A review of Macsyma

Fateman, Richard J.

doi:10.1109/69.43409

Cited by 11 publications

(7 citation statements)

References 24 publications

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“…Rather more detailed and technical comparisons are to be found in Stoutemeyer (1991), while two magnificent articles by Fateman give critiques of MACSYMA and MATHEMATICA which should be required reading for all serious users of computer algebra; Fateman (1989Fateman ( ), (1992.…”

Section: -3174 9 1994 Chapman and Hallmentioning

confidence: 99%

Book reviews

Kendall¹

1994

Stat Comput

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Section: -3174 9 1994 Chapman and Hallmentioning

confidence: 99%

Book reviews

Kendall¹

1994

Stat Comput

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“…Interesting in-depth discussions of MACSYMA and Mathernatica are to be found in FATEMAN (1989), FATEMAN (1992). DAVENPORT, SIRET and TOURNIER (1988) discuss the general techniques and algorithms of computer algebra and also provide a useful succinct description of REDUCE.…”

Section: Macsymamentioning

confidence: 99%

Computer algebra in probability and statistics

Kendall

1993

Statistica Neerlandica

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This paper discusses the uses of computer algebra within statistics and probability. A distinction is drawn between the use of computer algebra packages to support investigations, by performing calculations, ankl their use to implement structure; to build in elements of a theory (such as stochastic calculus or the Taylor string theory of Barndorff Nielsen and others) as a preliminary to research investigations. Brief surveys are given of instances in the literature of use of computer algebra in probability and statistics. Two examples of implementations of structure are discussed, both drawn from the author's own work with the computer algebra package REDUCE. One is a simple demonstration using moments of the Poisson distribution. The other is itovsn3, an implementation of the semimartingale stochastic calculus. It is described how itovsn3 may be used to derive the characteristic function of the Lévy stochastic area, following a proof due to S. Janson. Prospects for future work and for work in progress are discussed.

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“…An alternative strategy would be for us to interface with a computer algebra system such as MAXIMA (an open-source fork of MACSYMA [Fateman 1989]) or similar system that uses pattern matching of mathematical expressions to improve symbolic integration performance [Slagle 1963;Harrington 1979]. It is unclear how difficult this would be to implement.…”

Section: Symbolic Integrationmentioning

confidence: 99%

“…We currently use our own implementation of symbolic integration optimized for (and only applicable to) polynomials. To scale effectively, we suspect interfacing with a computer algebra system such as MAXIMA (an open-source fork of MACSYMA [Fateman 1989]) would be necessary. Our factorizer is only presented with the polynomial parts of expressions so the non-affine mappings would not cause an issue for this step.…”

Section: Future Workmentioning

confidence: 99%

“…The FINGER system [Wang 1986], uses MACSYMA [Fateman 1989] to perform symbolic integration, followed by a CSE (common sub-expression elimination) pass, performed by REDUCE. More recent work on the SyFi Form Compiler [Alnaes and Mardal 2010], explores performing both analytical and quadrature based integration on symbolic expressions for local assembly matrix entries before applying a CSE pass.…”

Section: Introductionmentioning

confidence: 99%

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Optimized code generation for finite element local assembly using symbolic manipulation

Russell

2013

ACM Trans. Math. Softw.

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Automated code generators for finite element local assembly have facilitated exploration of alternative implementation strategies within generated code. However, even for a theoretical performance indicator such as operation count, an optimal strategy for local assembly is unknown. We explore a code generation strategy based on symbolic integration and polynomial common sub-expression elimination (CSE). We present our implementation of a local assembly code generator using these techniques. We systematically evaluate the approach, measuring operation count, execution time and numerical error using a benchmark suite of synthetic variational forms, comparing against the FEniCS Form Compiler (FFC). Our benchmark forms span complexities chosen to expose the performance characteristics of different code generation approaches. We show that it is possible with additional computational cost, to consistently achieve much of, and sometimes substantially exceed, the performance of alternative approaches without compromising precision. Although the approach of using symbolic integration and CSE for optimizing local assembly is not new, we distinguish our work through our strategies for maintaining numerical precision and detecting common sub-expressions. We discuss the benefits of the symbolic approach for inferring numerical relationships, and analyze the relationship to other proposed techniques which also have greater computational complexity than those of FFC.

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A review of Macsyma

Cited by 11 publications

References 24 publications

Book reviews

Book reviews

Computer algebra in probability and statistics

Optimized code generation for finite element local assembly using symbolic manipulation

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