A Solution to the Polynomial Hensel Code Conversion Problem: A solution to the polynomial Hensel code conversion problem
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| Titel: | A Solution to the Polynomial Hensel Code Conversion Problem: A solution to the polynomial Hensel code conversion problem |
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| Autoren: | Asish Mukhopadhyay |
| Quelle: | Lecture Notes in Computer Science ISBN: 9783540159841 |
| Verlagsinformationen: | Institute of Electrical and Electronics Engineers (IEEE), 1985. |
| Publikationsjahr: | 1985 |
| Schlagwörter: | 0301 basic medicine, rational function representation, 03 medical and health sciences, arithmetic operations, conversion algorithm, polynomial Hensel code of a rational function, 0102 computer and information sciences, Symbolic computation and algebraic computation, Euclidean algorithm, 01 natural sciences, algebraic simplification, algorithm design |
| Beschreibung: | The polynomial Hensel code of a rational function a(x)/b(x)\(\in F(x)\), F is a field, is the pair \((c(x)d^{-1}(x)\) mod \(x^ r,n)\); r is a positive integer and \(a(x)/b(x)=(c(x))x^ n\) such that c(x) and d(x) have nonzero constant terms. Such a representation scheme was proposed, in analogy with the Hensel code representations of rational numbers, to facilitate arithmetic operations on rational functions and control intermediate expressions well. The difficulty with this scheme was the conversion of such a code to rational function form. In this correspondence, we have given sufficient conditions under which this can be done and have described an algorithm for effecting the conversion. We have also discussed an application, namely, the reduction of a rational function to its simplest form. |
| Publikationsart: | Article Part of book or chapter of book |
| Dateibeschreibung: | application/xml |
| ISSN: | 2326-3814 0018-9340 |
| DOI: | 10.1109/tc.1987.1676950 |
| DOI: | 10.1007/3-540-15984-3_288 |
| Zugangs-URL: | https://zbmath.org/3992931 https://doi.org/10.1109/tc.1987.1676950 https://dblp.uni-trier.de/db/journals/tc/tc36.html#Mukhopadhyay87 https://ieeexplore.ieee.org/document/1676950/ http://dblp.uni-trier.de/db/journals/tc/tc36.html#Mukhopadhyay87 http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.ieee-000001676950 https://www.computer.org/csdl/trans/tc/1987/05/01676950.html http://ieeexplore.ieee.org/document/1676950/ https://dblp.uni-trier.de/db/conf/eurocal/eurocal1985-2.html#Mukhopadhyay85 https://rd.springer.com/chapter/10.1007/3-540-15984-3_288 https://link.springer.com/content/pdf/10.1007%2F3-540-15984-3_288.pdf https://link.springer.com/chapter/10.1007/3-540-15984-3_288 |
| Rights: | IEEE Copyright |
| Dokumentencode: | edsair.doi.dedup.....c8b34fb9aabaf5060d3e7464cdeccc6b |
| Datenbank: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | The polynomial Hensel code of a rational function a(x)/b(x)\(\in F(x)\), F is a field, is the pair \((c(x)d^{-1}(x)\) mod \(x^ r,n)\); r is a positive integer and \(a(x)/b(x)=(c(x))x^ n\) such that c(x) and d(x) have nonzero constant terms. Such a representation scheme was proposed, in analogy with the Hensel code representations of rational numbers, to facilitate arithmetic operations on rational functions and control intermediate expressions well. The difficulty with this scheme was the conversion of such a code to rational function form. In this correspondence, we have given sufficient conditions under which this can be done and have described an algorithm for effecting the conversion. We have also discussed an application, namely, the reduction of a rational function to its simplest form. |
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| ISSN: | 23263814 00189340 |
| DOI: | 10.1109/tc.1987.1676950 |