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Page 6244 of Mathematical Reviews Vol. , Issue 94k [page]

1994 Mathematical Reviews  
divide and conqueralgorithm for Hilbert-Poincaré series, multiplicity and dimension of monomial ideals.  ...  The Hilbert series of A contains information about e.g. the dimension and de- gree of A.  ... 

Computation of Hilbert-Poincaré series

Anna M. Bigatti
1997 Journal of Pure and Applied Algebra  
We describe a new algorithm for computing standard and multi-graded Hilbert-Poincare series of a monomial ideal.  ...  We compare it with different strategies along with implementation details and timing data. @ 1997 Elsevier Science B.V.  ...  Yan and J. Hollman for their useful remarks and suggestions.  ... 
doi:10.1016/s0022-4049(96)00035-7 fatcat:sv2ofanl3rhold7vyskuc3ymvi

Computing the support of monomial iterated mapping cones

Eduardo Sáenz-de-Cabezón
2010 Journal of symbolic computation  
We derive in this way algorithms to obtain homological and numerical invariants of monomial ideals without actually computing their resolution.  ...  Our computations include Betti diagrams, Hilbert series and irreducible decompositions. The algorithms derived by the method presented in the paper are efficient in practice as shown by experiments.  ...  Acknowledgements The author was partially supported by Ministerio de Ciencia e Innovación (Spain), grant MTM2009-13842-C02-01 and Comunidad Autónoma de La Rioja (Spain), grant FOMENTA 2007/03.  ... 
doi:10.1016/j.jsc.2010.06.001 fatcat:2apqqvazzzhdvgyvtdifwkyfeq

A package for solving parametric polynomial systems

Jürgen Gerhard, D. J. Jeffrey, Guillaume Moroz
2010 ACM SIGSAM Bulletin  
Adivide and conqueralgorithm for Hilbert-Poincaré series, multiplicity and dimension of monomial ideals.  ...  Every multi-state coherent system has a monomial ideal associated to it and the knowledge of its multigraded Betti numbers and/or a certain form of its multigraded Hilbert series (based on free resolutions  ... 
doi:10.1145/1823931.1823933 fatcat:zulpwzkc6jdgrebkevri3jmqye

Algebraic Unimodular Counting [article]

Jesus A. De Loera, Bernd Sturmfels
2001 arXiv   pre-print
We study algebraic algorithms for expressing the number of non-negative integer solutions to a unimodular system of linear equations as a function of the right hand side.  ...  Our methods include Todd classes of toric varieties via Gr\"obner bases, and rational generating functions as in Barvinok's algorithm.  ...  Both the evaluation and the divide-and-conquer schemes depend on the specific matrix A. Mount reports the complete solution for contingency tables of size 4 × 4.  ... 
arXiv:math/0104286v1 fatcat:axybqsfi75hqhojnhjrjthws5i

Algebraic unimodular counting

Jes�s A. De Loera, Bernd Sturmfels
2003 Mathematical programming  
We study algebraic algorithms for expressing the number of non-negative integer solutions to a unimodular system of linear equations as a function of the right hand side.  ...  Our methods include Todd classes of toric varieties via Gröbner bases, and rational generating functions as in Barvinok's algorithm.  ...  Both the evaluation and the divide-and-conquer schemes depend on the specific matrix A. Mount reports the complete solution for contingency tables of size 4 × 4.  ... 
doi:10.1007/s10107-003-0383-9 fatcat:iq6nwj6xmbhihb2afr7hokt2ye

Koszul algebras and regularity [article]

Aldo Conca, Emanuela De Negri, Maria Evelina Rossi
2012 arXiv   pre-print
This is a survey paper on commutative Koszul algebras and Castelnuovo-Mumford regularity. We describe several techniques to establish the Koszulness of algebras.  ...  We discuss variants of the Koszul property such as strongly Koszul, absolutely Koszul and universally Koszul. We present several open problems related with these notions and their local variants.  ...  The Hilbert series and the Poincaré series of R are: H R (z) = H G (z) = ∑ i≥0 dim(m i / m i+1 )z i and P R (z) = ∑ i≥0 dim Tor R i (K, K)z i . 6.1. Koszul rings.  ... 
arXiv:1211.4324v1 fatcat:ltwu3vuvczg55luwddihm6du7u

