http://worldcat.org/entity/work/id/137163204

All algebraic functions can be computed fast

The expansions of algebraic functions can be computed 'fast' using the Newton Polygon Process and any 'normal' iteration. Let M(j) be the number of operations sufficient to multiply two jth degree polynomials. It is shown that the first N terms of an expansion of any algebraic function defined by an nth degree polynomial can be computed in O(n(M(N)) operations, while the classical method needs O(N sup n) operations. Among the numerous applications of algebraic functions are symbolic mathematics and combinatorial analysis. Reversion, reciprocation, and nth root of a polynomial are all special cases of algebraic functions.

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