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The “Seven Dwarfs” of symbolic computation. (English) Zbl 1257.65013
Langer, Ulrich (ed.) et al., Numerical and symbolic scientific computing. Progress and prospects. New York, NY: Springer (ISBN 978-3-7091-0793-5/pbk; 978-3-7091-0794-2/ebook). Texts & Monographs in Symbolic Computation, 95-104 (2012).
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.
    SymDwf 1. Exact linear algebra, integer lattices
    SymDwf 2. Exact polynomial and differential algebra, Gröbner bases
    SymDwf 3. Inverse symbolic problems, e.g. interpolation and parameterization
    SymDwf 4. Tarskio’s algebraic theory of real geometry
    SymDwf 5. Hybrid symbolic-numeric computation
    SymDwf 6. Computation of closed form solutions
    SymDwf 7. Rewrite rule systems and computational group theory
We elaborate on each dwarf and compare it with Colella’s seven and the Berkeley team’s thirteen dwarfs of scientific computing.
For the entire collection see [Zbl 1234.65014].
MSC:
65D99 Numerical approximation and computational geometry (primarily algorithms)
65Y05 Parallel numerical computation
68W30 Symbolic computation and algebraic computation
65F99 Numerical linear algebra
Software:
SPIRAL; RAGlib
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