The “Seven Dwarfs” of Symbolic Computation

  • Erich L. Kaltofen
Part of the Texts & Monographs in Symbolic Computation book series (TEXTSMONOGR)


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 lattices


SymDwf 2. Exact polynomial and differential algebra, Gröbner bases


SymDwf 3. Inverse symbolic problems, e.g., interpolation and parameterization


SymDwf 4. Tarski’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




I thank Bruno Salvy for his thoughtful comments. This material is based on work supported in part by the National Science Foundation under Grants CCF-0830347, CCF-0514585 and DMS-0532140.


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Copyright information

© Springer-Verlag/Wien 2012

Authors and Affiliations

  • Erich L. Kaltofen
    • 1
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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