AlgebraicKernel_d_2::ConstructAlgebraicReal_2

Definition

Constructs an AlgebraicKernel_d_2::Algebraic_real_2.

Refines

AdaptableFunctor

Types

typedef AlgebraicKernel_d_2::Algebraic_real_2
result_type;

Operations

result_type fo ( int x , int y ) introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to (x,y).

result_type fo ( AlgebraicKernel_d_2::Bound x , AlgebraicKernel_d_2::Bound y )
introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to (x,y).

result_type fo ( AlgebraicKernel_d_2::Coefficient x , AlgebraicKernel_d_2::Coefficient y )
introduces an AlgebraicKernel_d_2::Algebraic_real_2 initialized to (x,y).

result_type fo ( 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
fo ( 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.
Precondition:  g is square free.
Precondition:  f and g are coprime.

result_type
fo ( 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 = (xl,xu) × (yl,yu).
Precondition:  xl < xu
Precondition:  yl < yu
Precondition:  f is square free.
Precondition:  g is square free.
Precondition:  f and g are coprime.
Precondition:  f and g have exactly one common solution in B
Precondition:  f and g have no common solution on ∂B

See Also

AlgebraicKernel_d_1::ConstructAlgebraicReal_1