SIGSAM Bull.最新文献

{"title":"Polynomial transformations of Tschirnhaus, Bring and Jerrard","authors":"V. Adamchik, D. J. Jeffrey","doi":"10.1145/1093528.1093530","DOIUrl":"https://doi.org/10.1145/1093528.1093530","url":null,"abstract":"Tschirnhaus gave transformations for the elimination of some of the intermediate terms in a polynomial. His transformations were developed further by Bring and Jerrard, and here we describe all these transformations in modern notation. We also discuss their possible utility for polynomial solving, particularly with respect to the Mathematica poster on the solution of the quintic.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129927350","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":"On the relationship between the Dixon-based resultant construction and the supports of polynomial systems","authors":"Fabrizio Caruso","doi":"10.1145/990353.990358","DOIUrl":"https://doi.org/10.1145/990353.990358","url":null,"abstract":"Different matrix based resultant formulations use the support of the polynomials in a polynomial system in various ways for setting up resultant matrices for computing resultants. Every formulation suffers, however, from the fact that for most polynomial systems, the output is not a resultant, but rather a nontrivial multiple of the resultant, called a projection operator. It is shown that for the Dixon-based resultant methods, the degree of the projection operator of unmixed polynomial systems is determined by the support hull of the support of the polynomial system. This is similar to the property that the Newton polytope of a support determines the degree of the resultant for toric zeros.The support hull of a given support is similar to its convex hull (Newton polytope) except that instead of the Euclidean distance, the support hull is defined using relative quadrant (octant) position of points. The concept of a support hull interior point with respect to a support is defined. It is shown that for unmixed polynomial systems, generic inclusion of terms corresponding to support hull interior points does not change the size of the Dixon matrix (hence, the degree of the projection operator). The support hull of a support is the closure of the support with respect to support-interior points.The above results are shown to hold both for the generalized Dixon formulation as well as for Sylvester-type Dixon dialytic matrices constructed using the Dixon formulation.It is proved that for an unmixed polynomial system, the size of the Dixon matrix is less than or equal to the Minkowski sum of the alternating sums of the successive projections of the support of the polynomial system. This is a refinement of the result in Kapur and Saxena 1996 about the size of the Dixon matrix of a polynomial system, where it was shown that for the unmixed polynomial system, the size of the Dixon matrix is less than or equal to the Minkowski sum of the successive projection of the support.Many other combinatorial properties of the size of the Dixon matrix and the structure of the Dixon polynomial of a given polynomial system are related to the support hull of the polynomial system and their projections along different dimensions.This research is supported in part by NSF grant nos. CCR-0203051, CDA-9503064 and a grant from the Computer Science Research Institute at Sandia National Labs.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114605055","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":"MAD: a flexible system for authoring mathematical documents","authors":"L. Meunier","doi":"10.1145/990353.990365","DOIUrl":"https://doi.org/10.1145/990353.990365","url":null,"abstract":"MAD (Mathematical Abstract Document) is a document preparation system integrated with MAPLE. MAD provides a simplified model for describing a collection of logically structured documents with mathematical content. MAD also provides routines for manipulating the data structure that represents such documents and for exporting this data structure into standard formats, such as IbTEEX, PostScript, PDF and HTML. Integrating MAD into a computer algebra system such as MAPLE brings the following original features: 1) the automation of the computation and of the typesetting of mathematical formulae, graphs and tables; 2) the automation of the building of documents thanks to the underlying programming language. The system MAD was created in order to generate the interface of the Encyclopedia of Special Functions (ESF, h t t p : / / a 1 go . i n r i a . f r / e s f) [2]. The ESF is an automatically generated encyclopedia, where all mathematical formulae and graphs are computed by generic algorithms. The ESF can be compared up to some extent with the Abramowitz and Stegun's Handbook of Mathematical Functions [1] and the DLMF project 2. This kind of mathematical document sets the following requirements for it to be easily used: pretty display (human readable format) and semantics (machine understandable format) of the mathematical formulae, cross references for browsing and quoting, paper version in several formats. The system MAD is designed to automate the edition and the production of such mathematical documents.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123817653","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 limits of sequences","authors":"Manuel Kauers","doi":"10.1145/990353.990362","DOIUrl":"https://doi.org/10.1145/990353.990362","url":null,"abstract":"Automated asymptotic methods only recently became subject of symbolic computation. Contributions like [3, 12, 5, 10, 13] discuss a variety of aspects concerning the asymptotic analysis of continuous, real-valued functions. First approaches employed generalized series expansion [5, 3], later methods are based on the theory of Hardy fields [6]. So far, it seems that more emphasis was laid on the treatment of continuous functions, and although some mathematical fundaments are already available [1, 2], algorithmic approaches for the discrete case seem rare. Our poster focuses on limit computation of sequences in Q, more specifically, of sequences that can be defined by HE-expressions [7]. We will present a rather simple approach which avoids the use of heavy theory but whose first applications already give promising fine results.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"164 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116307862","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":"Exact implicitization of polynomial curves and surfaces","authors":"I. Kotsireas, Edmond Lau, Richard Voino","doi":"10.1145/990353.990364","DOIUrl":"https://doi.org/10.1145/990353.990364","url":null,"abstract":"Recent advances in the eigenvalue method for implicitization include an efficient C/GMP implementation for polynomial curves and surfaces and investigation of structural properties of implicitization matrices. These advances will be illustrated with numerous examples. CAGD applications will be discussed as well.