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polylib::coeffRing

Coefficient ring of a polynomial

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

polylib::coeffRing(P)
polylib::coeffRing(p)

Description

polylib::coeffRing(p) returns the coefficient ring of p.

polylib::coeffRing(p) allows to query in a uniform way the coefficient ring of the polynomial p or the polynomial domain P.

P can be any polynomial domain (Dom::UnivariatePolynomialx, Dom::DistributedPolynomial[x,y], ...).

P can also be of the form polylib::Poly([x,y],K). If K is Expr or IntMod(n), then the corresponding domains Dom::ExpressionField() or Dom::IntegerMod(p) is returned. See poly for the details about Expr and IntMod(n).

p can be a kernel polynomial (DOM_POLY), or an element of one of the above domains

Examples

Example 1

We define a polynomial ring over the ring of integers modulo 4, and query for its coefficient ring:

P := Dom::UnivariatePolynomial(x, Dom::IntegerMod(4)):
polylib::coeffRing(P)

The coefficient ring of the elements of this domain can be queried the same way:

polylib::coeffRing(P(x))

polylib::coeffRing(Dom::Matrix(Dom::IntegerMod(3)))

Example 2

When no coefficient ring is specified, poly currently constructs kernel polynomials over the fake domain Expr instead of the mathematically equivalent field Dom::ExpressionField() of arbitrary expression (this happens to be more efficient with the current kernels):

extop(poly(x))

polylib::coeffRing(poly(x))

This makes it possible to plug the result right away as coefficient ring of some other domain:

Dom::UnivariatePolynomial(x, polylib::coeffRing(poly(x)))

Parameters

P

A polynomial domain

p

A polynomial

Return Values

Domain

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