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Cat::Polynomial

Category of multivariate polynomials

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

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 — Return coefficients

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 — Return total degree

degree(p)

degree(p, x)

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

evalp — Evaluate at a point

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.

mapcoeffs — Map coefficients

mapcoeffs(p, f, <a, …>)

unitNormal — Return unit normal

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 — Return unit normal representation

unitNormalRep(p)

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

Mathematical Methods

solve — Solve polynomial equation

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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