A condition for associativity of univariate resultants
We provide a condition on the occurrences of variables in polynomials and show that it ensures associativity of univariate resultants in non-trivial cases. We give examples involving transformations and arithmetic with the zeros of polynomials. Associativity enables the composition of functions on t...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-11-01
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| Series: | Examples and Counterexamples |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X23000150 |
| _version_ | 1827917672277344256 |
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| author | D.A. Wolfram |
| author_facet | D.A. Wolfram |
| author_sort | D.A. Wolfram |
| collection | DOAJ |
| description | We provide a condition on the occurrences of variables in polynomials and show that it ensures associativity of univariate resultants in non-trivial cases. We give examples involving transformations and arithmetic with the zeros of polynomials. Associativity enables the composition of functions on the zeros of a polynomial by using resultants. The result is generalised to finite systems of polynomials. |
| first_indexed | 2024-03-13T03:31:45Z |
| format | Article |
| id | doaj.art-cd21bfc3cdd84a03b7c5d3141d58e4b5 |
| institution | Directory Open Access Journal |
| issn | 2666-657X |
| language | English |
| last_indexed | 2024-03-13T03:31:45Z |
| publishDate | 2023-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj.art-cd21bfc3cdd84a03b7c5d3141d58e4b52023-06-24T05:19:37ZengElsevierExamples and Counterexamples2666-657X2023-11-013100113A condition for associativity of univariate resultantsD.A. Wolfram0ANU College of Engineering, Computing and Cybernetics, Australian National University, Canberra, ACT 0200, AustraliaWe provide a condition on the occurrences of variables in polynomials and show that it ensures associativity of univariate resultants in non-trivial cases. We give examples involving transformations and arithmetic with the zeros of polynomials. Associativity enables the composition of functions on the zeros of a polynomial by using resultants. The result is generalised to finite systems of polynomials.http://www.sciencedirect.com/science/article/pii/S2666657X23000150PolynomialAssociativeUnivariate resultant |
| spellingShingle | D.A. Wolfram A condition for associativity of univariate resultants Examples and Counterexamples Polynomial Associative Univariate resultant |
| title | A condition for associativity of univariate resultants |
| title_full | A condition for associativity of univariate resultants |
| title_fullStr | A condition for associativity of univariate resultants |
| title_full_unstemmed | A condition for associativity of univariate resultants |
| title_short | A condition for associativity of univariate resultants |
| title_sort | condition for associativity of univariate resultants |
| topic | Polynomial Associative Univariate resultant |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X23000150 |
| work_keys_str_mv | AT dawolfram aconditionforassociativityofunivariateresultants AT dawolfram conditionforassociativityofunivariateresultants |