PolynomialTraits_d::Degree Concept Reference

Definition

This AdaptableUnaryFunction computes the degree of a PolynomialTraits_d::Polynomial_d with respect to a certain variable.

The degree of \( p\) with respect to a certain variable \( x_i\), is the highest power \( e\) of \( x_i\) such that the coefficient of \( x_i^{e}\) in \( p\) is not zero.

For instance the degree of \( p = x_0^2x_1^3+x_1^4\) with respect to \( x_1\) is \( 4\).

The degree of the zero polynomial is set to \( 0\). From the mathematical point of view this should be \( -infinity\), but this would imply an inconvenient return type.

Refines

AdaptableUnaryFunction

CopyConstructible

DefaultConstructible

See also

Polynomial_d

PolynomialTraits_d

PolynomialTraits_d::TotalDegree

PolynomialTraits_d::DegreeVector

Types
typedef int	result_type
typedef PolynomialTraits_d::Polynomial_d	argument_type

Operations
result_type	operator() (argument_type p)
	Computes the degree of \( p\) with respect to the outermost variable \( x_{d-1}\).
result_type	operator() (argument_type p, int i)
	Computes the degree of \( p\) with respect to variable \( x_i\).

Member Function Documentation

operator()()

result_type PolynomialTraits_d::Degree::operator()	(	argument_type	p,
		int	i
	)

Computes the degree of \( p\) with respect to variable \( x_i\).

Precondition

\( 0 \leq i < d\).