PolynomialTraits_d::Canonicalize Class Reference

#include <Concepts/PolynomialTraits_d--Canonicalize.h>

Definition

For a given polynomial \( p\) this AdaptableUnaryFunction computes the unique representative of the set.

\[ {\cal P} := \{ q\ |\ \lambda * q = p\ for\ some\ \lambda \in R \}, \]

where \( R\) is the base of the polynomial ring.

In case PolynomialTraits::Innermost_coefficient_type is a model of Field, the computed polynomial is the monic polynomial in \( \cal P\), that is, the innermost leading coefficient equals one.

In case PolynomialTraits::Innermost_coefficient_type is a model of UniqueFactorizationDomain, the computed polynomial is the one with a multivariate content of one.

For all other cases the notion of uniqueness is up to the concrete model.

Note that the computed polynomial has the same zero set as the given one.

Refines:

AdaptableUnaryFunction

CopyConstructible

DefaultConstructible

See also

Polynomial_d

PolynomialTraits_d

Types
typedef PolynomialTraits_d::Polynomial_d	result_type
typedef PolynomialTraits_d::Polynomial_d	argument_type

Operations
result_type	operator() (first_argument_type p)
	Returns the canonical representative of \( p\). More...

Member Typedef Documentation

argument_type

typedef PolynomialTraits_d::Polynomial_d PolynomialTraits_d::Canonicalize::argument_type

result_type

typedef PolynomialTraits_d::Polynomial_d PolynomialTraits_d::Canonicalize::result_type

Member Function Documentation

operator()()

result_type PolynomialTraits_d::Canonicalize::operator()

(

first_argument_type

p

)

Returns the canonical representative of \( p\).