A system for manipulating polynomials given by straight-line programs

Authors:
T. Freeman;G. Imirzian;E. Kaltofen
Affiliations:
Carnegie-Mellon Univ., Pittsburgh, PA;Rensselaer Polytechnic Institute, Troy, NY;Mathematical Sciences Research Institute, Berkeley, CA
Venue:
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Year:
1986

Citing 13
Cited 5

Irreducibility of multivariate polynomials

Journal of Computer and System Sciences
Factoring sparse 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
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
Determining the Equivalence of Algebraic Expressions by Hash Coding

Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities

Journal of the ACM (JACM)
Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs

Journal of the ACM (JACM)
Algebraic simplification: a guide for the perplexed

Communications of the ACM
Probabilistic algorithms for sparse polynomials

EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
The design of maple: A compact, portable and powerful computer algebra system

EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Sparse Hensel Lifting

EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Newton's iteration and the sparse Hensel algorithm (Extended Abstract)

SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
Determining equivalence of expressions in random polynomial time

STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing

Greatest common divisors of polynomials given by straight-line programs

Journal of the ACM (JACM)
Recovery of algebraic numbers from their p-adic approximations

ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
A toolbox for program manipulation and efficient code generation with an application to a problem in computer vision

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Equality in computer algebra and beyond

Journal of Symbolic Computation - Integrated reasoning and algebra systems
Software Engineering and complexity in effective Algebraic Geometry

Journal of Complexity

Quantified Score

Hi-index	0.00

Visualization

Abstract

We discuss the design, implementation, and benchmarking of a system that can manipulate symbolic expressions represented by their straight-line computations. Our system is capable of performing rational arithmetic, evaluating, differentiating, taking greatest common divisors of, and factoring polynomials in straight-line format. The straight-line results can also be converted to standard sparse format. We show by example that our system can handle problems for which conventional methods lead to excessive intermediate expression swell.