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.