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Towards more accurate separation bounds of empirical polynomials 趋向更精确的经验多项式分离界
SIGSAM Bull. Pub Date : 2004-12-01 DOI: 10.1145/1060328.1060330
Kosaku Nagasaka
{"title":"Towards more accurate separation bounds of empirical polynomials","authors":"Kosaku Nagasaka","doi":"10.1145/1060328.1060330","DOIUrl":"https://doi.org/10.1145/1060328.1060330","url":null,"abstract":"We study the problem of bounding a polynomial which is absolutely irreducible, away from polynomials which are not absolutely irreducible. These separation bounds are useful for testing whether an empirical polynomial is absolutely irreducible or not, for the given tolerance or error bound of its coefficients. Kaltofen and May studied a method which finds applicable separation bounds using an absolute irreducibility criterion due to Ruppert. In this paper, we study some improvements on their method, by which we are able to find more accurate separation bounds, for bivariate polynomials.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124971889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
A theorem for separating close roots of a polynomial and its derivatives 分离多项式及其导数的紧根的定理
SIGSAM Bull. Pub Date : 2004-09-01 DOI: 10.1145/1040034.1040039
Tateaki Sasaki
{"title":"A theorem for separating close roots of a polynomial and its derivatives","authors":"Tateaki Sasaki","doi":"10.1145/1040034.1040039","DOIUrl":"https://doi.org/10.1145/1040034.1040039","url":null,"abstract":"Let <i>P</i>(<i>z</i>) be a univariate polynomial over <b>C</b>, having <i>m</i> close roots around the origin. We present a theorem which separates a cluster of <i>m - k</i> close roots of <i>d<sup>k</sup> P</i>/d<i>z<sup>k</sup></i> around the origin from the other roots, where 0 ≤ <i>k</i> < <i>m</i>. We compare our theorem with those of Marden-Walsh and Yakoubsohn, and show superiority of our theorem.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116781308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
ANTS VI: algorithmic number theory symposium poster abstracts 蚂蚁VI:算法数论研讨会海报摘要
SIGSAM Bull. Pub Date : 2004-09-01 DOI: 10.1145/1040034.1040041
I. Kotsireas, Emil J. Volcheck
{"title":"ANTS VI: algorithmic number theory symposium poster abstracts","authors":"I. Kotsireas, Emil J. Volcheck","doi":"10.1145/1040034.1040041","DOIUrl":"https://doi.org/10.1145/1040034.1040041","url":null,"abstract":"The Algorithmic Number Theory Symposium (ANTS) meetings are held bianually since 1994, and have become the premier international forum for the presentation of new research in Computational Number Theory. Previous ANTS conferences have been held as follows: ANTS I, 1994, Cornell University, USA, ANTS II, 1996, University of Bordeaux, France, ANTS III, 1998 Reed College, USA, ANTS IV, 2000, University of Leiden, Netherlands, ANTS V, 2002, University of Sydney, Australia. ANTS VI was held on June 13-18, 2004 at the University of Vermont in the United States, http://web.ew.usna.edu/~ants. ANTS VII is scheduled to be held in Berlin in the summer of 2006. Below are six poster abstracts presented during ANTS VI. We thank the organizers for the opportunity to publish the ANTS VI posters. We hope to help bring this work to a wider audience, not only to computational number theorists, but throughout the Symbolic Computation community.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130447191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Not seeing the roots for the branches: multivalued functions in computer algebra 看不到分支的根:计算机代数中的多值函数
SIGSAM Bull. Pub Date : 2004-09-01 DOI: 10.1145/1040034.1040036
D. J. Jeffrey, A. Norman
