SIGSAM Bull.最新文献

{"title":"Computer algebra: the end of mathematics?","authors":"B. Buchberger","doi":"10.1145/565145.565147","DOIUrl":"https://doi.org/10.1145/565145.565147","url":null,"abstract":"Mathematical software systems, such as Mathematica, Maple, Derive, and so on, are substantially based on enormous advances in the area of mathematics known as Computer Algebra or Symbolic Mathematics. In fact, everything taught in high school and in the first semesters of a university mathematical education, is available in these systems 'at the touch of the button'. Will mathematics become unnecessary because of this? In the three sections of this essay, I answer this question for non-mathematicians, for mathematicians and for (future) students of mathematics.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125346184","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}

{"title":"Review of weighing the odds, by D. Williams","authors":"W. J. Braun, Hao Yu","doi":"10.1145/565145.565151","DOIUrl":"https://doi.org/10.1145/565145.565151","url":null,"abstract":"Weighing the Odds, by David Williams, is published by Cambridge University Press (publishing date 2001, ISBN 0-521-00618-X). 556 pp. £ 24.95 The author's motivation in writing this book might be inferred from a statement made at the end of the eighth chapter: 'that I have not been more actively involved in Statistics throughout my career and my wish to persuade others not to follow my example in that regard'. Weighing the Odds is a book on Probabili ty and Statistics, written from the perspective of a probabilist. Its intended audience is mathematics students who have not yet been exposed to these subjects. The author's objective is to entice these students by introducing the more mathematical elements of the subjects. The book is highly idiosyncratic, and the writer's personal views are never far from the surface. Thus, the book is perhaps the most lively account of these two subjects that we are aware of. The book contains a relatively small, but interesting treatment of traditional problems and some newer-looking problems. Some excellent hints are provided for some of the more challenging problems. A lot of statistics (all?) is based on conditioning. We cannot write down a model or compute a probability without conditioning on something. At the same time, conditioning is often one of the beginning student's greatest difficulties with the subject of probability and statistics. Therefore, it is refreshing to see a book which opens by addressing conditioning so boldly with an attempt at an intuitive look. Many of the examples are very good: the 'Monty Hall problem' (referred to as the 'Car and Goats Problem') , the 'Two Envelopes' problem, and the \"Birthday problem' are all described clearly, and analyzed carefully either in Chapter 1 or later on in the book. The example referencing system seems confusing, at first. The author warns that the preface should be read first; this warning should be heeded if for no other reason than to discover that problem 19A is really problem A on page 19. Chapter Two contains, among other things, a collection of measure-theoretic results. We're scratching our heads a bit, wondering why the author seems so insistent on avoiding measure theory, when he has gone almost halfway there. Some of the results, such as the monotone convergence theorem, are useful as 'Facts ' , but the description of the n system lemma seems to be deficient. We are not sure anyone without a background in measure theory already would really know what the author is talking about. Similarly, the Banach-Tarski paradox may be bewildering to many readers. On the plus side, we think that the hat-matching problem is a good nontrivial application of the inclusionexclusion principle. Chapter Three gives a concise discussion of random variables, density functions, mass functions, and expectation, and Chapter Four begins with a discussion of conditional probability and independence before moving into the laws of large numbers. The author claims that the","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128645571","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}

{"title":"The golden rule of complementary feedback","authors":"J. Dambacher, P. Rossignol","doi":"10.1145/509520.509522","DOIUrl":"https://doi.org/10.1145/509520.509522","url":null,"abstract":"This work demonstrates the occurrence of the Fibonacci sequence in the qualitative analysis of Lotka---Volterra dynamical systems. Herein we show the golden ratio to govern reciprocal effects between neighboring variables in simple food web models. Impacts to the entire community resulting from perturbation of a population variable can be predicted from the adjoint of the community (Jacobian) matrix, which we render in qualitative terms of complementary feedback cycles. Sequences of complementary feedback cycles follow the Fibonacci sequence, and are also configured as multiples and overlapping harmonics thereof. We derive an absolute-feedback matrix that clarifies the sequence. Patterns of complementary feedback cycles are determined by community structure, which can be portrayed and understood in terms of signed digraph structure.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126752147","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}

