInnerProduct8 but with other type constraints. It is applicable to  Spray Int sprays.0jackpolynomials)Complete symmetric homogeneous polynomial0putStrLn $ prettyQSpray (cshPolynomial 3 [2, 1])x^3 + 2*x^2.y + 2*x^2.z + 2*x.y^2 + 3*x.y.z + 2*x.z^2 + y^3 + 2*y^2.z + 2*y.z^2 + z^3jackpolynomialspower sum polynomial as a linear combination of complete symmetric homogeneous polynomialsjackpolynomialsmonomial symmetric polynomial as a linear combination of complete symmetric homogeneous polynomialsjackpolynomialssymmetric polynomial as a linear combination of complete symmetric homogeneous polynomials1jackpolynomialsSymmetric polynomial as a linear combination of complete symmetric homogeneous polynomials. Symmetry is not checked.2jackpolynomialsSymmetric polynomial as a linear combination of complete symmetric homogeneous polynomials. Same as cshCombination: but with other constraints on the base ring of the spray.3jackpolynomials Elementary symmetric polynomial./putStrLn $ prettyQSpray (esPolynomial 3 [2, 1])7x^2.y + x^2.z + x.y^2 + 3*x.y.z + x.z^2 + y^2.z + y.z^2jackpolynomialspower sum polynomial as a linear combination of elementary symmetric polynomialsjackpolynomialsmonomial symmetric polynomial as a linear combination of elementary symmetric polynomialsjackpolynomialssymmetric polynomial as a linear combination of elementary symmetric polynomials4jackpolynomialsSymmetric polynomial as a linear combination of elementary symmetric polynomials. Symmetry is not checked.5jackpolynomialsSymmetric polynomial as a linear combination of elementary symmetric polynomials. Same as  esCombination: but with other constraints on the base ring of the spray.jackpolynomialscomplete symmetric homogeneous polynomial as a linear combination of Schur polynomialsjackpolynomialssymmetric polynomial as a linear combination of Schur polynomials6jackpolynomialsSymmetric polynomial as a linear combination of Schur polynomials. Symmetry is not checked.7jackpolynomialsSymmetric polynomial as a linear combination of Schur polynomials. Same as schurCombination: but with other constraints on the base ring of the spray.jackpolynomials8monomial symmetric polynomials in Jack polynomials basisjackpolynomials8monomial symmetric polynomials in Jack polynomials basis8jackpolynomialsSymmetric polynomial as a linear combination of Jack polynomials with a given Jack parameter. Symmetry is not checked.9jackpolynomialsSymmetric parametric polynomial as a linear combination of Jack polynomials with a given Jack parameter. Symmetry is not checked. Similar to jackCombination but for a parametric spray.:jackpolynomialsSymmetric polynomial as a linear combination of Jack polynomials with symbolic parameter. Symmetry is not checked.;jackpolynomialsSymmetric parametric polynomial as a linear combination of Jack polynomials with symbolic parameter. Similar to jackSymbolicCombination but for a parametric spray.jackpolynomialssymmetric simple parametric spray as a linear combination of Hall-Littlewood P-polynomials <jackpolynomialsHall polynomials g^{\lambda}_{\mu,\nu}(t) for given integer partitions \mu and \nu. The keys of the map returned by this function are the partitions \lambda! and the value attached to a key \lambda is the Hall polynomial g^{\lambda}_{\mu,\nu}(t) (it is given as a QSpray9 spray but actually all its coefficients are integer). Warning: slow.=jackpolynomialsKostka-Foulkes polynomial of two given partitions. This is a univariate polynomial whose value at 1, is the Kostka number of the two partitions.>jackpolynomialsKostka-Foulkes polynomial of two given partitions. This is a univariate polynomial whose value at 1, is the Kostka number of the two partitions.?jackpolynomialsSkew Kostka-Foulkes polynomial. This is a univariate polynomial associated to a skew partition and a partition, and its value at 1< is the skew Kostka number associated to these partitions.