Analyzing the real roots

The procedure

 
int ALIAS_Min_Max_Is_Root(int Degree,  
  int NbParameter,
  int HasInterval,
  INTERVAL_VECTOR (* TheCoeff)(INTERVAL_VECTOR &), 
  int Iteration,
  INTERVAL_VECTOR &Par,
  double *Root,
  int Type,
  int (* Solve_Poly)(double *, int *,double
*))

may be used to rest if a polynomial in a set may have as real root one of two pre-defined value.

• Degree: the degree of the polynomial
• NbParameter: the number of parameters that appear in the coefficient of the polynomial
• HasInterval: 1 if the coefficient include intervals not defined by parameters, 0 otherwise
• TheCoeff: a procedure to calculate the coefficients of the polynomial being given range for the parameters
• Iteration: the maximum number of box that may be used by the algorithm
• Par: the ranges for the parameters
• Root: we look for polynomial whose real part of the root is either Root[0] or Root[1]
• Type:
  • -1 : if in a box we have found a polynomial with a root lower than Root[0]; we look for a polynomial in the box whose real root is exactly Root[0]. If no such polynomial is found the box is eliminated
  • 1 : if in a box we have found a polynomial with a root greater than Root[1]; we look for a polynomial in the box whose real root is exactly Root[1]. If no such polynomial is found the box
  • 2: if in a box we have found a polynomial with a root greater than Root[1] and a polynomial with a real root greater than Root[0]; we look for a polynomial in the box whose real root is exactly Root[1] and a polynomial whose real root is exactly Root[0]. If no such polynomials are found the box is eliminated
  • 0: general case;
• Solve_Poly: a procedure to solve polynomial with double floating point coefficients. The first argument are the coefficients, the second the degree of the polynomial and the third the real roots

This procedure returns -1 if no polynomial with real root Root exist, 1 if such polynomial exist and 0 if the algorithm has not be able to determine such polynomial