Decreasing the nesting depth of expressions involving square roots

Authors:
Allan Borodin;Ronald Fagin;John E. Hopcroft;Martin Tompa
Affiliations:
Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 1A4;IBM Research Laboratory, 5600 Cottle Road, San Jose, California 95193, U.S.A.;Department of Computer Science, Cornell University, Ithaca, New York 14853, U.S.A.;Department of Computer Science, University of Washington, Seattle, Washington 98195, U .S.A.
Venue:
Journal of Symbolic Computation
Year:
1985

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Cited References

Computer algebra handbook
Algebraic Condition for Decomposition of Large-Scale Linear Dynamic Systems

International Journal of Applied Mathematics and Computer Science
On the Complexity of Nash Equilibria and Other Fixed Points

SIAM Journal on Computing

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Abstract

We develop the theory for decreasing the depth of nesting in expressions that contain square roots. We show exactly when fourth roots enable denesting of expressions not denestable with square roots only, When we restrict our attention to denesting over the real numbers, we show in fact that no roots other than square roots or fourth roots are ever useful for denesting expressions containing square roots only, thus characterising the denestable expressions in this case . We then proceed to describe new algorithms that accomplish such denesting.