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article Free Access Share on Book Review: Polynomial and Matrix Computations Volume 1: Fundamental Algorithms by D. Bini and V. Pan Authors: I. Z. Emiris INRIA Sophia-Antipolis INRIA Sophia-AntipolisView Profile , A. Galligo INRIA Sophia-Antipolis INRIA Sophia-AntipolisView Profile Authors Info & Claims ACM SIGSAM BulletinVolume 30Issue 3Sept. 1996 pp 21–23https://doi.org/10.1145/240065.570109Published:01 September 1996Publication History 0citation124DownloadsMetricsTotal Citations0Total Downloads124Last 12 Months7Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

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article 1995 East Coast Computer Algebra Day Abstracts Share on Author: Grossman View Profile Authors Info & Claims ACM SIGSAM BulletinVolume 29Issue SIJune 1995 pp 21–28https://doi.org/10.1145/214441.570112Online:01 June 1995Publication History 0citation279DownloadsMetricsTotal Citations0Total Downloads279Last 12 Months0Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

In Electrical Engineering one of the most important problems to be solved for electrical networks is the load flow problem [6] [3]. Currently numerical solutions are provided by Newton's method, which involves recomputing the solution whenever the input data change. Given that this problem must be solved very often with different input data, the Gröbner basis can be an interesting approach since it can, in principle, provide a more algebraic solution of the input parameters and has to be solved completely only once, supplying formulas to compute single simulations. In this paper the basic ideas and a practical example are reported. Nevertheless, the required computations for practical network sizes are very complex and cannot yet be solved with the present algorithms.

This paper gives a short overview on PACLIB, a new system for parallel algebraic computation on shared memory computers. PACLIB has been developed as a professional tool for the simple design and efficient implementation of parallel algorithms in ...

Present computer algebra systems base their interactive sessions on a very simple model of mathematical discourse. The user's input to the system is a line containing a mathematical expression (an operation, a formula, a set of equations, etc) and the system's response to the user is an output line which contains a mathematical expression similar to the input. There are many situations, however, in which this is too simple a model of mathematics. Algebra systems should be allowed to reply 'Well ... it isn't quite that simple'.

An algorithm for computing a minimal invariant partition of a permutation group due to Atkinson is analysed. The analysis shows the algorithm is O ( n 2 ), where n is the degree of the group. The leading coefficient is 3/2. Some suggested speed-ups are also analysed. The speed-ups imply that the cost of testing primitivity is O ( n 3 ), with a leading coefficent of 19/16.Careful use of linked lists to represent subsets of the partition leads to an O ( nlogn ) algorithm for computing a minimal invariant partition, and an O ( n 2 logn ) algorithm for testing primitivity. For both algorithms, the leading coefficient is 1.The use of trees to represent subsets, and the technique of path compression, lead to an O ( nG ( n )|S|) algorithm, where S is the set of generators for the group, and G (n) is a very slow growing function related to Ackermann's function, for computing the minimal invariant partition. The leading coefficient is such that, for degrees less than 1,000,000, the linked list version gives a smaller bound.

In the early 1970s, a major paradigm shift took place in algorithms research, away from experimental results to asymptotic analysis. Knuth popularized the "Big O" notation, and Hopcroft says in his 1986 ACM Turing Award (with Robert Tarjan) address: "During the 1960s, research on algorithms had been very unsatisfying. A researcher would publish an algorithm in a journal along with execution times for a small set of sample problems, and then several years later, a second researcher would give an improved algorithm along with execution times for the same set of sample problems. The new algorithm would invariably be faster, since in the intervening years, both computer performance and programming languages had improved. The fact that the algorithms were run on different computers and programmed in different languages made me uncomfortable with the comparison. It was difficult to factor out both the effects of increased computer performance and the programming skills of the implementors---to discover the effects due to the new algorithm as opposed to its implementation. Furthermore, it was possible that the second researcher had inadvertently tuned his or her algorithm to the sample problems ... I set out to demonstrate that a theory of algorithm design based on worst-case asymptotic performance could be a valuable aid to the practitioner."

A. A. Reeves, "The worst order is not always the lexicographic order," ACM SIGSAM Bulletin , Volume 25, Number 4, pp. 18--19.