@jackpolynomialsSkew Kostka-Foulkes polynomial. This is a univariate polynomial associated to a skew partition and a partition, and its value at 1< is the skew Kostka number associated to these partitions.Ajackpolynomialsqt-Kostka polynomials, aka Kostka-Macdonald polynomials. These are bivariate polynomials usually denoted by K_{\lambda, \mu}(q,t) for two integer partitions \lambda and mu, and q and t denote the variables. One obtains the Kostka-Foulkes polynomials by substituting q with 0. For a given partition \mu(, the function returns the polynomials K_{\lambda, \mu}(q,t) for all partitions \lambda of the same weight as \mu.Bjackpolynomialsqt-Kostka polynomials, aka Kostka-Macdonald polynomials. These are bivariate polynomials usually denoted by K_{\lambda, \mu}(q,t) for two integer partitions \lambda and mu, and q and t denote the variables. One obtains the Kostka-Foulkes polynomials by substituting q with 0. For a given partition \mu(, the function returns the polynomials K_{\lambda, \mu}(q,t) for all partitions \lambda of the same weight as \mu.CjackpolynomialsSkew qt-Kostka polynomials. These are bivariate polynomials usually denoted by K_{\lambda/\mu, \nu}(q,t) for two integer partitions \lambda and mu3 defining a skew partition, an integer partition \nu, and q and t denote the variables. One obtains the skew Kostka-Foulkes polynomials by substituting q with 0. For given partitions \lambda and \mu), the function returns the polynomials K_{\lambda/\mu, \nu}(q,t) for all partitions \nu, of the same weight as the skew partition.DjackpolynomialsSkew qt-Kostka polynomials. These are bivariate polynomials usually denoted by K_{\lambda/\mu, \nu}(q,t) for two integer partitions \lambda and mu3 defining a skew partition, an integer partition \nu, and q and t denote the variables. One obtains the skew Kostka-Foulkes polynomials by substituting q with 0. For given partitions \lambda and \mu), the function returns the polynomials K_{\lambda/\mu, \nu}(q,t) for all partitions \nu, of the same weight as the skew partition.EjackpolynomialsHall-Littlewood polynomial of a given partition. This is a multivariate symmetric polynomial whose coefficients are polynomial in a single parameter usually denoted by t. When substituting t with 0 in the Hall-Littlewood P0-polynomials, one obtains the Schur polynomials.FjackpolynomialsHall-Littlewood polynomial of a given partition. This is a multivariate symmetric polynomial whose coefficients are polynomial in a single parameter usually denoted by t. When substituting t with 0 in the Hall-Littlewood P0-polynomials, one obtains the Schur polynomials.GjackpolynomialsHall-Littlewood polynomials as linear combinations of Schur polynomials.HjackpolynomialsSkew Hall-Littlewood polynomial of a given skew partition. This is a multivariate symmetric polynomial whose coefficients are polynomial in a single parameter usually denoted by t. When substituting t with 0 in the skew Hall-Littlewood P5-polynomials, one obtains the skew Schur polynomials.IjackpolynomialsSkew Hall-Littlewood polynomial of a given skew partition. This is a multivariate symmetric polynomial whose coefficients are polynomial in a single parameter usually denoted by t. When substituting t with 0 in the skew Hall-Littlewood P5-polynomials, one obtains the skew Schur polynomials.Jjackpolynomialst-Schur polynomial. This is a multivariate symmetric polynomial whose coefficients are polynomial in a single parameter usually denoted by t5. One obtains the Schur polynomials by substituting t with 04. The name "(t)-Schur polynomial" is taken from  https://www.sciencedirect.com/science/article/pii/S0097316518300724Wheeler and Zinn-Justin's paper 8Hall polynomials, inverse Kostka polynomials and puzzles.Kjackpolynomialst-Schur polynomial. This is a multivariate symmetric polynomial whose coefficients are polynomial in a single parameter usually denoted by t5. One obtains the Schur polynomials by substituting t with 03. The name "(t)-Schur polynomial" is taken from  https://www.sciencedirect.com/science/article/pii/S0097316518300724Wheeler and Zinn-Justin's paper 8Hall polynomials, inverse Kostka polynomials and puzzles.LjackpolynomialsSkew t-Schur polynomial of a given skew partition. This is a multivariate symmetric polynomial whose coefficients are polynomial in a single parameter usually denoted by t;. One obtains the skew Schur polynomials by substituting t with 0. MjackpolynomialsSkew t-Schur polynomial of a given skew partition. This is a multivariate symmetric polynomial whose coefficients are polynomial in a single parameter usually denoted by t;. One obtains the skew Schur polynomials by substituting t with 0. NjackpolynomialsMacdonald polynomial. This is a symmetric multivariate polynomial depending on two parameters usually denoted by q and t. Substituting q with 0( yields the Hall-Littlewood polynomials.