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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
The text passage describes a procedure for analyzing the real part of the roots of a parametric polynomial, detailing the parameters and functions required for the procedure.
no_question

the passage does not contain any mathematical questions or answers to such questions. it is purely descriptive of a procedure and its parameters.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Next: Utilities Up: Analyzing univariate polynomials Previous: Analyzing the real roots   Contents

# 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
user
The text passage describes a procedure for analyzing the real part of the roots of a parametric polynomial, detailing the parameters and functions required for the procedure.

TYPE: NO_QUESTION

The passage does not contain any mathematical questions or answers to such questions. It is purely descriptive of a procedure and its parameters.