The “Seven Dwarfs” of Symbolic Computation

We present the Seven Dwarfs of Symbolic Computation, which are sequential and parallel algorithmic methods that today carry a great majority of all exact and hybrid symbolic compute cycles. We will elaborate on each dwarf and compare with Colella’s seven and the Berkeley team’s thirteen dwarfs of sc...

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Bibliographic Details
Published inNumerical and Symbolic Scientific Computing pp. 95 - 104
Main Author Kaltofen, Erich L.
Format Book Chapter
LanguageEnglish
Published Vienna Springer Vienna 12.10.2011
SeriesTexts & Monographs in Symbolic Computation
Subjects
Cylindrical Algebraic Decomposition Algorithm
Exact Linear Algebra
High Productivity Computing Systems (HPCS)
Sparse Signal Processing
Symbolic Computation
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Summary:We present the Seven Dwarfs of Symbolic Computation, which are sequential and parallel algorithmic methods that today carry a great majority of all exact and hybrid symbolic compute cycles. We will elaborate on each dwarf and compare with Colella’s seven and the Berkeley team’s thirteen dwarfs of scientific computing. SymDwf 1. Exact linear algebra, integer latticesSymDwf 2. Exact polynomial and differential algebra, Gröbner basesSymDwf 3. Inverse symbolic problems, e.g., interpolation and parameterizationSymDwf 4. Tarski’s algebraic theory of real geometrySymDwf 5. Hybrid symbolic-numeric computationSymDwf 6. Computation of closed form solutionsSymDwf 7. Rewrite rule systems and computational group theory
ISBN:9783709107935
3709107938
ISSN:0943-853X
DOI:10.1007/978-3-7091-0794-2_5