Some minor modifications have been necessary due to the updates of some package dependencies. No change for the user.

The

`KostkaNumbers`

function has been renamed to`KostkaJackNumbers`

and it has a new argument`alpha`

, to compute the Kostka-Jack numbers (Kostka numbers with a Jack parameter) with Jack parameter`alpha`

(for`alpha=1`

these are the ordinary Kostka numbers) for all partitions having a given weight.New function

`KostkaJackNumbersWithGivenLambda`

, to compute the Kostka-Jack numbers with a given Jack parameter and a given partition`lambda`

.New function

`symbolicKostkaJackNumbers`

, to get the Kostka-Jack numbers with a symbolic Jack parameter for all partitions having a given weight.New function

`symbolicKostkaJackNumbersWithGivenLambda`

, to get the Kostka-Jack numbers with a symbolic Jack parameter for a given partition`lambda`

.New function

`skewKostkaJackNumbers`

, to get skew Kostka-Jack numbers with a given Jack parameter.New function

`symbolicSkewKostkaJackNumbers`

, to get skew Kostka-Jack numbers with a symbolic Jack parameter.New function

`JackCombination`

, to get a symmetric polynomial as a linear combination of some Jack polynomials with a fixed Jack parameter.New function

`symbolicJackCombination`

, to get a symmetric polynomial as a linear combination of some Jack polynomials with symbolic Jack parameter.New function

`SkewJackPol`

, to get a skew Jack polynomial with a given Jack parameter.New function

`SkewJackSymPol`

, to get a skew Jack polynomial with a symbolic Jack parameter.New function

`flaggedSchurPol`

, to get a flagged Schur polynomial.New function

`flaggedSkewSchurPol`

, to get a flagged skew Schur polynomial.New function

`factorialSchurPol`

, to get a factorial Schur polynomial.New function

`SkewFactorialSchurPol`

, to get a skew factorial Schur polynomial.New function

`tSchurPol`

, to get a t-Schur polynomial.New function

`tSkewSchurPol`

, to get a skew t-Schur polynomial.New function

`KostaFoulkesPolynomial`

, to get a Kostka-Foulkes polynomial. A Kostka-Foulkes polynomial is a univariate polynomial associated to a pair of integer partitions and its value at 1 is the Kostka number associated to these partitions.New function

`SkewKostkaFoulkesPolynomial`

, to get a skew Kostka-Foulkes polynomial.New function

`HallLittlewoodPol`

, to get a Hall-Littlewood polynomial. A Hall-Littlewood polynomial is a multivariate symmetric polynomial associated to an integer partition and depending on a parameter. When the value of this parameter is 0, then this is the Schur polynomial, and when the value of this parameter is 1, then this is the monomial symmetric polynomial.New function

`SkewHallLittlewoodPol`

, to get a skew Hall-Littlewood polynomial. A skew Hall-Littlewood polynomial is a multivariate symmetric polynomial associated to a skew integer partition and depending on a parameter. When the value of this parameter is 0, then this is the skew Schur polynomial.New function

`qtKostkaPolynomials`

, to get qt-Kostka polynomials, aka Kostka-Macdonald polynomials.New function

`qtSkewKostkaPolynomials`

, to get skew qt-Kostka polynomials.New function

`MacdonaldPol`

, to get a Macdonald polynomial.New function

`SkewMacdonaldPol`

, to get a skew Macdonald polynomial.New function

`modifiedMacdonaldPol`

, to get a modified Macdonald polynomial.New function

`HallPolynomials`

, to get the Hall polynomials.

It is now possible to get a Jack polynomial with a symbolic Jack parameter in its coefficients. Such polynomials are returned by the function

`JackSymPol`

. This big progress is the reason for which I increased the major component of the version of the package.Since the functions implemented with

**Rcpp**are highly more efficient, the functions`Jack`

,`JackPol`

,`Schur`

,`SchurPol`

,`Zonal`

,`ZonalPol`

,`ZonalQ`

,`ZonalQPol`

, have been renamed to`JackR`

,`JackPolR`

,`SchurR`

,`SchurPolR`

,`ZonalR`

,`ZonalPolR`

,`ZonalQR`

,`ZonalQPolR`

, and the functions`JackCPP`

,`JackPolCPP`

,`SchurCPP`

,`SchurPolCPP`

,`ZonalCPP`

,`ZonalPolCPP`

,`ZonalQCPP`

,`ZonalQPolCPP`

have been renamed to`Jack`

,`JackPol`

,`Schur`

,`SchurPol`

,`Zonal`

,`ZonalPol`

,`ZonalQ`

,`ZonalQPol`

.New function

`LRmult`

, to compute the expression of the product of two Schur polynomials as a linear combination of Schur polynomials, using the Littlewood-Richardson rule.New function

`LRskew`

, to compute the expression of a skew Schur polynomial as a linear combination of Schur polynomials, using the Littlewood-Richardson rule.Based on

`LRskew`

, the new function`SkewSchurPol`

computes the skew Schur polynomial of a given skew partition.Actually there are four possible Jack polynomials of a given partition for a given

`alpha`

, denoted by`J`

,`C`

,`Q`

or`P`

(they are the same up to a normalization constant). It is now possible to get any of them (the previous versions only allowed to get the`J`

polynomial).

The Julia stuff has been removed.

- Now the ‘Rcpp’ implementations for the evaluation of the
polynomials

(functions`SchurCPP`

,`JackCPP`

,`ZonalCPP`

and`ZonalQCPP`

) are not restricted to rational numbers: they also allow double numbers.

- Now there is a ‘Rcpp’ implementation for the evaluation of the
polynomials: functions
`SchurCPP`

,`JackCPP`

,`ZonalCPP`

and`ZonalQCPP`

.

Changed C++20 to C++17.

- Now there is a ‘Rcpp’ implementation of the polynomials: functions
`SchurPolCPP`

,`JackPolCPP`

,`ZonalPolCPP`

and`ZonalQPolCPP`

. It is faster than the Julia implementation.

- The package does not longer depend on the ‘gmpoly’ package. This dependency has been replaced with the ‘qspray’ package.

Now one can use a

`bigq`

number for`alpha`

in`JackPol`

, thanks to the ‘gmpoly’ package, and one can use`exact=TRUE`

with`algorithm=DK`

for`ZonalPol`

,`ZonalQPol`

and`SchurPol`

.Now one can get a

`gmpoly`

polynomial with Julia.

- New function
`Jack_julia`

, to evaluate the polynomials with Julia.

Fixed a test of empty partition

Added more checks of parameters validity

Added more unit tests

Improved documentation

- Some functions didn’t handle the empty partition.