On Computing the Resultant of a Polynomial and an Entire Function

Based on Newton’s recurrence formulas on the complex plane, the sums of values of one entire function at zeros of another entire function are found. This allows one to determine whether these functions have common zeros or not. An algorithm for computing an approximation to the resultant of a polyno...

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Bibliographic Details
Published inProgramming and computer software Vol. 48; no. 1; pp. 59 - 64
Main Authors Kuzovatov, V. I., Kytmanov, A. A., Myshkina, E. K.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.02.2022
Springer Nature B.V
Subjects
Algebra
Algorithms
Approximation
Artificial Intelligence
Computation
Computer algebra
Computer Science
Entire functions
Mathematical analysis
Operating Systems
Polynomials
Software Engineering
Software Engineering/Programming and Operating Systems
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Summary:Based on Newton’s recurrence formulas on the complex plane, the sums of values of one entire function at zeros of another entire function are found. This allows one to determine whether these functions have common zeros or not. An algorithm for computing an approximation to the resultant of a polynomial (or an entire function with a finite number of zeros) and an entire function is presented. The algorithm is implemented in the Maple computer algebra system. Examples that illustrate the operation of the algorithm are considered.
ISSN:0361-7688
1608-3261
DOI:10.1134/S0361768822010066