*macPoly = macdonaldPolynomial 3 [2, 1] 'P'=putStrLn $ prettySymmetricParametricQSpray ["q", "t"] macPoly{ [ 1 ] }*M[2,1] + { [ 2*q.t^2 - q.t - q + t^2 + t - 2 ] %//% [ q.t^2 - 1 ] }*M[1,1,1]OjackpolynomialsMacdonald polynomial. This is a symmetric multivariate polynomial depending on two parameters usually denoted by q and t. Substituting q with 0( yields the Hall-Littlewood polynomials.PjackpolynomialsSkew Macdonald polynomial of a given skew partition. This is a multivariate symmetric polynomial with two parameters usually denoted by q and t. Substituting q with 0- yields the skew Hall-Littlewood polynomials.QjackpolynomialsSkew Macdonald polynomial of a given skew partition. This is a multivariate symmetric polynomial with two parameters usually denoted by q and t. Substituting q with 0- yields the skew Hall-Littlewood polynomials.RjackpolynomialsMacdonald J-polynomial. This is a multivariate symmetric polynomial whose coefficients are polynomial in two parameters.SjackpolynomialsMacdonald J-polynomial. This is a multivariate symmetric polynomial whose coefficients are polynomial in two parameters.TjackpolynomialsSkew Macdonald J-polynomial. This is a multivariate symmetric polynomial whose coefficients depend on two parameters.UjackpolynomialsSkew Macdonald J-polynomial. This is a multivariate symmetric polynomial whose coefficients depend on two parameters.VjackpolynomialsModified Macdonald polynomial. This is a multivariate symmetric polynomial whose coefficients are polynomials in two parameters.WjackpolynomialsModified Macdonald polynomial. This is a multivariate symmetric polynomial whose coefficients are polynomials in two parameters.XjackpolynomialsFlagged Schur polynomial. A flagged Schur polynomial is not symmetric in general.YjackpolynomialsFlagged Schur polynomial. A flagged Schur polynomial is not symmetric in general.ZjackpolynomialsFlagged skew Schur polynomial. A flagged skew Schur polynomial is not symmetric in general.[jackpolynomialsFlagged skew Schur polynomial. A flagged skew Schur polynomial is not symmetric in general.\jackpolynomials!Factorial Schur polynomial. See  https://www.combinatorics.org/ojs/index.php/eljc/article/view/v15i1r84/pdfKreiman's paper %Products of factorial Schur functions for the definition.]jackpolynomials!Factorial Schur polynomial. See  https://www.combinatorics.org/ojs/index.php/eljc/article/view/v15i1r84/pdfKreiman's paper %Products of factorial Schur functions for the definition.^jackpolynomials'Skew factorial Schur polynomial. See  https://www.kurims.kyoto-u.ac.jp/EMIS/journals/SLC/opapers/s28macdonald.pdfMacdonald's paper %Schur functions: theme and variations$, 6th variation, for the definition._jackpolynomials'Skew factorial Schur polynomial. See  https://www.kurims.kyoto-u.ac.jp/EMIS/journals/SLC/opapers/s28macdonald.pdfMacdonald's paper %Schur functions: theme and variations$, 6th variation, for the definition./jackpolynomialsnumber of variablesjackpolynomialsinteger partition$jackpolynomialsnumber of variablesjackpolynomialsinteger partition'jackpolynomialsparametric sprayjackpolynomialssprayjackpolynomialssprayjackpolynomials parameter(jackpolynomialssprayjackpolynomialssprayjackpolynomials parameter)jackpolynomialssprayjackpolynomialssprayjackpolynomials parameter*jackpolynomialssprayjackpolynomialssprayjackpolynomials parameter+jackpolynomialsparametric sprayjackpolynomialsparametric sprayjackpolynomials parameter,jackpolynomialsparametric sprayjackpolynomialsparametric sprayjackpolynomials parameter0jackpolynomialsnumber of variablesjackpolynomialsinteger partition3jackpolynomialsnumber of variablesjackpolynomialsinteger