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Cat::Polynomial

Category of multivariate polynomials

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Syntax

Cat::Polynomial(R)

Description

Cat::Polynomial(R) represents the category of multivariate polynomials over R.

A Cat::Polynomial(R) is a multivariate polynomial ring over a commutative coefficient ring R.

Parameters

R

A domain which must be from the category Cat::CommutativeRing.

Entries

"coeffRing"

The coefficient ring R.

"characteristic"

The characteristic of this domain, which is the same as that of the ring R.

Methods

expand all

Basic Methods

coeff(p)

coeff(p, x, n)

coeff(p, n)

Must return the coefficient of x^n of p, which is a polynomial in the remaining indeterminates.

Must return the coefficient of x^n of p, where x is the main variable of p.

degree(p)

degree(p, x)

Must return the degree of p with respect to the indeterminate x.

degreevec(p)

evalp(p, x = v, …)

More than one evaluation point may be given. The result must be a polynomial in the remaining indeterminates or an element of R.

indets(p)

lcoeff(p)

lmonomial(p)

lterm(p)

mainvar(p)

mapcoeffs(p, f, <a, …>)

multcoeffs(p, c)

nterms(p)

nthcoeff(p, n)

nthmonomial(p, n)

nthterm(p, n)

tcoeff(p)

unitNormal(p)

An implementation is provided if R has the axiom Ax::canonicalUnitNormal: In this case p is multiplied by an unit of R such that the leading coefficient has unit normal representation in R.

unitNormalRep(p)

An implementation is provided if R has the axiom Ax::canonicalUnitNormal.

Mathematical Methods

content(p)

isUnit(p)

primpart(p)

poly2list(p)

solve(p, x, <opt, …>)

solve(p, x = T, <opt, …>)

solve(p)

Solves the polynomial equation p = 0 with respect to x over the domain T. See the function solve for details about the optional arguments opt, ...

The polynomial p must be univariate. Solves the polynomial equation p = 0 with respect to the indeterminate of p over the domain R.

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