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  # Analyzing the real part of the roots
  
  For some applications it may be interesting to determine if a polynomial in a set defined by a parametric polynomial has the real part of one of its roots equal to a pre-defined value. This may be done by using the procedure
  
  ```
  int ALIAS_Is_Root_RealPart(int Degree,
  int NbParameter,
  int HasInterval,
  INTERVAL_VECTOR (* TheCoeff)(INTERVAL_VECTOR &),
  INTERVAL_VECTOR (* TheCoeffCentered)(INTERVAL_VECTOR&,double a),
  int Iteration,
  INTERVAL_VECTOR &Par,
  double *Root,
  INTERVAL_VECTOR (* EvaluateComplex)(int,int,INTERVAL_VECTOR &),
  int (* Simp)(INTERVAL_VECTOR &))
  ```
  where
  • 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
  • TheCoeffCentered: a procedure to calculate the coefficients of the polynomial
  • 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]
  • EvaluateComplex: a procedure that returns 4 intervals. The input interval vector has dimension NbParameter+1 elements, the first one being the parameters, the last one being . The procedure should evaluate and should return the real part of , the complex part of , the real part of and the complex part of
  • Simp: an optional simplification procedure that returns -1 if the polynomials in a set cannot roots with real part equal to Root[0] or Root[1]
  
  Next: Utilities Up: Analyzing univariate polynomials Previous: Analyzing the real roots   Contents
  Jean-Pierre Merlet 2012-12-20