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 $\partial B$