{"title":"Not seeing the roots for the branches: multivalued functions in computer algebra","authors":"D. J. Jeffrey, A. Norman","doi":"10.1145/1040034.1040036","DOIUrl":"https://doi.org/10.1145/1040034.1040036","url":null,"abstract":"We discuss the multiple definitions of multivalued functions and their suitability for computer algebra systems. We focus the discussion by taking one specific problem and considering how it is solved using different definitions. Our example problem is the classical one of calculating the roots of a cubic polynomial from the Cardano formulae, which contain fractional powers. We show that some definitions of these functions result in formulae that are correct only in the sense that they give candidates for solutions; these candidates must then be tested. Formulae that are based on single-valued functions, in contrast, are efficient and direct.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133081761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
On the size of minimal blocking sets of Q(4; q), for q = 5,7 Q(4)的最小块集的大小Q)，对于Q = 5,7
SIGSAM Bull. Pub Date : 2004-09-01 DOI: 10.1145/1040034.1040037
J. Beule, A. Hoogewijs, L. Storme
{"title":"On the size of minimal blocking sets of Q(4; q), for q = 5,7","authors":"J. Beule, A. Hoogewijs, L. Storme","doi":"10.1145/1040034.1040037","DOIUrl":"https://doi.org/10.1145/1040034.1040037","url":null,"abstract":"Let Q(2n + 2; <i>q</i>) denote the non-singular parabolic quadric in the projective geometry PG(2<i>n</i> + 2; <i>q</i>). We describe the implementation in GAP of an algorithm to study the problem of the minimal number of points of a minimal blocking set, different from an ovoid, of Q(4; <i>q</i>), for <i>q</i> = 5; 7.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132993403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Review of "Computational Commutative Algebra I by Martin Kreuzer and Lorenzo Robbiano", Springer Verlag, 2000, ISBN 3-540-67733-X. 《计算交换代数I: Martin Kreuzer and Lorenzo Robbiano》，Springer出版社，2000,ISBN 3-540-67733-X。
SIGSAM Bull. Pub Date : 2004-06-01 DOI: 10.1145/1041791.1041797
L. González-Vega, T. Recio
{"title":"Review of \"Computational Commutative Algebra I by Martin Kreuzer and Lorenzo Robbiano\", Springer Verlag, 2000, ISBN 3-540-67733-X.","authors":"L. González-Vega, T. Recio","doi":"10.1145/1041791.1041797","DOIUrl":"https://doi.org/10.1145/1041791.1041797","url":null,"abstract":"Authors, we can assume, start writing a book with pleasure. As their project progresses, their basic mood might turn to hope (of soon getting to the end of an overwhelming project). Conversely, readers, we assume, to start browsing a book with hope (of learning something interesting) but only in some special cases do they continue reading it with pleasure.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127537467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
MKM: a new interdisciplinary field of research MKM:一个新的跨学科研究领域
SIGSAM Bull. Pub Date : 2004-06-01 DOI: 10.1145/1041791.1041795
W. Farmer
{"title":"MKM: a new interdisciplinary field of research","authors":"W. Farmer","doi":"10.1145/1041791.1041795","DOIUrl":"https://doi.org/10.1145/1041791.1041795","url":null,"abstract":"Mathematical Knowledge Management (MKM) is a new interdisciplinary field of research in the intersection of mathematics, computer science, library science, and scientific publishing. Its objective is to develop new and better ways of managing mathematical knowledge using sophisticated software tools. Its grand challenge is to create a universal digital mathematics library (UDML), accessible via the World-Wide Web, that contains essentially all mathematical knowledge (intended for the public). The challenges facing MKM are daunting, but a UDML, even just partially constructed, would transform how mathematics is learned and practiced.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"186 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122594711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 19
Solving parametric linear systems: an experiment with constraint algebraic programming 求解参数线性系统:约束代数规划的实验
SIGSAM Bull. Pub Date : 2004-06-01 DOI: 10.1145/1041791.1041793
C. Ballarin, Manuel Kauers
