Mathematics for Computer Algebra:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1992
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book corresponds to a mathematical course given in 1986/87 at the University Louis Pasteur, Strasbourg. This work is primarily intended for graduate students. The following are necessary prerequisites : a few standard definitions in set theory, the definition of rational integers, some elementary facts in Combinatorics (maybe only Newton's binomial formula), some theorems of Analysis at the level of high schools, and some elementary Algebra (basic results about groups, rings, fields and linear algebra). An important place is given to exercises. These exercises are only rarely direct applications of the course. More often, they constitute complements to the text. Mostly, hints or references are given so that the reader should be able to find solutions. Chapters one and two deal with elementary results of Number Theory, for example : the euclidean algorithm, the Chinese remainder theorem and Fermat's little theorem. These results are useful by themselves, but they also constitute a concrete introduction to some notions in abstract algebra (for example, euclidean rings, principal rings ... ). Algorithms are given for arithmetical operations with long integers. The rest of the book, chapters 3 through 7, deals with polynomials. We give general results on polynomials over arbitrary rings. Then polynomials with complex coefficients are studied in chapter 4, including many estimates on the complex roots of polynomials. Some of these estimates are very useful in the subsequent chapters |
| Beschreibung: | 1 Online-Ressource (XIV, 346p) |
| ISBN: | 9781461391715 9781461391739 |
| DOI: | 10.1007/978-1-4613-9171-5 |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Mignotte, Maurice |
| author_facet | Mignotte, Maurice |
| author_role | aut |
| author_sort | Mignotte, Maurice |
| author_variant | m m mm |
| building | Verbundindex |
| bvnumber | BV042420770 |
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| dewey-full | 518.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.1 |
| dewey-search | 518.1 |
| dewey-sort | 3518.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-9171-5 |
| format | Electronic eBook |
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| id | DE-604.BV042420770 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461391715 9781461391739 |
| language | English |
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| spelling | Mignotte, Maurice Verfasser aut Mathematics for Computer Algebra by Maurice Mignotte New York, NY Springer New York 1992 1 Online-Ressource (XIV, 346p) txt rdacontent c rdamedia cr rdacarrier This book corresponds to a mathematical course given in 1986/87 at the University Louis Pasteur, Strasbourg. This work is primarily intended for graduate students. The following are necessary prerequisites : a few standard definitions in set theory, the definition of rational integers, some elementary facts in Combinatorics (maybe only Newton's binomial formula), some theorems of Analysis at the level of high schools, and some elementary Algebra (basic results about groups, rings, fields and linear algebra). An important place is given to exercises. These exercises are only rarely direct applications of the course. More often, they constitute complements to the text. Mostly, hints or references are given so that the reader should be able to find solutions. Chapters one and two deal with elementary results of Number Theory, for example : the euclidean algorithm, the Chinese remainder theorem and Fermat's little theorem. These results are useful by themselves, but they also constitute a concrete introduction to some notions in abstract algebra (for example, euclidean rings, principal rings ... ). Algorithms are given for arithmetical operations with long integers. The rest of the book, chapters 3 through 7, deals with polynomials. We give general results on polynomials over arbitrary rings. Then polynomials with complex coefficients are studied in chapter 4, including many estimates on the complex roots of polynomials. Some of these estimates are very useful in the subsequent chapters Mathematics Algorithms Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Polynom (DE-588)4046711-9 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 s Algebra (DE-588)4001156-2 s 1\p DE-604 Computeralgebra (DE-588)4010449-7 s 2\p DE-604 Polynom (DE-588)4046711-9 s 3\p DE-604 Zahlentheorie (DE-588)4067277-3 s 4\p DE-604 https://doi.org/10.1007/978-1-4613-9171-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mignotte, Maurice Mathematics for Computer Algebra Mathematics Algorithms Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Polynom (DE-588)4046711-9 gnd Zahlentheorie (DE-588)4067277-3 gnd Algebra (DE-588)4001156-2 gnd Datenverarbeitung (DE-588)4011152-0 gnd Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4046711-9 (DE-588)4067277-3 (DE-588)4001156-2 (DE-588)4011152-0 (DE-588)4010449-7 |
| title | Mathematics for Computer Algebra |
| title_auth | Mathematics for Computer Algebra |
| title_exact_search | Mathematics for Computer Algebra |
| title_full | Mathematics for Computer Algebra by Maurice Mignotte |
| title_fullStr | Mathematics for Computer Algebra by Maurice Mignotte |
| title_full_unstemmed | Mathematics for Computer Algebra by Maurice Mignotte |
| title_short | Mathematics for Computer Algebra |
| title_sort | mathematics for computer algebra |
| topic | Mathematics Algorithms Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Polynom (DE-588)4046711-9 gnd Zahlentheorie (DE-588)4067277-3 gnd Algebra (DE-588)4001156-2 gnd Datenverarbeitung (DE-588)4011152-0 gnd Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Mathematics Algorithms Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Polynom Zahlentheorie Algebra Datenverarbeitung Computeralgebra |
| url | https://doi.org/10.1007/978-1-4613-9171-5 |
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