This poster presentation is an opportunity to try the downloadable AskConstants program. This copy of some posters is a sequence of images of the program in operation.
{"title":"AskConstants proposes concise non-floats close to floats","authors":"D. R. Stoutemyer","doi":"10.1145/3096730.3096739","DOIUrl":"https://doi.org/10.1145/3096730.3096739","url":null,"abstract":"This poster presentation is an opportunity to try the downloadable AskConstants program. This copy of some posters is a sequence of images of the program in operation.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"529 1","pages":"32-34"},"PeriodicalIF":0.0,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77363274","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}
we present an upper bound for the order of each irreducible component of finite order of a differential algebraic variety V in the context of partial differential fields of characteristic zero. This bound is constructed recursively in terms of explicit data obtained from V.
{"title":"An upper bound for the order of a differential algebraic variety","authors":"O. Sánchez","doi":"10.1145/3096730.3096736","DOIUrl":"https://doi.org/10.1145/3096730.3096736","url":null,"abstract":"we present an upper bound for the order of each irreducible component of finite order of a differential algebraic variety V in the context of partial differential fields of characteristic zero. This bound is constructed recursively in terms of explicit data obtained from V.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"99 1","pages":"23-25"},"PeriodicalIF":0.0,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85887095","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}
Recent breakthroughs have been made in the use of semi-definite programming and its application to real polynomial solving. For example, the real radical of a zero dimensional ideal, can be determined by such approaches. Some progress has been made on the determination of the real radical in positive dimension by Ma, Wang and Zhi[5, 4]. Such work involves the determination of maximal rank semidefinite matrices. Existing methods are computationally expensive and have poorer accuracy on larger examples. In previous work we showed that regularity in the form of the Slater constraint qualification (strict feasibility) fails for the moment matrix in the SDP feasibility problem[6]. We used facial reduction to obtain a smaller regularized problem for which strict feasibility holds. However we did not have a theoretical guarantee that our methods, based on facial reduction and Douglas-Rachford iteration ensured the satisfaction of the maximum rank condition. Our work is motivated by the problems above. We discuss how to compute the moment matrix and its kernel using facial reduction techniques where the maximum rank property can be guaranteed by solving the dual problem. The facial reduction algorithms on the primal form is presented. We give examples that exhibit for the first time additional facial reductions beyond the first which are effective in practice with much better accuracy than SeDuMi(CVX).
{"title":"Finding maximum rank moment matrices by facial reduction on primal form and Douglas-Rachford iteration","authors":"Fei Wang, G. Reid, Henry Wolkowicz","doi":"10.1145/3096730.3096740","DOIUrl":"https://doi.org/10.1145/3096730.3096740","url":null,"abstract":"Recent breakthroughs have been made in the use of semi-definite programming and its application to real polynomial solving. For example, the real radical of a zero dimensional ideal, can be determined by such approaches. Some progress has been made on the determination of the real radical in positive dimension by Ma, Wang and Zhi[5, 4]. Such work involves the determination of maximal rank semidefinite matrices. Existing methods are computationally expensive and have poorer accuracy on larger examples.\u0000 In previous work we showed that regularity in the form of the Slater constraint qualification (strict feasibility) fails for the moment matrix in the SDP feasibility problem[6]. We used facial reduction to obtain a smaller regularized problem for which strict feasibility holds. However we did not have a theoretical guarantee that our methods, based on facial reduction and Douglas-Rachford iteration ensured the satisfaction of the maximum rank condition.\u0000 Our work is motivated by the problems above. We discuss how to compute the moment matrix and its kernel using facial reduction techniques where the maximum rank property can be guaranteed by solving the dual problem. The facial reduction algorithms on the primal form is presented. We give examples that exhibit for the first time additional facial reductions beyond the first which are effective in practice with much better accuracy than SeDuMi(CVX).","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"51 1","pages":"35-37"},"PeriodicalIF":0.0,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91515622","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}
We consider the problem of sparse interpolation of a multivariate black-box polynomial in floatingpoint arithmetic. More specifically, we assume that we are given a black-box polynomial f (x1,...xn) = Σtj=1cjx1dj, 1 ...xndj, n ∈ C[x1,...,xn] (cj ≠ 0)and the number of terms t, and that we can evaluate the value of f (x1,...,xn) at any point in Cn in floating-point arithmetic. The problem is to find the coefficients c1, ..., ct and the exponents d1,1,..., dt,n. We propose an efficient algorithm to solve the problem.
