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Cat::Polynomial -- the category of multivariate polynomials

Introduction

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

Generating the category

Cat::Polynomial(R)

Parameters

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

Categories

if R is a Cat::FactorialDomain then
Cat::FactorialDomain
if R is a Cat::GcdDomain then
Cat::GcdDomain
if R is a Cat::IntegralDomain then
Cat::IntegralDomain
Cat::PartialDifferentialRing

, Cat::Algebra(R)

Axioms

if R has Ax::canonicalUnitNormal then
Ax::canonicalUnitNormal
if R has Ax::closedUnitNormals then
Ax::closedUnitNormals

Details

Entries

coeffRing

The coefficient ring R.

characteristic

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

Method coeff: returns coefficients

Method degree: returns total degree

Method degreevec: returns degree vector

Method evalp: evaluates at a point

Method indets: returns indeterminates

Method lcoeff: returns leading coefficient

Method lmonomial: returns leading monomial

Method lterm: returns leading term

Method mainvar: returns main variable

Method mapcoeffs: map coefficients

Method multcoeffs: multiply coefficients

Method nterms: return number of terms

Method nthcoeff: return n-th coefficient

Method nthmonomial: return n-th monomial

Method nthterm: return n-th term

Method tcoeff: return trailing coefficient

Method unitNormal: returns unit normal

Method unitNormalRep: returns unit normal representation

Method content: return content

Method isUnit: tests if element is a unit

Method primpart: returns primitive part

Method solve: solves polynomial equation

Changes




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