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

1994
*
Mathematical Reviews
*

“

*divide**and**conquer*”*algorithm**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*. ...##
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Computation of Hilbert-Poincaré series

1997
*
Journal of Pure and Applied Algebra
*

We describe

doi:10.1016/s0022-4049(96)00035-7
fatcat:sv2ofanl3rhold7vyskuc3ymvi
*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. ...##
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Computing the support of monomial iterated mapping cones

2010
*
Journal of symbolic computation
*

We derive in this way

doi:10.1016/j.jsc.2010.06.001
fatcat:2apqqvazzzhdvgyvtdifwkyfeq
*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. ...##
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A package for solving parametric polynomial systems

2010
*
ACM SIGSAM Bulletin
*

*A*“

*divide*

*and*

*conquer*”

*algorithm*

*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 ...

##
###
Algebraic Unimodular Counting
[article]

2001
*
arXiv
*
pre-print

We study algebraic

arXiv:math/0104286v1
fatcat:axybqsfi75hqhojnhjrjthws5i
*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. ...##
###
Algebraic unimodular counting

2003
*
Mathematical programming
*

We study algebraic

doi:10.1007/s10107-003-0383-9
fatcat:iq6nwj6xmbhihb2afr7hokt2ye
*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. ...##
###
Koszul algebras and regularity
[article]

2012
*
arXiv
*
pre-print

This is

arXiv:1211.4324v1
fatcat:ltwu3vuvczg55luwddihm6du7u
*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. ...##
###
Polynomial invariants of finite groups. A survey of recent developments

1997
*
Bulletin of the American Mathematical Society
*

The polynomial invariants

doi:10.1090/s0273-0979-97-00724-6
fatcat:ybr37be3sffa5g6rnye3bkt7pa
*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 ...##
###
Probabilistic algorithms for polynomial absolute factorization

2010
*
ACM SIGSAM Bulletin
*

Abstract We provide

doi:10.1145/1823931.1823936
fatcat:paopikhxnzao7ez5vjkcp6gi3y
*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. ...##
###
Unit normalization of multinomials over Gaussian integers

2010
*
ACM SIGSAM Bulletin
*

The

doi:10.1145/1823931.1823934
fatcat:kn6vfhc32jdclccybwj7diuamm
*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). ...##
###
Enhanced Koszul properties in Galois cohomology
[article]

2020
*
arXiv
*
pre-print

In fact, these versions

arXiv:1811.09272v3
fatcat:jhcubvmbwncuzerd2ig2nedpfa
*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 ...##
###
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)

*A*“*divide**and**conquer*”*algorithm**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*. ...##
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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)

*A*“*divide**and**conquer*”*algorithm**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)

*A*“*divide**and**conquer*”*algorithm**for**Hilbert*-*Poincaré**series*,*multiplicity**and**dimension**of**monomial**ideals*...*Hilbert*-*Poincaré**series*. ...##
###
Numerical path following
[chapter]

1997
*
Handbook of Numerical Analysis
*

This is

doi:10.1016/s1570-8659(97)80002-6
fatcat:y5echiq6ofawxp3urpn5q3alee
*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*. ...
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