{"title":"An algorithm for symbolic-numeric sparse interpolation of multivariate polynomials whose degree bounds are unknown","authors":"Dai Numahata, Hiroshi Sekigawa","doi":"10.1145/3096730.3096734","DOIUrl":"https://doi.org/10.1145/3096730.3096734","url":null,"abstract":"We consider the problem of sparse interpolation of a multivariate black-box polynomial in floatingpoint arithmetic. More specifically, we assume that we are given a black-box polynomial <i>f</i> (<i>x</i><sub>1</sub>,...<i>x</i><sub>n</sub>) = Σ<sup><i>t</i></sup><sub><i>j</i>=1</sub> <i>c</i><sub><i>j</i></sub><i>x</i><sub>1</sub><sup><i>d</i><sub><i>j</i>, 1</sub></sup> ...<i>x</i><sub><i>n</i></sub><sup><i>d</i><sub><i>j</i>, n</sub></sup> ∈ C[<i>x</i><sub>1</sub>,...,<i>x</i><sub><i>n</i></sub>] (<i>c<sub>j</sub></i> ≠ 0)and the number of terms <i>t</i>, and that we can evaluate the value of <i>f</i> (<i>x<sup>1</sup>,...,x<sub>n</sub>)</i> at any point in C<sup><i>n</i></sup> in floating-point arithmetic. The problem is to find the coefficients <i>c<sub>1</sub></i>, ..., <i>c<sub>t</sub></i> and the exponents <i>d<sub>1,1,</sub>..., d<sub>t,n</sub></i>. We propose an efficient algorithm to solve the problem.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"2 1","pages":"18-20"},"PeriodicalIF":0.0,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82975243","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}
We have used antiquantization of deformed Heun class equations for programming the generation of Painlevé equations with the CAS Maple.
利用CAS Maple对变形Heun类方程进行反量化，实现了painlevel方程的生成。
{"title":"Antiquantization of deformed Heun class equations as a tool for symbolic generation of Painlevé equations","authors":"S. Slavyanov, O. Stesik","doi":"10.1145/3096730.3096738","DOIUrl":"https://doi.org/10.1145/3096730.3096738","url":null,"abstract":"We have used antiquantization of deformed Heun class equations for programming the generation of Painlevé equations with the CAS Maple.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"395 1","pages":"29-31"},"PeriodicalIF":0.0,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91195313","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}
We want to investigate on the sequence of minimal polynomials of the sequence below.
我们要研究下面这个序列的最小多项式序列。
{"title":"Linearization of a specific family of Bézout matrices","authors":"Leili Rafiee Sevyeri, Robert M Corless","doi":"10.1145/3096730.3096735","DOIUrl":"https://doi.org/10.1145/3096730.3096735","url":null,"abstract":"We want to investigate on the sequence of minimal polynomials of the sequence below.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"104 1","pages":"21-22"},"PeriodicalIF":0.0,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87603216","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}
Mathematical software plays an increasing role in mathematics and key technologies. But to find and get information about software is expensive. Missing metadata standards, e.g., the citation of software, are one of the reasons. In the following some recent developmentsare described how the community can contribute to a better information system for mathematical software.
{"title":"Some steps to improve software information","authors":"A. Heinle, W. Koepf, Wolfram Sperber","doi":"10.1145/3096730.3096731","DOIUrl":"https://doi.org/10.1145/3096730.3096731","url":null,"abstract":"Mathematical software plays an increasing role in mathematics and key technologies. But to find and get information about software is expensive. Missing metadata standards, e.g., the citation of software, are one of the reasons. In the following some recent developmentsare described how the community can contribute to a better information system for mathematical software.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"33 1","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83971608","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}
In [3] the following polynomial evaluation problem arises. Let A be a sparse polynomial with s terms in Zp[x0,x1,...,xn]. Suppose we seek evaluations of A into t bivariate images in Zp[x0,x1], for some t ≪ s. We do not know a priori the exact number of images t needed. This will be determined by using a trial value T for t, and increasing T as required.
