Computational methods in commutative algebra and algebraic geometry

Wolmer V. Vasconcelos · Algorithms and Computation in Mathematics · 1997

Summary

The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation.

Type: book
Published: 1997-11-06
Cited by: 424
References: 201
DOI: https://doi.org/10.1007/978-3-642-58951-5
OpenAlex: https://openalex.org/W1535646580
Semantic Scholar: https://api.semanticscholar.org/CorpusID:117657329

Keywords

Algebra over a field, Algebraic geometry, Mathematics, Commutative property, Differential algebraic geometry

References

Anneaux locaux henséliensMichel Raynaud — 1970
Die Frage der endlich vielen Schritte in der Theorie der PolynomidealeGrete Hermann — 1926
Buchsbaum rings and applicationsJürgen Stückrad, Wolfgang Vogel — 1986
Theorie der algebraischen Functionen einer Veränderlichen.H. Wéber, Richard Dedekind — 1882
Commutative Semigroup RingsRobert Gilmer — 1984
Algèbre locale : multiplicitésJean Pierre Serre, Peter Gabriel — 1957
An introduction to Gröbner basesRalf Fröberg — 1997
A constructive approach to commutative ring theoryD. A. Spear — 1977
The top of a system of equationsW.V Vasconcelos — 1992
Commutative Algebra: with a View Toward Algebraic GeometryD. Eisenbud — 1995
Arithmetic of Blowup AlgebrasWolmer V. Vasconcelos — 1994
On a problem of ZariskiD. Andrew S. Rees — 1958
Modules over unramified regular local ringsMaurice Auslander — 1961
Fields and ringsIrving Kaplansky — 1969
Maple V Library Reference ManualBruce W. Char, K. O. Geddes, Gastón H. Gonnet — 1992
On the vanishing of Tor in regular local ringsStephen Lichtenbaum — 1966
Algebraic geometry for scientists and engineersShreeram S. Abhyankar — 1990
The homological degree of a moduleWolmer V. Vasconcelos — 1998
Castelnuovo's regularity of graded rings and modulesAkira Ooishi — 1982
Degree bounds in monomial subringsWinfried Bruns, Wolmer V. Vasconcelos, Rafael H. Villarreal — 1997

Cited by

Transfer Operators and State Spaces for Discrete Multidimensional Linear SystemsSigurd Kleon, Ulrich Oberst — 1999
Algoritmos de álgebra conmutativa en anillos de polinomiosSantiago Laplagne — 2012
GEOMETRIC AUSLANDER CRITERION FOR FLATNESS OF AN ANALYTIC MAPPINGJanusz Adamus, Edward Bierstone, Pierre D. Milman — 2009
Symbolic Powers and other Contractions of Ideals in Noetherian RingsAjinkya A. More — 2012
Monoid Congruences, Binomial Ideals, and Their DecompositionsChristopher O’Neill — 2014
Irreducible decomposition of binomial idealsThomas Kahle, Ezra Miller, Christopher O’Neill — 2015
Some Applications of Bezoutians in Effective Algebraic GeometryMohamed Elkadi, Bernard Mourrain — 1998
Étude du résultant sur une variété algébriqueLaurent Busé — 2001
Computer algebra methods for equivariant dynamical systemsKarin Gatermann — 2000
Profondeur, dimension et résolutions en algèbre commutative : quelques aspects effectifsC. Tête — 2014
EFFECTIVE REGULARITY CRITERIA FOR ANALYTIC MAPPINGSJanusz Adamus — 2010
Sobre a fibra especial e o teorema de Risler-Teissier para filtraçõesP. H. Lima — 2013
Alexander Duality for Monomial Ideals and Their ResolutionsEzra Miller — 1998
On Fitting ideals of logarithmic vector fields and Saito's criterionBrian Pike — 2013
Classes of Monomial IdealsAnda Olteanu — 2008
Complexity Degrees of Algebraic StructuresWolmer V. Vasconcelos — 2014
Elimination theory in codimension one and applicationsLaurent Busé — 2006
On Castelnuovo-Mumford regularity of projective curvesIsabel Bermejo, Philippe Giménez — 1999
Linearity conditions on the Jacobian ideal and logarithmic--meromorphic comparison for free divisorsLuis Narváez Macarro — 2008
Edge ideals: algebraic and combinatorial propertiesSusan Morey, Rafael H. Villarreal — 2010

Computational methods in commutative algebra and algebraic geometry

Summary

Keywords

References

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