Simplification of expressions involving radicals

Authors:
Richard Zippel
Affiliations:
Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A.
Venue:
Journal of Symbolic Computation
Year:
1985

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Computer algebra handbook
Understanding expression simplification

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Automated simplification of large symbolic expressions

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Abstract

Algebraically dependent expressions arise in a large variety of symbolic computations. People seem to have the best intuition about expressions involving radicals. Symbolic computations with simple, non-nested, radicals is relatively straightforward; however, when the radicals are nested the problem becomes more difficult, This paper presents an algorithm for determining a linearly independent basis for a set of radicals (nested or not). This allows elementary techniques to be used for arithmetic operations on expressions involving elements of this set. In addition we provide a structure theorem that provides a sufficient condition for a nested radical to be expressed in terms of radicals of lower nesting level. These two techniques are powerful tools for computations involving radicals.