Copyright (C) 2021 Parker Edwards
Maple library for evaluating functions at roots of polynomials. See the article (Article placeholder) for theoretical details and Section 5 of that article for discussion of the included examples. It has been tested on Maple 2020.
The included workbooks for detailed examples highlight different input options. The main library is EvalCertificaiton.mpl.
To read the library into your project, assuming the file is in your current Maple directory.
read("EvalCertification.mpl")The main export is the procedure EstimateRootsAndCertifyEvaluations
S := EstimateRootsAndCertifyEvaluations(
polynomial_to_solve,
[function_to_evaluate_1,function_to_evaluate_2,...,function_to_evaluate_n],
HolderFunction,
EstimationPrecision)- polynomial_to_solve is a polynomial with rational coefficients.
- [function_to_evaluate_1,...,function_to_evaluate_n] is a list of locally Hölder continuous functions.
- HolderFunction is a procedure which computes Hölder information for functions in the evaluation list. For example, if the functions are polynomials, then HolderFunction could be the built in procedure HolderInformationForPolynomial provided by EvalCertification.
- EstimationPrecision is a positive rational number.
The object S is a Record with fields
- S:-root-values a list of the estimated roots of polynomial_to_solve.
- S:-evaluations_functions_i for i=1,2,..., n is a list of certified evaluations of function_to_evaluate_i at the roots of polynomial_to_solve. The evaluations are in the same order as the roots in S:-root_values.
EvalCertification is licensed under an MIT license.