General Theory of Algebraic Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
2006
|
| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UPA01 Volltext Volltext |
| Beschreibung: | Main description: This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field |
| Beschreibung: | 1 Online-Ressource (368 S.) |
| ISBN: | 9781400826964 |
| DOI: | 10.1515/9781400826964 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042522321 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150423s2006 |||| o||u| ||||||eng d | ||
| 020 | |a 9781400826964 |9 978-1-4008-2696-4 | ||
| 024 | 7 | |a 10.1515/9781400826964 |2 doi | |
| 035 | |a (OCoLC)890472513 | ||
| 035 | |a (DE-599)BVBBV042522321 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-859 |a DE-860 |a DE-Aug4 |a DE-739 |a DE-1046 |a DE-1043 |a DE-858 | ||
| 100 | 1 | |a Bézout, Etienne |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a General Theory of Algebraic Equations |
| 264 | 1 | |a Princeton, N.J. |b Princeton University Press |c 2006 | |
| 300 | |a 1 Online-Ressource (368 S.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Main description: This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field | ||
| 650 | 0 | 7 | |a Algebraische Gleichung |0 (DE-588)4001162-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Gleichung |0 (DE-588)4001162-8 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Feron, Eric |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400826964 |x Verlag |3 Volltext |
| 856 | 4 | 0 | |u http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400826964&searchTitles=true |x Verlag |3 Volltext |
| 912 | |a ZDB-23-DGG | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027956660 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1515/9781400826964?locatt=mode:legacy |l FAB01 |p ZDB-23-DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826964?locatt=mode:legacy |l FAW01 |p ZDB-23-DGG |q FAW_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826964?locatt=mode:legacy |l FCO01 |p ZDB-23-DGG |q FCO_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826964?locatt=mode:legacy |l FHA01 |p ZDB-23-DGG |q FHA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826964?locatt=mode:legacy |l FKE01 |p ZDB-23-DGG |q FKE_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826964?locatt=mode:legacy |l FLA01 |p ZDB-23-DGG |q FLA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9781400826964?locatt=mode:legacy |l UPA01 |p ZDB-23-DGG |q UPA_PDA_DGG |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804153274918502400 |
|---|---|
| any_adam_object | |
| author | Bézout, Etienne |
| author_facet | Bézout, Etienne |
| author_role | aut |
| author_sort | Bézout, Etienne |
| author_variant | e b eb |
| building | Verbundindex |
| bvnumber | BV042522321 |
| collection | ZDB-23-DGG |
| ctrlnum | (OCoLC)890472513 (DE-599)BVBBV042522321 |
| doi_str_mv | 10.1515/9781400826964 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03678nmm a2200457zc 4500</leader><controlfield tag="001">BV042522321</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150423s2006 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400826964</subfield><subfield code="9">978-1-4008-2696-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400826964</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)890472513</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042522321</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-859</subfield><subfield code="a">DE-860</subfield><subfield code="a">DE-Aug4</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-1046</subfield><subfield code="a">DE-1043</subfield><subfield code="a">DE-858</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bézout, Etienne</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">General Theory of Algebraic Equations</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, N.J.</subfield><subfield code="b">Princeton University Press</subfield><subfield code="c">2006</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (368 S.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Main description: This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Gleichung</subfield><subfield code="0">(DE-588)4001162-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraische Gleichung</subfield><subfield code="0">(DE-588)4001162-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Feron, Eric</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400826964</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400826964&searchTitles=true</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027956660</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826964?locatt=mode:legacy</subfield><subfield code="l">FAB01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826964?locatt=mode:legacy</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAW_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826964?locatt=mode:legacy</subfield><subfield code="l">FCO01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FCO_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826964?locatt=mode:legacy</subfield><subfield code="l">FHA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FHA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826964?locatt=mode:legacy</subfield><subfield code="l">FKE01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FKE_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826964?locatt=mode:legacy</subfield><subfield code="l">FLA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FLA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9781400826964?locatt=mode:legacy</subfield><subfield code="l">UPA01</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">UPA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV042522321 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:01Z |
| institution | BVB |
| isbn | 9781400826964 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027956660 |
| oclc_num | 890472513 |
| open_access_boolean | |
| owner | DE-859 DE-860 DE-Aug4 DE-739 DE-1046 DE-1043 DE-858 |
| owner_facet | DE-859 DE-860 DE-Aug4 DE-739 DE-1046 DE-1043 DE-858 |
| physical | 1 Online-Ressource (368 S.) |
| psigel | ZDB-23-DGG ZDB-23-DGG FAW_PDA_DGG ZDB-23-DGG FCO_PDA_DGG ZDB-23-DGG FHA_PDA_DGG ZDB-23-DGG FKE_PDA_DGG ZDB-23-DGG FLA_PDA_DGG ZDB-23-DGG UPA_PDA_DGG |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Princeton University Press |
| record_format | marc |
| spelling | Bézout, Etienne Verfasser aut General Theory of Algebraic Equations Princeton, N.J. Princeton University Press 2006 1 Online-Ressource (368 S.) txt rdacontent c rdamedia cr rdacarrier Main description: This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field Algebraische Gleichung (DE-588)4001162-8 gnd rswk-swf Algebraische Gleichung (DE-588)4001162-8 s 1\p DE-604 Feron, Eric Sonstige oth https://doi.org/10.1515/9781400826964 Verlag Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400826964&searchTitles=true Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bézout, Etienne General Theory of Algebraic Equations Algebraische Gleichung (DE-588)4001162-8 gnd |
| subject_GND | (DE-588)4001162-8 |
| title | General Theory of Algebraic Equations |
| title_auth | General Theory of Algebraic Equations |
| title_exact_search | General Theory of Algebraic Equations |
| title_full | General Theory of Algebraic Equations |
| title_fullStr | General Theory of Algebraic Equations |
| title_full_unstemmed | General Theory of Algebraic Equations |
| title_short | General Theory of Algebraic Equations |
| title_sort | general theory of algebraic equations |
| topic | Algebraische Gleichung (DE-588)4001162-8 gnd |
| topic_facet | Algebraische Gleichung |
| url | https://doi.org/10.1515/9781400826964 http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400826964&searchTitles=true |
| work_keys_str_mv | AT bezoutetienne generaltheoryofalgebraicequations AT feroneric generaltheoryofalgebraicequations |