FactoringUtilities(E, OV, R, P)¶
This package provides utilities used by the factorizers which operate on polynomials represented as univariate polynomials with multivariate coefficients.
- completeEval: (SparseUnivariatePolynomial P, List OV, List R) -> SparseUnivariatePolynomial R
completeEval(upoly, lvar, lval)evaluates the polynomial
upolywith each variable in
lvarreplaced by the corresponding value in lval. Substitutions are done for all variables in
upolyproducing a univariate polynomial over
- degree: (SparseUnivariatePolynomial P, List OV) -> List NonNegativeInteger
degree(upoly, lvar)returns a list containing the maximum degree for each variable in lvar.
- lowerPolynomial: SparseUnivariatePolynomial P -> SparseUnivariatePolynomial R
upolyto be a univariate polynomial over
R. An error if the coefficients contain variables.
- normalDeriv: (SparseUnivariatePolynomial P, Integer) -> SparseUnivariatePolynomial P
normalDeriv(poly, i)computes the
ith derivative of
polydivided by i!.
- raisePolynomial: SparseUnivariatePolynomial R -> SparseUnivariatePolynomial P
rpolyfrom a univariate polynomial over
rto be a univariate polynomial with polynomial coefficients.
- ran: Integer -> R
ran(k)computes a random integer between
kas a member of