PolynomialTraits_d::MakeSquareFree Class Reference

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

Definition

This AdaptableUnaryFunction computes the square-free part of a polynomial of type PolynomialTraits_d::Polynomial_d up to a constant factor.

A polynomial \( p\) can be factored into square-free and pairwise coprime non-constant factors \( g_i\) with multiplicities \( m_i\) and a constant factor \( a\), such that \( p = a \cdot g_1^{m_1} \cdot ... \cdot g_n^{m_n}\), where all \( g_i\) are canonicalized.

Given this decomposition, the square free part is defined as the product \( g_1 \cdot ... \cdot g_n\), which is computed by this functor.

Refines:

AdaptableUnaryFunction

CopyConstructible

DefaultConstructible

See also

Polynomial_d

PolynomialTraits_d

PolynomialTraits_d::Canonicalize

PolynomialTraits_d::SquareFreeFactorize

PolynomialTraits_d::IsSquareFree

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

Operations
result_type	operator() (argument_type p)
	Returns the square-free part of \( p\). More...

Member Typedef Documentation

argument_type

typedef PolynomialTraits_d::Polynomial_d PolynomialTraits_d::MakeSquareFree::argument_type

result_type

typedef PolynomialTraits_d::Polynomial_d PolynomialTraits_d::MakeSquareFree::result_type

Member Function Documentation

operator()()

result_type PolynomialTraits_d::MakeSquareFree::operator()

(

argument_type

p

)

Returns the square-free part of \( p\).