Computing in algebraic geometry
a quick start using SINGULAR
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Word Count
81,750 words, Guess
Page Count
327 pages
Identifiers
- Open LibraryOL22729572M
- ISBN-103540289925
- OCLC Control Number64626287
- OCLC Control Numbercomputingalgebra00deck_931
- Library of Congress Control Number2005938498
and 1 more
- Goodreads4287049
Classifications
- LCCQA
Description
Systems of polynomial equations are central to mathematics and its appli- tion to science and engineering. Their solution sets, called algebraic sets, are studied in algebraic geometry, a mathematical discipline of its own. Algebraic geometry has a rich history, being shaped by di?erent schools. We quote from Hartshorne’s introductory textbook (1977): “Algebraic geometry has developed in waves, each with its own language and point of view. The late nineteenth century saw the function-theoretic approach of Brill and Noether, and the purely algebraic approach of K- necker, Dedekind, and Weber. The Italian school followed with Cast- nuovo, Enriques, and Severi, culminating in the classi?cation of algebraic surfaces. Then came the twentieth-century “American school” of Chow, Weil, and Zariski, which gave ?rm algebraic foundations to the Italian - tuition. Mostrecently,SerreandGrothendieck initiatedthe Frenchschool, which has rewritten the foundations of algebraic geometry in terms of schemes and cohomology, and which has an impressive record of solving old problems with new techniques. Each of these schools has introduced new concepts and methods. ” As a result of this historical process, modern algebraic geometry provides a multitude oftheoreticalandhighly abstracttechniques forthe qualitativeand quantitative study of algebraic sets, without actually studying their de?ning equations at the ?rst place. On the other hand, due to the development of powerful computers and e?ectivecomputer algebraalgorithmsatthe endof the twentiethcentury,it is nowadayspossibletostudyexplicitexamplesviatheirequationsinmanycases ofinterest. Inthisway,algebraicgeometrybecomes accessibleto experiments. Theexperimentalmethod,whichhasproventobehighlysuccessfulinnumber theory, now also adds to the toolbox of the algebraic geometer.
Subjects
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- Computing in algebraic geometry: a quick start using SINGULAR
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