Computer Algebra Systems

Hulzen, J. A. van; Calmet, Jacques

doi:10.1007/978-3-7091-7551-4_14

Cited by 6 publications

(9 citation statements)

References 48 publications

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“…This algorithm is different from Breuer's growth algorithm [14,15], where a larger subexpression that generates a bigger decrease in cost is determined. Finding that subexpression is computationally harder than counting our small subexpressions, and this has to be calculated repeatly.…”

Section: Greedy Optimizationsmentioning

confidence: 99%

Code optimization in FORM

Kuipers

Ueda

Vermaseren

2015

Computer Physics Communications

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Section: Greedy Optimizationsmentioning

confidence: 99%

Code optimization in FORM

Kuipers

Ueda

Vermaseren

2015

Computer Physics Communications

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“…Many other systems were developed at that time (see Moses 2012 ) and since. van Hulzen and Calmet ( 1983 ) reported an estimate that there were then about 60 systems, and the 2003 handbook (Grabmeier et al. 2003 ) describes 9 general purpose systems, 43 special purpose systems and 15 packages.…”

Section: Introductionmentioning

confidence: 99%

“…Yun and Stoutemyer ( 1980 ), Gerdt et al. ( 1980 ) and van Hulzen and Calmet ( 1983 ) give useful surveys of the early systems. Among those systems, Macsyma and Reduce have been the most used in GR.…”

Section: Introductionmentioning

confidence: 99%

“…The main reasons for using computer algebra (CA) are speed and accuracy, the ability to handle more complicated calculations than can be done by hand, and relief from the boredom of repetitive tasks. These all apply to applications in GR, so much so that GR, celestial mechanics and quantum electrodynamics supplied much of the early motivation for developers (Yun and Stoutemyer 1980 ; van Hulzen and Calmet 1983 ); Barton and Fitch ( 1972 ) gave a survey covering early use in all those three areas.…”

Section: Introductionmentioning

confidence: 99%

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Computer algebra in gravity research

MacCallum

2018

Living Rev Relativ

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The complicated nature of calculations in general relativity was one of the driving forces in the early development of computer algebra (CA). CA has become widely used in gravity research (GR) and its use can be expected to grow further. Here the general nature of computer algebra is discussed, along with some aspects of CA system design; features particular to GR’s requirements are considered; information on packages for CA in GR is provided, both for those packages currently available and for their predecessors; and applications of CA in GR are outlined.

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“…Applications abound, ranging from fast calculation on embedded devices and real-time calculations to high-energy physics (HEP), where one needs to perform Monte Carlo integrations of extremely large polynomials in many variables [1][2][3][4]. Numerous methods to optimize polynomial evaluation have been proposed, such as Horner's method [5][6][7], common subexpression elimination [8], Breuer's growth algorithm [9,10] and, recently, partial syntactic factorization [11].…”

Section: Introductionmentioning

confidence: 99%

Improving multivariate Horner schemes with Monte Carlo tree search

Kuipers

Plaat

Vermaseren

et al. 2013

Computer Physics Communications

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Optimizing the cost of evaluating a polynomial is a classic problem in computer science. For polynomials in one variable, Horner's method provides a scheme for producing a computationally efficient form. For multivariate polynomials it is possible to generalize Horner's method, but this leaves freedom in the order of the variables. Traditionally, greedy schemes like most-occurring variable first are used. This simple textbook algorithm has given remarkably efficient results. Finding better algorithms has proved difficult. In trying to improve upon the greedy scheme we have implemented Monte Carlo tree search, a recent search method from the field of artificial intelligence. This results in better Horner schemes and reduces the cost of evaluating polynomials, sometimes by factors up to two.Comment: 5 page

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Computer Algebra Systems

Cited by 6 publications

References 48 publications

Code optimization in FORM

Code optimization in FORM

Computer algebra in gravity research

Improving multivariate Horner schemes with Monte Carlo tree search

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