Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients
We provide irreducibility criteria for multiplicative convolutions of polynomials with integer coefficients, that is, for polynomials of the form hdeg f · f(g/h), where f, g, h are polynomials with integer coefficients, and g and h are relatively prime. The irreducibility conditions are expressed in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2014-12-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2014-0007 |
| _version_ | 1811272398640513024 |
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| author | Bonciocat Anca Iuliana Bonciocat Nicolae Ciprian Cipu Mihai |
| author_facet | Bonciocat Anca Iuliana Bonciocat Nicolae Ciprian Cipu Mihai |
| author_sort | Bonciocat Anca Iuliana |
| collection | DOAJ |
| description | We provide irreducibility criteria for multiplicative convolutions of polynomials with integer coefficients, that is, for polynomials of the form hdeg f · f(g/h), where f, g, h are polynomials with integer coefficients, and g and h are relatively prime. The irreducibility conditions are expressed in terms of the prime factorization of the leading coefficient of the polynomial hdeg f · f(g/h), the degrees of f, g, h, and the absolute values of their coefficients. In particular, by letting h = 1 we obtain irreducibility conditions for compositions of polynomials with integer coefficients. |
| first_indexed | 2024-04-12T22:39:37Z |
| format | Article |
| id | doaj.art-9afa2f2257104177a309feb2e03bcf98 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-12T22:39:37Z |
| publishDate | 2014-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-9afa2f2257104177a309feb2e03bcf982022-12-22T03:13:47ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352014-12-01221738410.2478/auom-2014-0007Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer CoefficientsBonciocat Anca Iuliana0Bonciocat Nicolae Ciprian1Cipu Mihai2Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 2, P.O. Box 1-764, Bucharest 014700, RomaniaSimion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 5, P.O. Box 1-764, Bucharest 014700, RomaniaSimion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 5, P.O. Box 1-764, Bucharest 014700, RomaniaWe provide irreducibility criteria for multiplicative convolutions of polynomials with integer coefficients, that is, for polynomials of the form hdeg f · f(g/h), where f, g, h are polynomials with integer coefficients, and g and h are relatively prime. The irreducibility conditions are expressed in terms of the prime factorization of the leading coefficient of the polynomial hdeg f · f(g/h), the degrees of f, g, h, and the absolute values of their coefficients. In particular, by letting h = 1 we obtain irreducibility conditions for compositions of polynomials with integer coefficients.https://doi.org/10.2478/auom-2014-0007multiplicative convolution of polynomialsresultantsirreducible polynomials |
| spellingShingle | Bonciocat Anca Iuliana Bonciocat Nicolae Ciprian Cipu Mihai Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica multiplicative convolution of polynomials resultants irreducible polynomials |
| title | Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients |
| title_full | Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients |
| title_fullStr | Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients |
| title_full_unstemmed | Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients |
| title_short | Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients |
| title_sort | irreducibility criteria for compositions and multiplicative convolutions of polynomials with integer coefficients |
| topic | multiplicative convolution of polynomials resultants irreducible polynomials |
| url | https://doi.org/10.2478/auom-2014-0007 |
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