SIGSAM Bull.最新文献

{"title":"In memoriam: Professor Eiichi Goto","authors":"T. Ida","doi":"10.1145/1113439.1113440","DOIUrl":"https://doi.org/10.1145/1113439.1113440","url":null,"abstract":"Prof. Eiichi Goto passed away on June 12, 2005 at the age of 74 after a long struggle with illness that was initially caused by diabetes. Despite his suffering, he continued to actively pursue his goals as a scientist, an engineer and an educator until his death. He was a Japanese pioneer in computing. His contributions in computing are so varied that one would need many pages to describe his achievements.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126721526","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":"Mobile mathematics communication","authors":"N. Belov, Colin Koeck, W. Krandick, J. Shaffer","doi":"10.1145/1113439.1113459","DOIUrl":"https://doi.org/10.1145/1113439.1113459","url":null,"abstract":"We present a system [1] that allows wireless smartphones to beused for mathematics communication, that is, for the creation andexchange of mathematical formulas, diagrams, and text between twoor more participants. The system enables two or more persons withsmartphones or traditional computers to participate in a session.Each of the participants may convey textual, graphical andmathematical information to the other participants. Users can draw,edit, and label geometric shapes, send chat messages, and composeformulas. A turn taking mechanism moderates the communication. Thesystem also supports the integration of services that can be usedto provide individual users with additional functionality.Currently, a LATEX rendering service is available to allow users tocreate and share mathematical formulas in typeset quality.\u0000Wireless smartphones are becoming the medium of choice forimprovised synchronous collaboration since increasing numbers ofusers carry their smartphones at all times. It is true that thesmall size of the devices---while necessary for theirubiquity---limits the complexity of collaborative tasks that can becarried out effectively. On the other hand, there is a need tocapture inspiration, to access and evaluate information on the go,and to make decisions on the spot.\u0000The domain of mathematics is ideally suited to explore---andpush---the limits of smartphone communication. The challenge ofrepresenting mathematics in typeset form has led to the developmentof document preparation systems such as TEX, LATEX, and LYX whichare in widespread use today. Mathematical handwriting recognitioncontinues to push the limits of general handwriting recognition[2]. Many of the cognitive challenges that arise in mathematicalcollaboration also arise in intellectual teamwork in otherdomains.\u0000Some of the challenges of developing a system for mobilemathematics communication are posed by the input and outputlimitations of the devices and the enormous heterogeneity of theavailable hardware platforms.\u0000We use the Treo 600/650 as our hardware platform. Our softwareis written in pure Java and can be run on any platform thatsupports the Java Virtual Machine. Our software architecture makesit easy to add new local or remote services to enhance thecommunication.\u0000The poster presents use-case diagrams, architecture diagrams,and a series of screenshots that describe the user's interactionwith the system. The poster also shows how we solved the problemsof cross-referencing and turn-taking in mobile collaboration. A7.5-minute video shows users interacting with the system.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131353185","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":"2D and 3D generalized Stewart Platforms","authors":"X. Gao, Gui-Fang Zhang","doi":"10.1145/1113439.1113451","DOIUrl":"https://doi.org/10.1145/1113439.1113451","url":null,"abstract":"The Stewart Platform (SP) is a parallel manipulator consisting of a moving platform and a base. The position and orientation (pose) of the base are fixed. The base and platform are connected with six extensible legs. The SP has been studied extensively in the past 20 years and has many applications. A large portion of the work on SP is focused on the direct kinematics: for a given set of lengths of the legs, determine the pose of the platform. It is known that the direct kinematics have 40 solutions. But, closed form solutions are not found yet.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126607080","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 RegularChains library in MAPLE","authors":"F. Lemaire, M. M. Maza, Yuzhen Xie","doi":"10.1145/1113439.1113456","DOIUrl":"https://doi.org/10.1145/1113439.1113456","url":null,"abstract":"Performing calculations modulo a set of relations is a basictechnique in algebra. For instance, computing the inverse of aninteger modulo a prime integer or computing the inverse of thecomplex number 3 + 2<i>t</i> modulo the relation&ell;² + 1 = 0. Computing modulo a set<i>S</i> containing more than one relation requiresfrom <i>S</i> to have some mathematical structure. Forinstance, computing the inverse of <i>p</i> =<i>x</i> + <i>y</i> modulo<i>S</i> ={<i>x</i>² +<i>y</i> +1,<i>y</i>² +<i>x</i> + 1} is difficult unless one realizes thatthis question is equivalent to computing the inverse of<i>p</i> modulo <i>C</i> ={<i>x</i>⁴ +2<i>x</i>² +<i>x</i> + 2,<i>y</i> +<i>x</i>² + 1}. Indeed, fromthere one can simplify <i>p</i> using<i>y</i> =-<i>x</i>² - 1 leading to<i>q</i> =-<i>x</i>² +<i>x</i> - 1 and compute the inverse of<i>q</i> modulo<i>x</i>⁴ +2<i>x</i>² +<i>x</i> + 2 (using the extended Euclidean algorithm)leading to -1/2<i>x</i>³ -1/2<i>x</i>. One commonly used mathematical structurefor a set of algebraic relations is that of a<i>Gr&ouml;bner basis.