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Dom::Polynomial -- the domains of polynomials in arbitrarily many indeterminates

Introduction

Dom::Polynomial(R, ..) creates the domain of polynomials in arbitrarily many indeterminates over the commutative ring R in distributed representation.

Domain

Dom::Polynomial( <R <, Order>>)

Parameters

R - a commutative ring, i.e., a domain of category Cat::CommutativeRing. Default: Dom::ExpressionField(normal).
Order - a monomial ordering, i.e., one of the predefined orderings LexOrder, DegreeOrder, or DegInvLexOrder or an element of the domain Dom::MonomOrdering. Default: LexOrder.

Details

Creating Elements

Dom::Polynomial(R <, Order>)(p)
Dom::Polynomial(R <, Order>)(lm,v)

Parameters

p - a polynomial or a polynomial expression.
lm - list of monomials, which are represented as lists containing the coefficients together with the exponents or exponent vectors.
v - list of indeterminates.

Categories

Cat::Polynomial(R)

Related Domains

Dom::DistributedPolynomial, Dom::MultivariatePolynomial, Dom::UnivariatePolynomial

Entries

characteristic

The characteristic of this domain, which is the characteristic of R.

coeffRing

The coefficient ring of this domain as defined by the parameter R.

key

The name of the domain created.

one

The neutral element w.r.t. "_mult", which is R::one.

ordering

The monomial order as defined by the parameter Order.

zero

The neutral element w.r.t. "_plus", which is R::zero.

Example 1

The following call creates the polynomial domain over the rationals.

>> PR:=Dom::Polynomial(Dom::Rational)
                 Dom::Polynomial(Dom::Rational, LexOrder)

Since the monomial ordering was not specified, this domain is created with the default value for this parameter.

It is rather easy to create elements of this domain, as, e.g.,

>> a := PR(x*(2*x + y^3) - 7/2)
                                2      3
                             2 x  + x y  - 7/2
>> b := PR(x*(2*t + z^3) - 6)        
                                        3
                             2 t x + x z  - 6
>> c := a^2-b/3+3
                     4      3  3    2  6       2        3
      - 2/3 t x + 4 x  + 4 x  y  + x  y  - 14 x  - 7 x y  -
      
                3
         1/3 x z  + 69/4

Super-Domain

Dom::DistributedPolynomial

Axioms

if R has Ax::normalRep, then
Ax::normalRep
if R has Ax::canonicalRep, then
Ax::canonicalRep

Background

Changes




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