partition8jackpolynomialsJack parameterjackpolynomialswhich Jack polynomials, J, C, P or Qjackpolynomials)spray representing a symmetric polynomialjackpolynomials5map representing the linear combination; a partition lambda1 in the keys of this map corresponds to the term &coeff *^ jackPol' n lambda alpha which, where coeff' is the value attached to this key and n( is the number of variables of the spray9jackpolynomialsJack parameterjackpolynomialswhich Jack polynomials, J, C, P or Qjackpolynomials4parametric spray representing a symmetric polynomial:jackpolynomialswhich Jack polynomials, J, C, P or Qjackpolynomials)spray representing a symmetric polynomialjackpolynomials5map representing the linear combination; a partition lambda1 in the keys of this map corresponds to the term (coeff *^ jackSymbolicPol' n lambda which, where coeff' is the value attached to this key and n( is the number of variables of the spray;jackpolynomialswhich Jack polynomials, J, C, P or Qjackpolynomials4parametric spray representing a symmetric polynomialjackpolynomials5map representing the linear combination; a partition lambda1 in the keys of this map corresponds to the term (coeff *^ jackSymbolicPol' n lambda which, where coeff' is the value attached to this key and n( is the number of variables of the spray<jackpolynomialsthe integer partition \mujackpolynomialsthe integer partition \nu?jackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomialsinteger partition; the equality of the weight of this partition with the weight of the skew partition is a necessary condition to get a non-zero polynomial@jackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomialsinteger partition; the equality of the weight of this partition with the weight of the skew partition is a necessary condition to get a non-zero polynomialCjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionDjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionEjackpolynomialsnumber of variablesjackpolynomialsinteger partitionjackpolynomials"which Hall-Littlewood polynomial, P or QFjackpolynomialsnumber of variablesjackpolynomialsinteger partitionjackpolynomials"which Hall-Littlewood polynomial, P or QGjackpolynomials;weight of the partitions of the Hall-Littlewood polynomialsjackpolynomials#which Hall-Littlewood polynomials, P or QHjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomials'which skew Hall-Littlewood polynomial, P or QIjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomials'which skew Hall-Littlewood polynomial, P or QJjackpolynomialsnumber of variablesjackpolynomialsinteger partitionKjackpolynomialsnumber of variablesjackpolynomialsinteger partitionLjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionMjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionNjackpolynomialsnumber of variablesjackpolynomialsinteger partitionjackpolynomialswhich Macdonald polynomial, P or QOjackpolynomialsnumber of variablesjackpolynomialsinteger partitionjackpolynomialswhich Macdonald polynomial, P or QPjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomials!which skew Macdonald polynomial, P or QQjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomials!which skew Macdonald polynomial, P or QRjackpolynomialsnumber of variablesjackpolynomialsinteger partitionSjackpolynomialsnumber of variablesjackpolynomialsinteger partitionTjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionUjackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionVjackpolynomialsnumber of variablesjackpolynomialsinteger partitionWjackpolynomialsnumber of variablesjackpolynomialsinteger partitionXjackpolynomialsinteger partitionjackpolynomials lower boundsjackpolynomials upper boundsYjackpolynomialsinteger partitionjackpolynomials lower boundsjackpolynomials upper boundsZjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomials lower boundsjackpolynomials upper bounds[jackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomials lower boundsjackpolynomials upper bounds\jackpolynomialsnumber of variablesjackpolynomialsinteger partitionjackpolynomialsthe sequence denoted by y in the reference paper ]jackpolynomialsnumber of variablesjackpolynomialsinteger partitionjackpolynomialsthe sequence denoted by y in the reference paper^jackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomialsthe sequence denoted by a in the reference paper_jackpolynomialsnumber of variablesjackpolynomials%outer partition of the skew partitionjackpolynomials%inner partition of the skew partitionjackpolynomialsthe sequence denoted by a in the reference paper$03%&'12456789:; !"