</i> It is particularly wellsuited for deciding whether a quantity is null or not modulo a setof relations. For inverse computations, the notion of a<i>regular chain</i> is more adequate. For instance,computing the inverse of <i>p</i> =<i>x</i> + <i>y</i> modulo the set<i>C</i> ={<i>y</i>² -2<i>x</i> +1,<i>x</i>² -3<i>x</i> + 2}, which is both a Gr&ouml;bner basisand a regular chain, is easily answered in this latter point ofview. Indeed, it naturally leads to consider the GCD of<i>p</i> and<i>C<inf>y</inf></i> =<i>y</i>² -2<i>x</i> + 1 modulo the relation<i>C<inf>x</inf></i> =<i>x</i>² -3<i>x</i> + 2 = 0, which is\u0000[EQUATION]\u0000This shows that <i>p</i> has no inverse if<i>x</i> = 1 and has an inverse (which can be computedand which is -<i>y</i> + 2) if <i>x</i> =2.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132071414","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":"Polynomial root-finding with matrix eigen-solving","authors":"V. Pan","doi":"10.1145/1113439.1113448","DOIUrl":"https://doi.org/10.1145/1113439.1113448","url":null,"abstract":"Numerical matrix methods are increasingly popular for polynomial root-finding. This approach usually amounts to the application of the QR algorithm to the highly structured Frobenius companion matrix of the input polynomial. The structure, however, is routinely destroyed already in the first iteration steps. To accelerate this approach, we exploit the matrix structure of the Frobenius and generalized companion matrices, employ various known and novel techniques for eigen-solving and polynomial root-finding, and in addition to the Frobenius input allow other highly structured generalized companion matrices. Employing polynomial root-finders for eigen-solving is a harder task because of the potential numerical stability problems, but we found some new promising directions, particularly for sparse and/or structured input matrices.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"340 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122545191","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":"Offsets from the perspective of computational algebraic geometry","authors":"F. Segundo, J. Sendra, J. Sendra","doi":"10.1145/1113439.1113449","DOIUrl":"https://doi.org/10.1145/1113439.1113449","url":null,"abstract":"The offset hypersurface Od(V), at distance d, to an irreducible hypersurface V is essentially the envelope of the system of spheres centered at the points of V with fixed radius d (for a formal definition, and for basic properties of offsets, see [2] and [9]). This type of geometric objects have been studied extensively by many authors in the frame of CAGD applications (see [4]). As a consequence of this research, many interesting theoretical and algorithmic questions related to algebraic and differential geometric properties of offsets have been addressed. In this context, one usually analyzes whether a certain property of the original variety V is translated to Od(V) when offsetting.In this poster we present several efficient algorithms (and examples thereof) developed in our research group for the computation of algebraic and geometric properties of offset hypersurfaces.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"160 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128049922","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":"Intrinsic topological representation of real algebraic surfaces","authors":"Jin-San Cheng, X. Gao, Ming Li","doi":"10.1145/1113439.1113444","DOIUrl":"https://doi.org/10.1145/1113439.1113444","url":null,"abstract":"Determining the topology of an algebraic surface is not only an interesting mathematical problem, but also a key issue in computer graphics and CAGD. An algorithm is proposed to determine the intrinsic topology of an implicit real algebraic surface f(x,y,z) = 0 in R3, where f(x,y,z) ∈ Q[x,y,z] and Q is the field of rational numbers. There exist algorithms to determine the topology for algebraic surfaces of special type [2, 3, 4, 7]. The CAD method proposed by Collins [1] can divide the space into cylindrical parts. But it does not give the connection information neither the intrinsic representation.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131663695","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":"Irreducible decomposition of monomial ideals","authors":"Shuhong Gao, Mingfu Zhu","doi":"10.1145/1113439.1113458","DOIUrl":"https://doi.org/10.1145/1113439.1113458","url":null,"abstract":"In this paper we present two algorithms for irreducible decomposition of monomial ideals. We first use staircase structures to study the monomial ideals. We generalize the shifting degrees rule from two variables to three variables and then arbitrary case. With the aid of monomial tree representation, a new algorithm for irreducible decomposition of monomial ideals is provided. For the second method, we associate a monomial ideal with a Scarf complex, which is introduced by Herbert Scarf. Every facet of the Scarf complex corresponds to an irreducible component, and vice versa. Milowski(2004) developed a method to enumerate all the facets based on reverse search by exchanging one monomial at a time. We define a facet graph where nodes are facets and there is an edge from a facet FA to another facet FB if FB can be obtained from FA by exchanging one vertex. We give a new generic deformation called ordinal deformation and prove that the facet graph of an ordinally generic monomial ideal is strongly connected. This yields a simpler and more efficient enumeration algorithm.