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001 978-3-642-38742-5
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020 _a9783642387425
_9978-3-642-38742-5
024 7 _a10.1007/978-3-642-38742-5
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
245 1 0 _aMonomial Ideals, Computations and Applications
_h[electronic resource] /
_cedited by Anna M. Bigatti, Philippe Gimenez, Eduardo Sáenz-de-Cabezón.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXI, 194 p. 42 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2083
505 0 _aA survey on Stanley depth -- Stanley decompositions using CoCoA -- A beginner’s guide to edge and cover ideals -- Edge ideals using Macaulay2 -- Local cohomology modules supported on monomial ideals -- Local Cohomology using Macaulay2.
520 _aThis work covers three important aspects of monomials ideals in the three chapters "Stanley decompositions" by Jürgen Herzog, "Edge ideals" by Adam Van Tuyl and "Local cohomology" by Josep Álvarez Montaner. The chapters, written by top experts, include computer tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the main objects of combinatorial commutative algebra. Also, they are of major importance for at least three reasons. Firstly, Gröbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals. Secondly, the combinatorial structure of monomial ideals connects them to other combinatorial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. And thirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures.
650 0 _aAlgebra.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
700 1 _aBigatti, Anna M.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aGimenez, Philippe.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aSáenz-de-Cabezón, Eduardo.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642387432
776 0 8 _iPrinted edition:
_z9783642387418
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2083
856 4 0 _uhttps://doi.org/10.1007/978-3-642-38742-5
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10568
_d10568