Computer algebra handbook
Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning +2 more
- 01 Jan 2003
- pp 176-179
137
About: The article was published on 01 Jan 2003. The article focuses on the topics: Symbolic computation.
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Citations
•Journal Article
Automatic differentiation in machine learning: a survey
TL;DR: Automatic differentiation (AD) is a family of techniques similar to but more general than backpropagation for efficiently and accurately evaluating derivatives of numeric functions expressed as computer programs as discussed by the authors, which is a small but established field with applications in areas including computational uid dynamics, atmospheric sciences, and engineering design optimization.
Accurate Sum and Dot Product
TL;DR: Algorithms for summation and dot product of floating-point numbers are presented which are fast in terms of measured computing time and it is shown that the computed results are as accurate as if computed in twice or K-fold working precision.
443
GeM software package for computation of symmetries and conservation laws of differential equations
TL;DR: The package contains a collection of powerful easy to use routines for mathematicians and applied researchers for automated symmetry and conservation law analysis of systems of partial and ordinary difierential equations (DE).
255
Computation of fluxes of conservation laws
TL;DR: The direct method for the construction of local conservation laws of partial differential equations (PDE) is a systematic method applicable to a wide class of PDE systems (S. Anco and G. Bluman, Eur J Appl Math 13:567-585, 2002).
Symmetry of Planar Four-Body Convex Central Configurations
TL;DR: In this article, the relationship between the masses and the geometric properties of central configurations was studied and it was shown that a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two masses on the other diagonal are equal, and if these two masses are unequal, then the less massive one is closer to the former diagonal.
67
References
Arithmetic of Polynomials, Rational Functions, and Power Series
Keith O. Geddes,S. R. Czapor,George Labahn +2 more
- 01 Jan 1992
TL;DR: In this article, the authors describe the arithmetic operations of addition, subtraction, multiplication, and division for the ring of integers modulo n, ring of formal power series over a field, and ring of polynomials over an integral domain along with their quotient fields.
1
Algorithms for matrix canonical forms
Arne Storjohann
- 01 Jan 2000
TL;DR: In this article, generic algorithms for computing the Hermite and Smith forms of an integer matrix are presented, with respect to the worst case, in terms of number of required operations from the ring.
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