qspray3.1.0 package

Multivariate Polynomials with Rational Coefficients

getCoefficient

Get a coefficient in a 'qspray' polynomial

getConstantTerm

Get the constant term of a 'qspray' polynomial

qsprayMaker

Make a 'qspray' object

qzero

The null 'qspray' polynomial

rQspray

Random 'qspray'

showMonomialOld

Print a monomial

isSymmetricQspray

Check symmetry of a polynomial

isUnivariate

Whether a 'qspray' is univariate

leadingCoefficient

Leading coefficient of a 'qspray' polynomial

leadingTerm

Leading term of a 'qspray' polynomial

MSFpoly

Monomial symmetric function

qlone

Polynomial variable

qone

The unit 'qspray' polynomial

qspray_from_list

(internal) Make a 'qspray' object from a list

qspray-unary

Unary operators for qspray objects

qsprayDivision

Division of two polynomials

as.function.qspray

Multivariate polynomial as function

as.qspray

Coercion to a 'qspray' object

evalQspray

Evaluate a 'qspray' object

changeVariables

Change of variables in a 'qspray' polynomial

characteristicPolynomial

Characteristic polynomial

collinearQsprays

Whether two 'qspray' polynomials are collinear

compactSymmetricQspray

Compact symmetric qspray

composeQspray

Compose 'qspray' polynomials

CSHFpoly

Complete homogeneous symmetric function

derivQspray

Partial derivative

dQspray

Partial differentiation

ESFpoly

Elementary symmetric polynomial

isQzero

Whether a 'qspray' polynomial is null

groebner

Gröbner basis

HallInnerProduct

Hall inner product

implicitization

Implicitization with Gröbner bases

integratePolynomialOnSimplex

Integral of a multivariate polynomial over a simplex

involvedVariables

Variables involved in a 'qspray' polynomial

isConstant

Whether a 'qspray' polynomial is constant

isHomogeneousQspray

Whether a 'qspray' polynomial is homogeneous

isPolynomialOf

Whether a 'qspray' is a polynomial of some given 'qsprays'

isQone

Whether a 'qspray' polynomial is the unit polynomial

MSPcombination

Symmetric polynomial in terms of the monomial symmetric polynomials

numberOfTerms

Number of terms in a 'qspray' polynomial

numberOfVariables

Number of variables in a 'qspray' polynomial

orderedQspray

Ordered 'qspray'

permuteVariables

Permute variables

prettyQspray

Pretty polynomial

PSFpoly

Power sum polynomial

PSPcombination

Symmetric polynomial as a linear combination of some power sum polynom...

PSPexpression

Symmetric polynomial in terms of the power sum polynomials

qdivision

Division of a qspray polynomial

showMonomialX1X2X3

Print a monomial

showMonomialXYZ

Print a monomial

showQspray

Print a 'qspray' object

showQsprayOption-set

Set a show option to a 'qspray' object

showQsprayX1X2X3

Print a 'qspray' object

showQsprayXYZ

Print a polynomial

substituteQspray

Substitutions in a 'qspray' polynomial

swapVariables

Swap variables

Symbolic calculation and evaluation of multivariate polynomials with rational coefficients. This package is strongly inspired by the 'spray' package. It provides a function to compute Gröbner bases (reference <doi:10.1007/978-3-319-16721-3>). It also includes some features for symmetric polynomials, such as the Hall inner product. The header file of the C++ code can be used by other packages. It provides the templated class 'Qspray' that can be used to represent and to deal with multivariate polynomials with another type of coefficients.

  • Maintainer: Stéphane Laurent
  • License: GPL-3
  • Last published: 2024-07-27