Irreducibility of multivariate polynomials
Journal of Computer and System Sciences
Uniform closure properties of P-computable functions
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Efficient parallel evaluation of straight-line code and arithmetic circuits
Proc. of the Aegean workshop on computing on VLSI algorithms and architectures
Computing with polynomials given by straight-line programs I: greatest common divisors
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
Multivariate Polynomial Factorization
Journal of the ACM (JACM)
Algebraic simplification: a guide for the perplexed
Communications of the ACM
ACM '73 Proceedings of the ACM annual conference
ACM SIGSAM Bulletin
Greatest common divisors of polynomials given by straight-line programs
Journal of the ACM (JACM)
On computing sparse shifts for univariate polynomials
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Algorithms for computing sparse shifts for multivariate polynomials
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
On Implications between P-NP-Hypotheses: Decision versus Computation in Algebraic Complexity
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
On lacunary polynomial perfect powers
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Detecting lacunary perfect powers and computing their roots
Journal of Symbolic Computation
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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, that polynomial also admits a polynomial bounded straight-line computation. Second, any factor of a multivariate polynomial given by a division-free straight-line program with relatively prime co-factor also admits a straight-line computation of length polynomial in the input length and the degree of the factor. This result is based on a new Hensel lifting process, one where only one factor image is lifted back to the original factor. As an application we get that the greatest common divisor of polynomials given by a division-free straight-line program has polynomial straight-line complexity in terms of the input length and its own degree.