# Multivariate Polynomials with Rational Coefficients

## Documentation for package ‘qspray’ version 3.1.0

- DESCRIPTION file.
- Package NEWS.

## Help Pages

+-method | Unary operators for qspray objects
--method | Unary operators for qspray objects
as.function.qspray | Multivariate polynomial as function
as.qspray | Coercion to a 'qspray' object
as.qspray-method | Coercion to a 'qspray' object
changeVariables | Change of variables in a 'qspray' polynomial
changeVariables-method | Change of variables in a 'qspray' polynomial
characteristicPolynomial | Characteristic polynomial
collinearQsprays | Whether two 'qspray' polynomials are collinear
compactSymmetricQspray | Compact symmetric qspray
compactSymmetricQspray-method | Compact symmetric qspray
composeQspray | Compose 'qspray' polynomials
CSHFpoly | Complete homogeneous symmetric function
derivQspray | Partial derivative
dQspray | Partial differentiation
ESFpoly | Elementary symmetric polynomial
evalQspray | Evaluate a 'qspray' object
getCoefficient | Get a coefficient in a 'qspray' polynomial
getCoefficient-method | Get a coefficient in a 'qspray' polynomial
getConstantTerm | Get the constant term of a 'qspray' polynomial
getConstantTerm-method | Get the constant term of a 'qspray' polynomial
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
involvedVariables-method | Variables involved in a 'qspray' polynomial
isConstant | Whether a 'qspray' polynomial is constant
isConstant-method | 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
isQone-method | Whether a 'qspray' polynomial is the unit polynomial
isQzero | Whether a 'qspray' polynomial is null
isQzero-method | Whether a 'qspray' polynomial is null
isSymmetricQspray | Check symmetry of a polynomial
isUnivariate | Whether a 'qspray' is univariate
isUnivariate-method | Whether a 'qspray' is univariate
leadingCoefficient | Leading coefficient of a 'qspray' polynomial
leadingTerm | Leading term of a 'qspray' polynomial
MSFpoly | Monomial symmetric function
MSPcombination | Symmetric polynomial in terms of the monomial symmetric polynomials
numberOfTerms | Number of terms in a 'qspray' polynomial
numberOfTerms-method | Number of terms in a 'qspray' polynomial
numberOfVariables | Number of variables in a 'qspray' polynomial
numberOfVariables-method | Number of variables in a 'qspray' polynomial
orderedQspray | Ordered 'qspray'
permuteVariables | Permute variables
permuteVariables-method | Permute variables
prettyQspray | Pretty polynomial
PSFpoly | Power sum polynomial
PSPcombination | Symmetric polynomial as a linear combination of some power sum polynomials
PSPexpression | Symmetric polynomial in terms of the power sum polynomials
qdivision | Division of a qspray polynomial
qlone | Polynomial variable
qone | The unit 'qspray' polynomial
qspray-unary | Unary operators for qspray objects
qsprayDivision | Division of two polynomials
qsprayMaker | Make a 'qspray' object
qspray_from_list | (internal) Make a 'qspray' object from a list
qzero | The null 'qspray' polynomial
rQspray | Random 'qspray'
showMonomialOld | Print a monomial
showMonomialX1X2X3 | Print a monomial
showMonomialXYZ | Print a monomial
showQspray | Print a 'qspray' object
showQsprayOption<- | 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
swapVariables-method | Swap variables