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CGAL 5.1.3 - Algebraic Kernel
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AlgebraicKernel_d_2::ConstructAlgebraicReal_2 Concept Reference

Definition

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