AlgebraicKernel_d_2::ConstructAlgebraicReal_2 Concept Reference

Definition

Constructs an AlgebraicKernel_d_2::Algebraic_real_2.

Refines:

AdaptableFunctor

See also

AlgebraicKernel_d_1::ConstructAlgebraicReal_1

Types
typedef AlgebraicKernel_d_2::Algebraic_real_2	result_type

Operations
result_type	operator() (int x, int y)
	introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to \( (x,y)\).
result_type	operator() (AlgebraicKernel_d_2::Bound x, AlgebraicKernel_d_2::Bound y)
	introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to \( (x,y)\).
result_type	operator() (AlgebraicKernel_d_2::Coefficient x, AlgebraicKernel_d_2::Coefficient y)
	introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to \( (x,y)\).
result_type	operator() (AlgebraicKernel_d_2::Algebraic_real_1 x, AlgebraicKernel_d_2::Algebraic_real_1 y)
	introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to \( (x,y)\).
result_type	operator() (AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g, AlgebraicKernel_d_2::size_type i)
	introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to the \( i\)-th real common solution of \( f\) and \( g\), with respect to xy-lexicographic order. More...
result_type	operator() (AlgebraicKernel_d_2::Polynomial_2 f, AlgebraicKernel_d_2::Polynomial_2 g, AlgebraicKernel_d_2::Bound x_l, AlgebraicKernel_d_2::Bound x_u, AlgebraicKernel_d_2::Bound y_l, AlgebraicKernel_d_2::Bound y_u)
	introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to the only real intersection of \( f\) and \( g\) in the open box \( B = (x_l,x_u)\times(y_l,y_u)\). More...

Member Function Documentation

operator()() [1/2]

result_type AlgebraicKernel_d_2::ConstructAlgebraicReal_2::operator()	(	AlgebraicKernel_d_2::Polynomial_2	f,
		AlgebraicKernel_d_2::Polynomial_2	g,
		AlgebraicKernel_d_2::size_type	i
	)

introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to the \( i\)-th real common solution of \( f\) and \( g\), with respect to xy-lexicographic order.

The index starts at \( 0\), that is, the system must have at least \( i+1\) real solutions.

Precondition

\( f\) is square free.

\( g\) is square free.

\( f\) and \( g\) are coprime.

operator()() [2/2]

result_type AlgebraicKernel_d_2::ConstructAlgebraicReal_2::operator()	(	AlgebraicKernel_d_2::Polynomial_2	f,
		AlgebraicKernel_d_2::Polynomial_2	g,
		AlgebraicKernel_d_2::Bound	x_l,
		AlgebraicKernel_d_2::Bound	x_u,
		AlgebraicKernel_d_2::Bound	y_l,
		AlgebraicKernel_d_2::Bound	y_u
	)

introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to the only real intersection of \( f\) and \( g\) in the open box \( B = (x_l,x_u)\times(y_l,y_u)\).

Precondition

\( x_l < x_u\)

\( y_l < y_u\)

\( f\) is square free.

\( g\) is square free.

\( f\) and \( g\) are coprime.

\( f\) and \( g\) have exactly one common solution in \( B\)

\( f\) and \( g\) have no common solution on \( \partial B\)