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
Efficient parallel evaluation of straight-line code and arithmetic circuits
Proc. of the Aegean workshop on computing on VLSI algorithms and architectures
On polynomials with symmetric Galois group which are easy to compute
Theoretical Computer Science
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
Parallel arithmetic computations: a survey
Proceedings of the 12th symposium on Mathematical foundations of computer science 1986
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A system for manipulating polynomials given by straight-line programs
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Subresultants and Reduced Polynomial Remainder Sequences
Journal of the ACM (JACM)
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
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)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
A Primer: 11 Keys to New Scratchpad
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
A Comparison of Algorithms for the Symbolic Computation of Padé Approximants
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
GCDHEU: Heuristic Polynomial GCD Algorithm Based on Integer GCD Computation
EUROSAM '84 Proceedings of the International Symposium on Symbolic and Algebraic Computation
Arithmetic in Quadratic Fields with Unique Factorization
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
ACM '73 Proceedings of the ACM annual conference
Functional decomposition ofpolynomials: the tame case
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On computing determinants of matrices without divisions
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Dagwood: a system for manipulating polynomials given by straight-line programs
ACM Transactions on Mathematical Software (TOMS)
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
MPP: a framework for distributed polynomial computations
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Checking polynomial identities over any field: towards a derandomization?
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
FOXBOX: a system for manipulating symbolic objects in black box representation
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
On the genericity of the modular polynomial GCD algorithm
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Arithmetic Circuits and Polynomial Replacement Systems
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
Decision Complexity in Dynamic Geometry
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Computer algebra handbook
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
On the complexity of factoring bivariate supersparse (Lacunary) polynomials
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms
Proceedings of the 2007 international workshop on Symbolic-numeric computation
The complexity of quantifier elimination and cylindrical algebraic decomposition
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
On exact and approximate interpolation of sparse rational functions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
The complexity of two problems on arithmetic circuits
Theoretical Computer Science
Computing Properties of Numerical Imperative Programs by Symbolic Computation
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
Expressing a fraction of two determinants as a determinant
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Solving structured linear systems with large displacement rank
Theoretical Computer Science
Interpolation of polynomials given by straight-line programs
Theoretical Computer Science
Evaluation properties of invariant polynomials
Journal of Symbolic Computation
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
Sparse interpolation of multivariate rational functions
Theoretical Computer Science
Supersparse black box rational function interpolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
On persistent homotopy, knotted complexes and the Alexander module
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
On the complexity of hilbert’s 17th problem
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and 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
Computing Properties of Numerical Imperative Programs by Symbolic Computation
Fundamenta Informaticae - Half a Century of Inspirational Research: Honoring the Scientific Influence of Antoni Mazurkiewicz
Software Engineering and complexity in effective Algebraic Geometry
Journal of Complexity
Sparse multivariate function recovery from values with noise and outlier errors
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Modular Composition Modulo Triangular Sets and Applications
Computational Complexity
Hi-index | 0.01 |
Algorithms on multivariate polynomials represented by straight-line programs are developed. First, it is shown that most algebraic algorithms can be probabilistically applied to data that are given by a straight-line computation. Testing such rational numeric data for zero, for instance, is facilitated by random evaluations modulo random prime numbers. Then, auxiliary algorithms that determine the coefficients of a multivariate polynomial in a single variable are constructed. The first main result is an algorithm that produces the greatest common divisor of the input polynomials, all in straight-line representation. The second result shows how to find a straight-line program for the reduced numerator and denominator from one for the corresponding rational function. Both the algorithm for that construction and the greatest common divisor algorithm are in random polynomial time for the usual coefficient fields and output a straight-line program, which with controllably high probability correctly determines the requested answer. The running times are polynomial functions in the binary input size, the input degrees as unary numbers, and the logarithm of the inverse of the failure probability. The algorithm for straight-line programs for the numerators and denominators of rational functions implies that every degree-bounded rational function can be computed fast in parallel, that is, in polynomial size and polylogarithmic depth.