Review2 of Solving polynomial equation systems II: Macaulay s paradigm and Gr bner technology o Author of Book: Teo Mora Cambridge University Press (2005), 759 pages ISBN 0 521 81156 2, Price $150.00 new3 Review by S. C. Coutinho collier@impa.br4 Introduction to the area One of the most important areas of algebra for most of the 19th century was the theory of algebraic invariants. Take a group acting on a polynomial ring with n variables over a eld. The polynomials that are xed points for this action form another ring, called its ring of invariants. The best known example is given by the symmetric group on n symbols acting on the ring of polynomials by permuting the n variables x1 , . . . , xn . In this case, a polynomial is xed by the action if it remains unchanged under any permutation of its variables. In other words, the xed points are the symmetric polynomials. Moreover, it is known at least since the 17th century that every symmetric polynomial can be written in terms of a nite set of so-called elementary symmetric polynomials. For n = 3, this set consists of only three polynomials, x1 +
End of preview. The entire article is 4 pages. To view the full-text, please rent this article to continue.
/lp/association-for-computing-machinery/review-of-solving-polynomial-equation-systems-ii-macaulay-s-paradigm-f1GO59CH7X
Welcome to DeepDyve! Rent Premier Research Articles and Save Up to 90%
Review of solving polynomial equation systems II: Macaulay's paradigm and Gröbner technology by Teo Mora (Cambridge University Press 2005)
Reviewer-Coutinho, S. C.
Follow ACM SIGACT News
, Volume 40 (1)
Association for Computing Machinery – Feb 28, 2009
More Info
More Like This Article
View All dataSource[]=actageo&dataSource[]=aspet&dataSource[]=aaos&dataSource[]=aacc&dataSource[]=aacr&dataSource[]=aea&dataSource[]=aip&dataSource[]=ajnr&dataSource[]=ams&dataSource[]=aps_physical&dataSource[]=appi_book&dataSource[]=appi_journal&dataSource[]=apha&dataSource[]=asip&dataSource[]=asm&dataSource[]=asn&dataSource[]=aspb&dataSource[]=avs&dataSource[]=annual_reviews&dataSource[]=arxiv&dataSource[]=acm&dataSource[]=berghahn&dataSource[]=cabi&dataSource[]=clinical_trials&dataSource[]=dailymed&dataSource[]=degruyter&dataSource[]=du_press&dataSource[]=esa&dataSource[]=eu_press&dataSource[]=elsevier&dataSource[]=emerald&dataSource[]=ejtr&dataSource[]=emea&dataSource[]=epo&dataSource[]=faseb&dataSource[]=gsa&dataSource[]=health_affairs&dataSource[]=hindawi&dataSource[]=imanager&dataSource[]=imedpub&dataSource[]=informa_healthcare&dataSource[]=informs&dataSource[]=iop&dataSource[]=iucr&dataSource[]=iospress&dataSource[]=jbjs&dataSource[]=leftcoast&dataSource[]=lu_press&dataSource[]=mesharpe&dataSource[]=mary_ann_liebert&dataSource[]=medline&dataSource[]=mit_press&dataSource[]=nature&dataSource[]=oxford&dataSource[]=pier_professional&dataSource[]=pnas&dataSource[]=portlandpress&dataSource[]=psyc_articles&dataSource[]=psyc_books&dataSource[]=psyc_critiques&dataSource[]=plos_journal&dataSource[]=pubmed_central&dataSource[]=rsna&dataSource[]=rockefeller&dataSource[]=rcn&dataSource[]=ria&dataSource[]=rsc&dataSource[]=sage&dataSource[]=spie&dataSource[]=springer_journal&dataSource[]=springer&dataSource[]=taylor_francis&dataSource[]=aps&dataSource[]=the_scientist&dataSource[]=uc_press&dataSource[]=uspto_abstract&dataSource[]=wiley&dataSource[]=pct
© 2012 DeepDyve, Inc. All rights reserved.
Terms of Service | Privacy Policy