#()*+,-./=>?@ABCDEFGHI?@ABCDEFGHI?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqr s t u v w x y z { | } ~                                       .jackpolynomials-1.4.7.0-2pD60lMcroZBCW2FX1yjVBMath.Algebra.JackMath.Algebra.Jack.HypergeoPQMath.Algebra.JackPolMath.Algebra.JackSymbolicPol!Math.Algebra.SymmetricPolynomialsMath.Combinatorics.KostkaMath.Combinatorics.TableauxjackpolynomialsMath.Algebra.Jack.Internal Partitionjack'jackzonal'zonalschur'schur skewSchur' skewSchur hypergeoPQjackPol'jackPol skewJackPol skewJackPol' zonalPol'zonalPol skewZonalPol' skewZonalPol schurPol'schurPol skewSchurPol' skewSchurPoljackSymbolicPol'jackSymbolicPolskewJackSymbolicPolskewJackSymbolicPol' msPolynomialisSymmetricSpray msCombinationprettySymmetricNumSprayprettySymmetricQSprayprettySymmetricQSpray'prettySymmetricParametricQSpray%prettySymmetricSimpleParametricQSpraylaplaceBeltramicalogeroSutherland psPolynomial psCombinationpsCombination'psCombination''hallInnerProducthallInnerProduct'hallInnerProduct''hallInnerProduct'''hallInnerProduct''''symbolicHallInnerProductsymbolicHallInnerProduct'symbolicHallInnerProduct'' cshPolynomialcshCombinationcshCombination' esPolynomial esCombinationesCombination'schurCombinationschurCombination'jackCombinationjackCombination'jackSymbolicCombinationjackSymbolicCombination'hallPolynomialskostkaFoulkesPolynomialkostkaFoulkesPolynomial'skewKostkaFoulkesPolynomialskewKostkaFoulkesPolynomial'qtKostkaPolynomialsqtKostkaPolynomials'qtSkewKostkaPolynomialsqtSkewKostkaPolynomials'hallLittlewoodPolynomialhallLittlewoodPolynomial' transitionsSchurToHallLittlewoodskewHallLittlewoodPolynomialskewHallLittlewoodPolynomial'tSchurPolynomialtSchurPolynomial'tSkewSchurPolynomialtSkewSchurPolynomial'macdonaldPolynomialmacdonaldPolynomial'skewMacdonaldPolynomialskewMacdonaldPolynomial'macdonaldJpolynomialmacdonaldJpolynomial'skewMacdonaldJpolynomialskewMacdonaldJpolynomial'modifiedMacdonaldPolynomialmodifiedMacdonaldPolynomial'flaggedSchurPolflaggedSchurPol'flaggedSkewSchurPolflaggedSkewSchurPol'factorialSchurPolfactorialSchurPol'skewFactorialSchurPolskewFactorialSchurPol'kostkaNumbersWithGivenLambda kostkaNumberssymbolicKostkaNumbers$symbolicKostkaNumbersWithGivenLambdaskewKostkaNumberssymbolicSkewKostkaNumbersskewGelfandTsetlinPatterns#skewTableauxWithGivenShapeAndWeight+semiStandardTableauxWithGivenShapeAndWeightmsPolynomialUnsafe _esPolynomial jackJpol0msPolynomialsInSchurBasis_msPolynomialInHLPbasis jackCoeffP jackCoeffQ jackCoeffCjackSymbolicCoeffCjackSymbolicCoeffPinvjackSymbolicCoeffQinv _betaratio_betaRatioOfSprays _isPartition_N_fromIntskewSchurLRCoefficientsisSkewPartition sprayToMap comboToSpray_kostkaNumbersWithGivenLambda_kostkaNumbers_inverseKostkaMatrix%_symbolicKostkaNumbersWithGivenLambda_symbolicKostkaNumbers_inverseSymbolicKostkaMatrix_kostkaFoulkesPolynomial&_hallLittlewoodPolynomialsInSchurBasis$_transitionMatrixHallLittlewoodSchurskewHallLittlewoodPskewHallLittlewoodQ flaggedSemiStandardYoungTableaux tableauWeight isIncreasingflaggedSkewTableauxskewTableauWeight_skewKostkaFoulkesPolynomialmacdonaldPolynomialPmacdonaldPolynomialQskewMacdonaldPolynomialPskewMacdonaldPolynomialQchi_lambda_mu_rhoclambda clambdamumacdonaldJinMSPbasisinverseKostkaNumbersskewSymbolicJackInMSPbasisskewJackInMSPbasis_skewGelfandTsetlinPatterns$_skewTableauxWithGivenShapeAndWeight,_semiStandardTableauxWithGivenShapeAndWeight%hspray-0.5.4.0-FHJYMcPTniXHnraXbQeRQLMath.Algebra.HsprayQSpray' mspInPSbasiszlambda_psCombination_hallInnerProduct_symbolicHallInnerProduct pspInCSHbasis mspInCSHbasis_cshCombination pspInESbasis mspInESbasis_esCombinationcshInSchurBasis_schurCombinationmsPolynomialsInJackBasis msPolynomialsInJackSymbolicBasishlpCombination