Polynomial invariants of finite groups. A survey of recent developments

Larry Smith
1997 Bulletin of the American Mathematical Society  
The polynomial invariants of finite groups have been studied for more than a century now and continue to find new applications and generate interesting problems.  ...  In this article we will survey some of the recent developments coming primarily from algebraic topology and the rediscovery of old open problems.  ...  The Poincaré series (also called the Hilbert series in much of the literature) of a graded vector space of finite type is defined to be the formal power series P (M, t) = dim F (M k )t k . 6 It should  ... 
doi:10.1090/s0273-0979-97-00724-6 fatcat:ybr37be3sffa5g6rnye3bkt7pa

Probabilistic algorithms for polynomial absolute factorization

C. Bertone, G. Chéze, A. Galligo
2010 ACM SIGSAM Bulletin  
Abstract We provide a method of determining whether there exist some p ∈ P and f ∈ F such that p is divisible by f for a pair of real multivariate interval polynomials, P and F .  ...  We show a fast algorithm to find a rational number in a given real interval whose denominator is minimal. The algorithm is similar to the regular continued fraction expansion for a real number.  ...  We applied the ISCZ method to Buchberger's algorithm that computes Gröbner bases w.r.t. the lexicographic order in Maple on a computer.  ... 
doi:10.1145/1823931.1823936 fatcat:paopikhxnzao7ez5vjkcp6gi3y

Unit normalization of multinomials over Gaussian integers

David R. Stoutemyer
2010 ACM SIGSAM Bulletin  
The algorithm is similar to the regular continued fraction expansion for a real number.  ...  A new Maple package for solving parametric systems of polynomial equations and inequalities is described. The main idea for solving such a system is as follows.  ...  Namely, if the given algorithm A terminates with an input I, then the ISCZ method for A always terminates in a finite number of steps and gives the same result as the output of A(I).  ... 
doi:10.1145/1823931.1823934 fatcat:kn6vfhc32jdclccybwj7diuamm

Enhanced Koszul properties in Galois cohomology [article]

Jan Minac, Marina Palaisti, Federico W. Pasini, Nguyen Duy Tan
2020 arXiv   pre-print
In fact, these versions of Koszulity hold for all finitely generated maximal pro-p quotients of absolute Galois groups which are currently understood.  ...  We prove that Galois cohomology satisfies several surprisingly strong versions of Koszul properties, under a well known conjecture, in the finitely generated case.  ...  In [Min93] , for any Pythagorean formally real field F with finitely many square classes, the Hilbert series of the algebra H • (G F (2), F 2 ) is introduced under the name of the Poincaré series of G  ... 
arXiv:1811.09272v3 fatcat:jhcubvmbwncuzerd2ig2nedpfa

Page 1352 of Mathematical Reviews Vol. 26, Issue Index [page]

Mathematical Reviews  
(English summary) 94e:68138 Bigatti, Anna Maria (with Conti, Pasqualina; Robbiano, Lorenzo; Traverso, Carlo) Adivide and conqueralgorithm for Hilbert-Poincaré series, multiplicity and dimension of  ...  (English summary) 94c:68060 Chazelle, Bernard An optimal algorithm for intersecting three-dimensional convex polyhedra. 94¢:68196 — Cutting hyperplanes for divide-and-conquer.  ... 

Page 120 of Mathematical Reviews Vol. 26, Issue Index [page]

Mathematical Reviews  
(Lé Tuan Hoa) 94a:13030 13P10 — (with Conti, Pasqualina; Robbiano, Lorenzo; Traverso, Carlo) Adivide and conqueralgorithm for Hilbert-Poincaré series, multiplicity and dimension of monomial ideals.  ...  (Ralf Fréberg) 94k:13033 13P10 (13-04, 13D40, 68Q25, 68Q40) — Upper bounds for the Betti numbers of a given Hilbert function. Comm. Algebra 21 (1993), no. 7, 2317-2334.  ... 

Page 1123 of Mathematical Reviews Vol. 26, Issue Index [page]

Mathematical Reviews  
(Lé Tuan Hoa) 94a:13030 13P10 — (with Bigatti, Anna Maria; Conti, Pasqualina; Traverso, Carlo) Adivide and conqueralgorithm for Hilbert-Poincaré series, multiplicity and dimension of monomial ideals  ...  Hilbert-Poincaré series.  ... 

Numerical path following [chapter]

Eugene L. Allgower, Kurt Georg
1997 Handbook of Numerical Analysis  
This is a Fortran subprogram for the evaluation of the dependence of the solution of a nonlinear system on a parameter.  ...  DYNAMICS This is a software for the numerical exploration of chaotic systems developed by Nusse and Yorke [1992] of the University of Maryland.  ...  ., of size < 50. This technique is referred to as divide and conquer.  ... 
doi:10.1016/s1570-8659(97)80002-6 fatcat:y5echiq6ofawxp3urpn5q3alee
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