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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.
SchurCPP, JackCPP,
ZonalCPP and ZonalQCPP) are not restricted to
rational numbers: they also allow double numbers.SchurCPP, JackCPP,
ZonalCPP and ZonalQCPP.Changed C++20 to C++17.
SchurPolCPP, JackPolCPP,
ZonalPolCPP and ZonalQPolCPP. It is faster
than the Julia implementation.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.
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
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.