Dagwood: a system for manipulating polynomials given by straight-line programs

Authors:
Timothy S. Freeman;Gregory M. Imirzian;Erich Kaltofen;Lakshman Yagati
Affiliations:
Department of Computer Science, Carnegie-Mellon University, Pittsburgh, PA;Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY;Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY;Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1988

Citing 16
Cited 13

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
Greatest common divisors of polynomials given by straight-line programs

Journal of the ACM (JACM)
A deterministic algorithm for sparse multivariate polynomial interpolation

STOC '88 Proceedings of the twentieth 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)
Symbolic integration: the stormy decade

Communications of the ACM
Improved Sparse Multivariate Polynomial Interpolation Algorithms

ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Probabilistic algorithms for sparse polynomials

EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Early detection of true factors in univariate polynominal factorization

EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
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

Computing with polynomials given byblack boxes for their evaluations: Greatest common divisors, factorization, separation of numerators and denominators

Journal of Symbolic Computation - Special issue on computational algebraic complexity
On computing greatest common divisors with polynomials given by black boxes for their evaluations

ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
FOXBOX: a system for manipulating symbolic objects in black box representation

ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Symbolic computation in Java: an appraisement

ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Normal form algorithms for extended context-free grammars

Theoretical Computer Science
Functional programming concepts and straight-line programs in computer algebra

Mathematics and Computers in Simulation
An output-sensitive variant of the baby steps/giant steps determinant algorithm

Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Cited References

Computer algebra handbook
Early termination in sparse interpolation algorithms

Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Exploiting Vanishing Polynomials for Equivalence Veri.cation of Fixed-Size Arithmetic Datapaths

ICCD '05 Proceedings of the 2005 International Conference on Computer Design
Change of order for regular chains in positive dimension

Theoretical Computer Science
Hierarchical representations with signatures for large expression management

AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Structured FFT and TFT: symmetric and lattice polynomials

Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation

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 on, 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.