LEADER 03980nam 22006495 450 001 9910300247803321 005 20200704094323.0 010 $a3-662-48422-6 024 7 $a10.1007/978-3-662-48422-7 035 $a(CKB)3710000000541911 035 $a(EBL)4213055 035 $a(SSID)ssj0001597197 035 $a(PQKBManifestationID)16297504 035 $a(PQKBTitleCode)TC0001597197 035 $a(PQKBWorkID)14886729 035 $a(PQKB)11085523 035 $a(DE-He213)978-3-662-48422-7 035 $a(MiAaPQ)EBC4213055 035 $a(PPN)190885262 035 $a(EXLCZ)993710000000541911 100 $a20151223d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aComputational Invariant Theory /$fby Harm Derksen, Gregor Kemper 205 $a2nd ed. 2015. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2015. 215 $a1 online resource (387 p.) 225 1 $aEncyclopaedia of Mathematical Sciences,$x0938-0396 300 $aDescription based upon print version of record. 311 $a3-662-48420-X 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aPreface -- 1 Constructive Ideal Theory -- 2 Invariant Theory -- 3 Invariant Theory of Finite Groups -- 4 Invariant Theory of Reductive Groups -- 5 Applications of Invariant Theory -- A. Linear Algebraic Groups -- B. Is one of the two Orbits in the Closure of the Other? by V.L.Popov -- C. Stratification of the Nullcone by V.L.Popov -- Addendum to C. The Source Code of HNC by N.A?Campo and V.L.Popov -- Notation -- Index. . 330 $aThis book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimir Popov, and an addendum by Norbert A'Campo and Vladimir Popov. . 410 0$aEncyclopaedia of Mathematical Sciences,$x0938-0396 606 $aTopological groups 606 $aLie groups 606 $aAlgorithms 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018 615 0$aTopological groups. 615 0$aLie groups. 615 0$aAlgorithms. 615 14$aTopological Groups, Lie Groups. 615 24$aAlgorithms. 676 $a510 700 $aDerksen$b Harm$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755705 702 $aKemper$b Gregor$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300247803321 996 $aComputational Invariant Theory$92536260 997 $aUNINA