{"title":"Fast parallel multi-point evaluation of sparse polynomials","authors":"M. Monagan, Alan Wong","doi":"10.1145/3096730.3096732","DOIUrl":"https://doi.org/10.1145/3096730.3096732","url":null,"abstract":"In [3] the following polynomial evaluation problem arises. Let <i>A</i> be a sparse polynomial with <i>s</i> terms in <i>Z<sup>p</sup></i>[<i>x<sup>0</sup>,x<sup>1</sup>,...,x<sup>n</sup></i>]. Suppose we seek evaluations of <i>A</i> into <i>t</i> bivariate images in <i>Z<sup>p</sup></i>[<i>x<sup>0</sup>,x<sup>1</sup></i>], for some <i>t</i> ≪ <i>s</i>. We do not know <i>a priori</i> the exact number of images <i>t</i> needed. This will be determined by using a trial value <i>T</i> for <i>t</i>, and increasing <i>T</i> as required.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"16 1","pages":"12-14"},"PeriodicalIF":0.0,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89976913","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}
We are interested in seeking better algorithms by just slightly updating and combining the well-known algorithms for the following well-known problem in Symbolic-Numeric Computations.
我们有兴趣寻求更好的算法，通过稍微更新和组合已知的算法来解决符号数值计算中以下众所周知的问题。
{"title":"Seeking better algorithms for approximate GCD","authors":"Kosaku Nagasaka","doi":"10.1145/3096730.3096733","DOIUrl":"https://doi.org/10.1145/3096730.3096733","url":null,"abstract":"We are interested in seeking better algorithms by just slightly updating and combining the well-known algorithms for the following well-known problem in Symbolic-Numeric Computations.","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"272 1","pages":"15-17"},"PeriodicalIF":0.0,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89064741","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}
Contrary to that the general Hensel construction (GHC: [3]) uses univariate initial Hensel factors, the extended Hensel construction (EHC: [8]) uses multivariate initial Hensel factors determined by the Newton polygon (see below) of the given multivariate polynomial F (x, u) ∈ K[x, u], where (u) = (u1,...,uℓ), with ℓ ≥ 2, and K is a number field. The F(x, u) may be such that its leading coefficient may vanish at (u) = (0) = (0,...,0), and even may be F(x, 0) = 0. The EHC was used so far for computing series expansion of multivariate algebraic function determined by F(x, u) = 0, at critical points [8, 5] and for factorization [4, 1] and GCD computation [7] of F(x, u), without shifting the origin of u. It allows us to construct efficient algorithms for sparse multivariate polynomials [1, 7]. The EHC is another and promising approach than Zippel's sparse Hensel lifting [9, 10].
{"title":"Enhancing the extended hensel construction by using Gröbner basis","authors":"Tateaki Sasaki, D. Inaba","doi":"10.1145/3096730.3096737","DOIUrl":"https://doi.org/10.1145/3096730.3096737","url":null,"abstract":"Contrary to that the general Hensel construction (GHC: [3]) uses univariate initial Hensel factors, the extended Hensel construction (EHC: [8]) uses multivariate initial Hensel factors determined by the Newton polygon (see below) of the given multivariate polynomial <i>F (x, <b>u</b>)</i> ∈ K[<i>x</i>, <b><i>u</i></b>], where (<b><i>u</i></b>) = (<i>u</i><sub>1</sub>,...,<i>u</i><i><sub>ℓ</sub></i>), with <i>ℓ</i> ≥ 2, and K is a number field. The <i>F</i>(<i>x, <b>u</b></i>) may be such that its leading coefficient may vanish at (<b><i>u</i></b>) = (<b>0</b>) = (0,...,0), and even may be <i>F</i>(<i>x</i>, <b>0</b>) = 0. The EHC was used so far for computing series expansion of multivariate algebraic function determined by <i>F</i>(<i>x, <b>u</b></i>) = 0, at critical points [8, 5] and for factorization [4, 1] and GCD computation [7] of <i>F</i>(<i>x</i>, <b><i>u</i></b>), without shifting the origin of <b><i>u</i></b>. It allows us to construct efficient algorithms for sparse multivariate polynomials [1, 7]. The EHC is another and promising approach than Zippel's sparse Hensel lifting [9, 10].","PeriodicalId":7093,"journal":{"name":"ACM Commun. Comput. Algebra","volume":"10 1","pages":"26-28"},"PeriodicalIF":0.0,"publicationDate":"2017-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84317888","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}
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