{"title":"Computing the minimal telescoper for sums of hypergeometric terms","authors":"H. Q. Le","doi":"10.1145/569746.569748","DOIUrl":"https://doi.org/10.1145/569746.569748","url":null,"abstract":"Let <i>T</i> (<i>n, k</i>) be a hypergeometric term of <i>n</i> and <i>k.</i> We present in this paper an algorithm to construct the minimal telescoper for <i>U</i> (<i>n, k</i>) = ∑<inf><i>m=b</i></inf>^<i>n</i>-1 <i>T</i> (<i>m, k</i>), <i>b</i> ε ℤ, if it exists. We show a Maple implementation of this method and discuss the problem of finding closed forms of definite sums of <i>U</i> (<i>n, k</i>).","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"210 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121548416","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}

{"title":"Solving systems of algebraic equations","authors":"D. Lazard","doi":"10.1145/569746.569750","DOIUrl":"https://doi.org/10.1145/569746.569750","url":null,"abstract":"Let f1,…,fk be k multivariate polynomials which have a finite number of common zeros in the algebraic closure of the ground field, counting the common zeros at infinity. An algorithm is given and proved which reduces the computations of these zeros to the resolution of a single univariate equation whose degree is the number of common zeros. This algorithm gives the whole algebraic and geometric structure of the set of zeros (multiplicities, conjugate zeros,…). When all the polynomials have the same degree, the complexity of this algorithm is polynomial relative to the generic number of solutions.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130362771","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}

{"title":"Enumeration in the Chevalley algebras","authors":"G. Egorychev, V. M. Levchuk","doi":"10.1145/511988.511991","DOIUrl":"https://doi.org/10.1145/511988.511991","url":null,"abstract":"We consider the maximal nilpotent subalgebra NΦ(<i>K</i>) of the Chevalley algebra of the type Φ over an arbitrary field <i>K</i>. Our purpose is enumeration of ideals of NΦ(<i>K</i>) that are invariant under the subgroup <i>D</i> of all diagonal automorphisms. Connections between ideals of NΦ(<i>K</i>) and normal subgroups of the unipotent subgroup of the Chevalley group of the type Φ over <i>K</i> are used. Finally, we use methods of integral representation of sums and of listing lattice paths. We also discuss some other problems of the enumeration of ideals.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130387744","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}

{"title":"Homotopies and polynomial system solving I: basic principles","authors":"I. Kotsireas","doi":"10.1145/504331.504334","DOIUrl":"https://doi.org/10.1145/504331.504334","url":null,"abstract":"We present a survey of some basic ideas involved in the use of homotopies for solving systems of polynomial equations. These ideas are illustrated with many concrete examples. An introductory section on systems of polynomial equations and their solutions contains some necessary terminology that will be used in the sequel. We also describe a general algorithm to solve polynomial systems of n equations in n unknowns using homotopies. A Maple V implementation of the algorithm as well as a few accompanying Maple 6 worksheets are publicly available from the author's web page.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129356918","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}

{"title":"Factoring a binary polynomial of degree over one million","authors":"Olaf Bonorden, J. Gathen, J. Gerhard, Olaf Müller","doi":"10.1145/504331.504333","DOIUrl":"https://doi.org/10.1145/504331.504333","url":null,"abstract":"On 22 May 2000, the factorization of a pseudorandom polynomial of degree 1 048 543 over the binary field Z2 was completed on a 4-processor Linux PC, using roughly 100 CPU-hours. The basic approach is a combination of the factorization software BIPOLAR and a parallel version of Cantor's multiplication algorithm. The PUB-library (Paderborn University BSP library) is used for the implementation of the parallel communication.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128117126","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}

{"title":"An extensible differential equation solver","authors":"B. L. Willis","doi":"10.1145/504331.504332","DOIUrl":"https://doi.org/10.1145/504331.504332","url":null,"abstract":"We describe a method for solving linear second order differential equations in terms of hypergeometric and other (less well known) special functions. Intended as a method for computer algebra systems, the solver described in this article uses a database of functions to construct an anstatz for the solution. A user may extend the solver by appending functions to the database. An overview of a Macsyma language implementation, with sample calculations, is given.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129950133","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}

{"title":"An elementary solution of a minimax problem arising in algorithms for automatic mesh selection","authors":"Robert M Corless","doi":"10.1145/377626.377633","DOIUrl":"https://doi.org/10.1145/377626.377633","url":null,"abstract":"We fill in some details in the solution of a minimax problem arising in automatic mesh selection. We supply two proofs of a result that, while simple, deserves the attention, in particular because we will need it to establish the complexity of an algorithm for factorization of bivariate approximate polynomials in an upcoming paper.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128520982","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}