AlgebraicKernel_d_1::ConstructAlgebraicReal_1 Concept Reference

Definition

Constructs AlgebraicKernel_d_1::Algebraic_real_1.

Refines

AdaptableFunctor

See also

AlgebraicKernel_d_2::ConstructAlgebraicReal_2

Types
typedef AlgebraicKernel_d_1::Algebraic_real_1	result_type

Operations
result_type	operator() (int a)
	introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to \( a\).
result_type	operator() (AlgebraicKernel_d_1::Bound a)
	introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to \( a\).
result_type	operator() (AlgebraicKernel_d_1::Coefficient a)
	introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to \( a\).
result_type	operator() (AlgebraicKernel_d_1::Polynomial_1 p, AlgebraicKernel_d_1::size_type i)
	introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to the \( i\)-th real root of \( p\).
result_type	operator() (AlgebraicKernel_d_1::Polynomial_1 p, AlgebraicKernel_d_1::Bound l, AlgebraicKernel_d_1::Bound u)
	introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to the only real root of \( p\) in the open interval \( I = (l,u)\).

Member Function Documentation

operator()() [1/2]

result_type AlgebraicKernel_d_1::ConstructAlgebraicReal_1::operator()	(	AlgebraicKernel_d_1::Polynomial_1	p,
		AlgebraicKernel_d_1::Bound	l,
		AlgebraicKernel_d_1::Bound	u
	)

introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to the only real root of \( p\) in the open interval \( I = (l,u)\).

Precondition

\( l < u\)

\( p\) is square free.

\( p\) has exactly one real root in \( I\)

\( p\) has no real root on \( \partial I\)

operator()() [2/2]

result_type AlgebraicKernel_d_1::ConstructAlgebraicReal_1::operator()	(	AlgebraicKernel_d_1::Polynomial_1	p,
		AlgebraicKernel_d_1::size_type	i
	)

introduces an AlgebraicKernel_d_1::Algebraic_real_1 initialized to the \( i\)-th real root of \( p\).

The index starts at \( 0\), that is, \( p\) must have at least \( i+1\) real roots.

Precondition

\( p\) is square free.

\( p\) has at least \( i+1\) real roots.