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133498706","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":"Using computer algebra system SINGULAR:PLURAL for computations in noncommutative polynomial algebras","authors":"V. Levandovskyy, H. Schönemann","doi":"10.1145/990353.990363","DOIUrl":"https://doi.org/10.1145/990353.990363","url":null,"abstract":"We give a detailed account of algorithms and applications provided with SINGULAR:PLURAL (we call it PLURAL for short). The poster is done in form of (big) one-page introduction to the capabilities of the system.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130182972","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":"Validated numerical methods for systems and control engineering","authors":"M. Kanno, Malcolm C. Smith","doi":"10.1145/990353.990361","DOIUrl":"https://doi.org/10.1145/990353.990361","url":null,"abstract":"The aim of this research is to investigate the development of numerical methods for systems and control which have a guarantee on accuracy. An end-product of such research is an algorithm which could be described as \"infallible\" in the following sense: the user would specify a priori a tolerance as small as desired, and the computer would provide an answer which was guaranteed to be accurate to the specified tolerance. Though this is an established subject within Computer Science [5], as well as a few application areas in science and engineering (see [1, Part III]), the direction appears to be quite new in the control systems area. A characteristic feature of previous work is the application of computer algebra tools and the avoidance of floating-point arithmetic.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127112605","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":"Contributions to constructive polynomial ideal theory XXIII: forgotten works of Leningrad mathematician N. M. Gjunter on polynomial ideal theory","authors":"Bodo Renschuch, H. Roloff, G. G. Rasputin, Michael Abramson","doi":"10.1145/944567.944569","DOIUrl":"https://doi.org/10.1145/944567.944569","url":null,"abstract":"In a 1941 paper (which is condensed here), N. M. Gjunter refers to some of his unknown papers from 1910, 1913 and 1925, which are partially written in context with the 1941 paper. Thus Gjunter had already pursued a constructive theory of polynomial ideals in 1913. Among other results, he proves the inequality attributed to Macaulay/Sperner in 1913 (from 1927 and 1930, respectively). Also discussed are results analogous to more recent work. The author hereby finishes his sequence of articles.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"7 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125797264","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":"Symbolic computation of integrals by recurrence","authors":"M. P. Barnett","doi":"10.1145/944567.944571","DOIUrl":"https://doi.org/10.1145/944567.944571","url":null,"abstract":"We discuss (1) the construction of recurrence formulas for several types of indefinite and definite integral, (2) the conversion of some of the recurrence schemes to general closed formulas, (3) the mechanization of these processes, (4) \"vectorized\" recurrence, (5) \"telescoped\" recurrence, (6) the outperformance of present automatic integration software by the procedures that use our formulas, and (7) the interface between symbolic computation (computer algebra) and mathematical discourse.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123306657","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":"A method for removing all intermediate terms from a given equation","authors":"Ehrenfried Walter von Tschirnhaus, R. Green","doi":"10.1145/844076.844078","DOIUrl":"https://doi.org/10.1145/844076.844078","url":null,"abstract":"We have learned from DesCartes’ geometry by what method the second term might reliably be removed from a given equation; but on the question of removing multiple intermediate terms I have seen nothing hitherto in the analytic arts. On the contrary, I have encountered not a few who believed that the thing could not be done by any art. For this reason I have decided to set down here some things concerning this business, enough at least for those who have some grounding in the analytic art, since the others could scarcely be content with so brief an exposition: reserving the remainder (which they might wish to see here) for some other time. Thus, in the first place, this must be noted; let some given cubic equation be x3− px2 +qx− r = 0, in whichx signifies the roots of this equation; and p, q, r represent known quantities. Now in order to remove the second term, let us suppose that x = y+a; now with the aid of these 2 equations, a third may be discovered in which the quantity x is absent, and this will be 1 y3 z3ayy z3aay za3 = 0 −pyy −2pay −paa zqy zqa −r Now let the second term be made equal to zero (since this is the term we intend to remove) and we shall have 3 ay2− py2 = 0. Whencea= p 3 : which shows that, for removing the second term in the cubic equation, x = y+ a is to be replaced (as we have just done) by y = x+ p 3 . These things have been fully published, nor are they here spoken of for any other reason than that they serve to illustrate what is to follow, since when these things have been fully understood it is easier to grasp those things I am now about to propose. Secondly, now let there be two terms to be removed from a given equation, and I say that we must suppose x2 = bx+y+a; if three,x3 = cx2 +bx+y+a, if four x4 = dx3 +cx2 +bx+y+a and so to infinity. But I shall call theseassumed equations, in order to distinguish them from equations which may be considered as given. The reason for this is that, for the same reason that with the help of the equation x = y+a only one term at least can be removed (because of course at least only one indeterminant a exists), so by the same reason by the help of x2 = bx+y+a only two terms can be removed because just two indeterminants a andb are present; and so furthermore with the help of the followingx3 = cx2 +bx+y+a not more than three can be removed since there are only three indeterminants a, b, c. But since it may be understood by what reason this should follow, I shall show by what reason two terms may be removed from a given equation by means of the assumed [equation] x2 = bx+y+a, and from this it will be easily established by what method one must proceed in this matter however far one might wish (since one may everywhere proceed by the same method). So be it. Thirdly, [there is] the cubic equation x3− px2 + qx− r = 0, from which the two intermediate terms are to be removed: first, the second term is removed (which is certainly of no help, but may at least be omitted here for the sake of time","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131470276","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}