scispace - formally typeset
Search or ask a question
Conference

International Symposium on Symbolic and Algebraic Computation 

About: International Symposium on Symbolic and Algebraic Computation is an academic conference. The conference publishes majorly in the area(s): Polynomial & Symbolic computation. Over the lifetime, 1922 publications have been published by the conference receiving 35227 citations.


Papers
More filters
Proceedings ArticleDOI
01 Jul 1990
TL;DR: This algorithm allows us to calculate definite and indefinite integrals of the products of elementary and special functions of hypergeometric type and its realization in the REDUCE system during the process of creation of INTEGRATOR system.
Abstract: The most voluminous bibliography of the analytical methods for calculating of integrals is represented in the article [19]. It is shown there that the most effective and the simplest algorithm of analytical integration was made by O.I. Marichev [8, 9, 12]. Later it was realized in the reference-books [16-18, 20]. This algorithm allows us to calculate definite and indefinite integrals of the products of elementary and special functions of hypergeometric type. It embraces about 70 per cent of integrals which are included in the world reference-literature. It allows to calculate many other integrals too.The present article contains short description of this algorithm and its realization in the REDUCE system during the process of creation of INTEGRATOR system. Only one general method of integration is known to be realized on the computers, i.e. criterion algorithm for calculating of indefinite integrals of elementary functions through elementary functions by themselves (the authors of it are M. Bronstein and other).The idea of our algorithm is in the following. The initial integrals is transformed to contour integral from the ratio of products of gamma-functions by means of Mellin transform and parseval equality. The residue theorem is used for the calculating of the received integral which due to the strict rules results in sums of hypergeometric series. The value of integral itself and the integrand functions are the special cases of the well-known Meijer's G-function [4, 7, 8, 12, 14, 18].Programming packet is realized in programming languages PASCAL and REDUCE. It also offers the opportunity of finding the values for some classical integral transforms (Laplace, Hankel, Fourier, Mellin and etc.). The REDUCE's part of packet contains the main properties of the well-known special functions, such as the Bessel and gamma-functions and kindred functions, Anger function, Weber function, Whittaker functions, generalized hypergeometric functions. Special place in the packet is occupied by Meijers's G-function for which the main properties such as finding the particular cases and representation by means of hypergeometric series are realized.

1,028 citations

Proceedings ArticleDOI
23 Jul 2014
TL;DR: This paper presents a method to analyze the powers of a given trilinear form and obtain upper bounds on the asymptotic complexity of matrix multiplication and obtains the upper bound ω < 2.3728639 on the exponent of square matrix multiplication, which slightly improves the best known upper bound.
Abstract: This paper presents a method to analyze the powers of a given trilinear form (a special kind of algebraic construction also called a tensor) and obtain upper bounds on the asymptotic complexity of matrix multiplication. Compared with existing approaches, this method is based on convex optimization, and thus has polynomial-time complexity. As an application, we use this method to study powers of the construction given by Coppersmith and Winograd [Journal of Symbolic Computation, 1990] and obtain the upper bound ω

815 citations

Proceedings ArticleDOI
10 Jul 2002
TL;DR: In this article, the Buchberger criteria were replaced by an optimal criteria and the resulting algorithm (called F5) was shown to generate no useless critical pairs if the input is a regular sequence.
Abstract: This paper introduces a new efficient algorithm for computing Grobner bases. We replace the Buchberger criteria by an optimal criteria. We give a proof that the resulting algorithm (called F5) generates no useless critical pairs if the input is a regular sequence. This a new result by itself but a first implementation of the algorithm F5 shows that it is also very efficient in practice: for instance previously untractable problems can be solved (cyclic 10). In practice for most examples there is no reduction to zero. We illustrate this algorithm by one detailed example.

774 citations

Proceedings Article
04 Jul 1988
TL;DR: It is argued that generically programmed software component libraries have important advantages for achieving software productivity and reliability.
Abstract: Generic programming centers around the idea of abstracting from concrete ef cient algorithms to obtain generic algorithms that can be combined with di erent data representations to produce a wide variety of useful software For example a class of generic sorting algorithms can be de ned which work with nite sequences but which can be instantiated in di erent ways to produce algorithms working on arrays or linked lists Four kinds of abstraction data algorithmic structural and representational are discussed with examples of their use in building an Ada library of software components The main topic discussed is generic algorithms and an approach to their formal speci cation and veri cation with illustration in terms of a partitioning algorithm such as is used in the quicksort algorithm It is argued that generically programmed software component libraries o er important advantages for achieving software productivity and reliability This paper was presented at the First International Joint Conference of ISSAC and AAECC Rome Italy July ISSAC stands for International Symposium on Symbolic and Algebraic Computation and AAECC for Applied Algebra Algebraic Algorithms and Error Correcting Codes It was published in Lecture Notes in Computer Science Springer Verlag pp The rst author s work was sponsored in part through a subcontract from Computational Logic Inc which was sponsored in turn by the Defense Advanced Research Projects Agency ARPA order The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the o cial policies either expressed or implied of the Defense Advanced Research Projects Agency the U S Government or Computational Logic Inc

337 citations

Proceedings ArticleDOI
01 Apr 1995
TL;DR: An algorithm is given which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals and provides an algorithm for testing membership in J.
Abstract: We give an algorithm which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals. The computed representation provides an algorithm for testing membership in J. This algorithm works over either an ordinary or a partial differential polynomial ring of characteristic zero. It has been programmed. We also give a method to obtain a obtain a characteristic set of J, if the ideal is prime.

243 citations

Performance
Metrics
No. of papers from the Conference in previous years
YearPapers
202360
202252
202148
202064
201949
201853