Single-Factor Hensel Lifting and its Application to the Straight-Line Complexity of Certain Polynomials

@inproceedings{Kaltofen1987SingleFactorHL,
title={Single-Factor Hensel Lifting and its Application to the Straight-Line Complexity of Certain Polynomials},
author={Erich Kaltofen},
booktitle={STOC},
year={1987}
}

Three theorems are presented that establish polynomial straight-line complexity for certain operations on polynomials given by straight-line programs of unbounded input degree. The first theorem shows how to compute a higher order partial derivative in a single variable. The other two theorems impose the degree of the output polynomial as a parameter of the length of the output program. First it is shown that if a straight-line program computes an arbitrary power of a multivariate polynomial… CONTINUE READING