Parallel algorithms for algebraic problems
SIAM Journal on Computing
A taxonomy of problems with fast parallel algorithms
Information and Control
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
Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Representations and parallel computations for rational functions
SIAM Journal on 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
Dagwood: a system for manipulating polynomials given by straight-line programs
ACM Transactions on Mathematical Software (TOMS)
Multivariate Polynomial Factorization
Journal of the ACM (JACM)
Improved Sparse Multivariate Polynomial Interpolation Algorithms
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Factoring Polynomials over Algebraic Number Fields
SIAM Journal on Computing
Modular rational sparse multivariate polynomial interpolation
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Effective Noether irreducibility forms and applications
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
DSC: a system for distributed symbolic computation
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
On computing determinants of matrices without divisions
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
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 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
A black box approach to the algebraic set decomposition problem
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 bivariate Hensel and its parallelization
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
Interpolation of sparse multivariate polynomials over large finite fields with applications
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Extended Hilbert irreducibility and its applications
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Equality in computer algebra and beyond
Journal of Symbolic Computation - Integrated reasoning and algebra systems
On the Computational Hardness of Testing Square-Freeness of Sparse Polynomials
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Factoring multivariate polynomials via partial differential equations
Mathematics of Computation
Algorithms for computing the sparsest shifts of polynomials via the Berlekamp/Massey algorithm
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
An output-sensitive variant of the baby steps/giant steps determinant algorithm
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Polynomial factorization: a success story
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Computer algebra handbook
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Factoring polynomials via polytopes
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Complexity issues in bivariate polynomial factorization
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Approximate factorization of multivariate polynomials via differential equations
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Algorithms for the non-monic case of the sparse modular GCD algorithm
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Generic matrix multiplication and memory management in linBox
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Probabilistic algorithms for computing resultants
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Factorization of multivariate polynomials by extended Hensel construction
ACM SIGSAM Bulletin
On computing polynomial GCDs in alternate bases
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Symbolic-numeric sparse interpolation of multivariate polynomials
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Improved dense multivariate polynomial factorization algorithms
Journal of Symbolic Computation
Interpolation of depth-3 arithmetic circuits with two multiplication gates
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On exact and approximate interpolation of sparse rational functions
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation
An axiomatic approach to algebrization
Proceedings of the forty-first annual ACM symposium on Theory of computing
Symbolic-numeric sparse interpolation of multivariate 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
Arithmetic Circuits: A survey of recent results and open questions
Foundations and Trends® in Theoretical Computer Science
Sparse interpolation of multivariate rational functions
Theoretical Computer Science
A note on Gao's algorithm for polynomial factorization
Theoretical Computer Science
Diversification improves interpolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Supersparse black box rational function interpolation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Reconstruction of depth-4 multilinear circuits with top fan-in 2
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On the bit-complexity of sparse polynomial and series multiplication
Journal of Symbolic Computation
Extracting sparse factors from multivariate integral polynomials
Journal of Symbolic Computation
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
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Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. We show that within this representation the polynomial greatest common divisor and factorization problems, as well as the problem of extracting the numerator and denominator of a rational function, can all be solved in random polynomial-time. Since we can convert black boxes efficiently to sparse format, problems with sparse solutions, e.g., sparse polynomial factorization and sparse multivariate rational function interpolation, are also in random polynomial time. Moreover, the black box representation is one of the most space efficient implicit representations that we know. Therefore, the output programs can be easily distributed over a network of processors for further manipulation, such as sparse interpolation.