ACM Communications in Computer Algebra, Vol. 45, No. 3, Issue 177, September 2011 Software for Exact Integration of Polynomials over Polyhedra J. A. De Loera, B. Dutra, M. K¨ppe, S. Moreinis, G. Pinto, J. Wu o Department of Mathematics, University of California Davis, CA, 95616, USA latte@math.ucdavis.edu Abstract We are interested in quickly computing the exact value of integrals of polynomial functions over domains that are decomposable into convex polyhedra (e.g., a tetrahedral or cubical mesh decomposition of space). We describe a software implementation, part of the software LattE, and provide benchmark computations. Introduction The computer algebra community has dedicated a great deal of e ort to developing fast symbolic integration, understood to be the automatic computation of the antiderivatives of functions, as predicted by the fundamental theorem of Calculus. In this work we are instead interested in the exact fast evaluation of integrals over polyhedral regions. More precisely, let P be a d-dimensional rational convex polyhedron inside Rn and let f Q[x1 , . . . , xn ] be a polynomial with rational coe cients. We consider the problem of e ciently computing the exact value of the integral of the polynomial f over P
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/software-for-exact-integration-of-polynomials-over-polyhedra-LeXNIuCjjP
Welcome to DeepDyve! Rent Premier Research Articles and Save Up to 90%
Software for exact integration of polynomials over polyhedra
De Loera, J. A.; Dutra, B.; Köppe, M.; Moreinis, S.; Pinto, G.; Wu, J.
Follow ACM Communications in Computer Algebra
, Volume 45 (3/4)
Association for Computing Machinery – Jan 23, 2012
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