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133880256","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":"Rational and replacement invariants of a group action","authors":"E. Hubert, I. Kogan","doi":"10.1145/1113439.1113447","DOIUrl":"https://doi.org/10.1145/1113439.1113447","url":null,"abstract":"Group actions are ubiquitous in mathematics. They arise indiverse areas of applications, from classical mechanics to computervision. A classical but central problem is to compute a generatingset of invariants.\u0000We consider a rational group action on the affine space andpropose a construction of a finite set of rational invariants and asimple algorithm to rewrite any rational invariant in terms ofthose generators. The construction comes into two variants bothconsisting in computing a reduced Gr&ouml;bner basis of apolynomial ideal. That polynomial ideal is of dimension zero in thesecond variant that relies on the choice of a cross-section, avariety that intersects generic orbits in a finite number ofpoints. A generic linear space of complementary dimension to theorbits can be chosen for cross-section.\u0000When the intersection of a generic orbit with the cross-sectionconsists of a single point, the rewriting of any rational invariantin terms of the computed generating set trivializes into areplacement. For general cross-sections we introduce a finite setof <i>replacement invariants</i> that are algebraicfunctions of the rational invariants. Any rational invariant can berewritten in terms of those by simple substitution.\u0000We have therefore obtained an algebraic formulation of themoving frame construction of Fels and Olver [2], providing a bridgebetween the algebraic theory of polynomial and rational invariants[7, 1], and the differential-geometric theory of local smoothinvariants, [6].\u0000In this abstract we formalize our main results in the case whereK is an algebraically closed field of characteristic zero. Severalexamples, both classical and original, are treated in theposter.\u0000Take an algebraic group <i>G</i> given by an unmixeddimensional ideal <i>G</i> in a polynomial ringK[&lambda;<inf>1</inf>,...,&lambda;<inf>&ell;</inf>].A rational action of the group <i>G</i> on<i>K</i>^<i>n</i> isgiven as the rational map:\u0000[EQUATION]\u0000where<i>h,g</i>1,...,<i>g</i><inf><i>n</i></inf>are polynomial functions inK[&lambda;<inf>1</inf>,...,&lambda;<inf>&ell;</inf>,<i>z</i><inf>1</inf>,...,<i>z</i><inf><i>n</i></inf>].\u0000An element <i>p</i>/<i>q</i> &isin;<i>K</i>(<i>z</i>) is a <i>rationalinvariant</i> if<i>p</i>(&lambda;&middot;<i>z</i>)<i>q</i>(<i>z</i>)=<i>p</i>(<i>z</i>)<i>q</i>(&lambda;<i>z</i>)mod <i>G</i>. The set of rational invariants forms a(finitely generated) fieldK(<i>z</i>)^<i>G</i>.\u0000A <i>cross-section of degree d</i> &gt; 0 is anirreducible affine variety <i>P</i> that intersectsgeneric orbits in exactly <i>d</i> simple points. Whengeneric orbits are of dimension <i>r</i> &gt; 0, ageneric linear affine space of codimension <i>r</i> isa cross-section.\u0000Consider a new set of variables <i>Z</i> =(<i>Z</i><inf>1</inf>,...,<i>Z</i><inf><i>n</i></inf>).The ideal (<i>Z</i> - &lambda; &middot;<i>z</i>) is the saturation by <i>h</i> ofthe ideal generated by the polynomials<i>h</i>(&lambda;,<i>z</i>)<i>Z</i><inf><i>i</i></inf>-<i>g</i><inf><i>i</i>","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127060425","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":"Algebraic generalization","authors":"S. Watt","doi":"10.1145/1113439.1113452","DOIUrl":"https://doi.org/10.1145/1113439.1113452","url":null,"abstract":"We explore the notion of generalization in the setting of symbolic mathematical computing. By \"generalization\" we mean the process of taking a number of instances of mathematical expressions and producing new expressions that may be specialized to all the instances. We identify a number of ways in which generalization may be useful in the setting of computer algebra. We formalize this generalization as an antiunification problem.The process of antiunification is the dual of unification. It takes two expressions <i>E</i><inf>1</inf>, <i>E</i><inf>2</inf> ∈ <i>E</i> (Σ, <i>V</i>) and produces <i>E</i><inf>3</inf> ∈ <i>E</i> (Σ, <i>V</i>) such that there exist substitutions σ<inf>1</inf> and σ<inf>2</inf> such that σ<inf>1</inf> (<i>E</i><inf>3</inf>) = <i>E</i><inf>1</inf> and σ<inf>2</inf>(<i>E</i><inf>3</inf>) = <i>E</i><inf>2</inf>. We call the pair of substitutions an <i>antiunifier</i> and the resulting expression a <i>generalization</i> of the expressions. An antiunifier always exists, but is not necessarily unique. There is, however, a unique <i>most specific antiunifier</i> that places the most restrictions on the variables. This gives the <i>most specific generalization</i>, which is unique up to renaming of variables.","PeriodicalId":314801,"journal":{"name":"SIGSAM Bull.","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129222171","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}