{"title":"Solving parametric linear systems: an experiment with constraint algebraic programming","authors":"C. Ballarin, Manuel Kauers","doi":"10.1145/1041791.1041793","DOIUrl":"https://doi.org/10.1145/1041791.1041793","url":null,"abstract":"Algorithms in computer algebra are usually designed for a fixed set of domains. For example, algorithms over the domain of polynomials are not applicable to parameters because the inherent assumption that the indeterminate X bears no algebraic relation to other objects is violated.We propose to use a technique from model theory known as constraint programming to gain more flexibility, and we show how it can be applied to the Gaussian algorithm to be used for parametric systems. Our experiments suggest that in practice this leads to results comparable to the algorithm for parametric linear systems by Sit [9] --- at least if the parameters are sparse.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114494758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 24
Online Gröbner Basis [OGB] 网上Gröbner基础[OGB]
SIGSAM Bull. Pub Date : 2004-03-01 DOI: 10.1145/980175.980183
M. McGettrick
{"title":"Online Gröbner Basis [OGB]","authors":"M. McGettrick","doi":"10.1145/980175.980183","DOIUrl":"https://doi.org/10.1145/980175.980183","url":null,"abstract":"1 What OGB does OGB calculates in the polynomical ring Q[x1, x2, ..., xn], i.e the set of all polynomials in n variables with rational coefficients. It does all Gröbner Basis calculations using lexicographical ordering, defined as follows: A given term T1 = c1x 1 x a2 2 ...xn n is lexicographically greater than another term T2 = c2x b1 1 x2 2 ...xn n (and so we write T1 > T2) iff the first non-zero term in the vector (a1 − b1, a2 − b2, ..., an − bn) is positive. Here cj ∈ Q, i.e. cj = m/n with m, n ∈ Z. OGB calculates the Gröbner Basis, the minimal Gröbner Basis (with the property that the leading monomial in polynomial i is not a factor of the leading monomial in polynomial j for any i 6= j), or the reduced Gröbner Basis (with the property that the leading monomial in polynomial i is not a factor of any monomial in polynomial j for j 6= i). 2 ...yet another Gröbner Basis calculator??? This software implements known algorithms that have been implemented many other places. However the focus of OGB is on 1. Applicability to solving systems of equations: This is why the lexicographic ordering is chosen, and the reduced basis is calculated. It is known that if there are a sufficient number of equations, and if the system is solvable, the reduced basis under lexicographical ordering is always triangular and moreover the last polynomial is univariate. 2. Pedagogy: OGB is written to educate both students and academics who are not mathematicians but use mathematics (scientists, engineers,...)","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121934181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The TOP-C parallel model and symbolic algebra TOP-C并行模型与符号代数
SIGSAM Bull. Pub Date : 2004-03-01 DOI: 10.1145/980175.980181
G. Cooperman
{"title":"The TOP-C parallel model and symbolic algebra","authors":"G. Cooperman","doi":"10.1145/980175.980181","DOIUrl":"https://doi.org/10.1145/980175.980181","url":null,"abstract":"The TOP-C parallel model was specifically designed to be optimal for many symbolic algebra algorithms. Symbolic algebra problems are irregular and differ from typical problems of numerical analysis in two respects.1. They have large amounts of intermediate swell.2. They are usually not able to make good use of data parallelism.The TOP-C model was developed on the basis of experience over ten years. The model was first implemented for distributed memory for GCL (GNU Common LISP), and is currently available as ParGCL [1]. That work was extended to ParGAP [3], a binding to the interactive language GAP (Groups, Algorithms and Programming). Finally, a C/C++ version, Task Oriented Parallel C/C++, lent its acronym to the TOP-C model [2].A sign of the maturity of TOP-C is the parallelization of Geant4 (Geometry and Tracking) [4]. Geant4 is a million-line program for the simulation of particle-matter interaction used in the design of collider experiments at CERN. Current issues facing parallelization include the slowness of RAM [5] and the need for semi-automated marshalling (serialization of objects) [6].","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115036125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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