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Updated: April 5th, 2024 00:17

2022 article

Sparse Polynomial Hermite Interpolation

*PROCEEDINGS OF THE 2022 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2022*, pp. 469–478.

author keywords: model fitting; gradient data; measurement minimization

TL;DR:
These algorithms generalize to multivariate polynomials, higher derivatives and sparsity with respect to Chebyshev polynomial bases, and have algorithms that can correct errors in the points by oversampling at a limited number of good values.
(via Semantic Scholar)

Source: Web Of Science

Added: September 11, 2023

2022 article

The GKR Protocol Revisited: Nearly Optimal Prover-Complexity For Polynomial-Time Wiring Algorithms and For Primality Testing in n(1/2+o(1)) Rounds

*PROCEEDINGS OF THE 2022 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2022*, pp. 177–186.

author keywords: cloud computing; primality testing; proof-of-work certificate

TL;DR:
This protocol applies GKR recursively to the arising sumcheck problems on each level of the circuit whose values are verified, and deploys any of the prover-nearly-optimal versions of GKR on the constructed sorting/prefix circuits with log-depth wiring functions.
(via Semantic Scholar)

Source: Web Of Science

Added: September 11, 2023

2021 article

Foreword

*JOURNAL OF SYMBOLIC COMPUTATION*, Vol. 105, pp. 1–3.

Source: Web Of Science

Added: February 15, 2021

2021 journal article

On computing the degree of a Chebyshev Polynomial from its value

*JOURNAL OF SYMBOLIC COMPUTATION*, *104*, 159–167.

author keywords: Algorithms; Discrete logarithms; Chebyshev Polynomials; Interpolation in terms of the Chebyshev; Polynomials of the First Kind

TL;DR:
An algorithm is given that can determine the Chebyshev degrees modulo such primes in bit complexity log ( p ) O ( 1 ) times the squareroot of the largest prime factor of p − 1 (or p + 1 ).
(via Semantic Scholar)

Source: Web Of Science

Added: January 19, 2021

2021 journal article

Sparse Interpolation With Errors in Chebyshev Basis Beyond Redundant-Block Decoding

*IEEE TRANSACTIONS ON INFORMATION THEORY*, *67*(1), 232–243.

author keywords: Sparse polynomial interpolation; error correction; black box polynomial; list-decoding

TL;DR:
Sparse interpolation algorithms for recovering a polynomial with LaTeX terms from inline-formula evaluations at distinct values for the variable with Chebyshev Basis, which return a list of valid sparse interpolants for the algorithm.
(via Semantic Scholar)

Source: Web Of Science

Added: January 19, 2021

2020 journal article

A Note on Sparse Polynomial Interpolation in Dickson Polynomial Basis

*ACM COMMUNICATIONS IN COMPUTER ALGEBRA*, *54*(4), 125–128.

Source: Web Of Science

Added: June 10, 2021

2019 journal article

Computing Approximate Greatest Common Right Divisors of Differential Polynomials

*Foundations of Computational Mathematics*.

author keywords: Symbolic-numeric computation; Approximate polynomial computation; Approximate GCD; Differential polynomials; Linear differential operators

TL;DR:
The approximate greatest common right divisor problem (GCRD) of differential polynomials is introduced, as a non-commutative generalization of the well-studied approximate GCD problem.
(via Semantic Scholar)

Source: Crossref

Added: July 21, 2019

2019 article

Elimination-based certificates for triangular equivalence and rank profiles

*JOURNAL OF SYMBOLIC COMPUTATION*, Vol. 98, pp. 246–269.

author keywords: Interactive certificate; Rank profile; Linear algebra; Triangular equivalence; Verifiable computing

TL;DR:
Novel certificates for triangular equivalence and rank profiles are given, enabling somebody to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a negligible overall overhead.
(via Semantic Scholar)

Source: Web Of Science

Added: December 30, 2019

2018 article

Sparse Polynomial Interpolation With Arbitrary Orthogonal Polynomial Bases

*ISSAC'18: PROCEEDINGS OF THE 2018 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION*, pp. 223–230.

Source: Web Of Science

Added: February 25, 2019

2017 conference paper

Early Termination in Parametric Linear System Solving and Rational Function Vector Recovery with Error Correction

*Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17*. Presented at the the 2017 ACM.

Event: the 2017 ACM

UN Sustainable Development Goal Categories

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Crossref

Added: July 21, 2019

2017 conference paper

Polynomial Time Interactive Proofs for Linear Algebra with Exponential Matrix Dimensions and Scalars Given by Polynomial Time Circuits

*Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17*. Presented at the the 2017 ACM.

Event: the 2017 ACM

Source: Crossref

Added: July 21, 2019

2016 article

Linear Time Interactive Certificates for the Minimal Polynomial and the Determinant of a Sparse Matrix

*PROCEEDINGS OF THE 2016 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION (ISSAC 2016)*, pp. 199–206.

Source: Web Of Science

Added: August 6, 2018

2016 conference paper

Numerical Sparsity Determination and Early Termination

*Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16*. Presented at the the ACM.

Event: the ACM

author keywords: Hankel matrix; Vandermonde matrix; sparse polynomial interpolation; condition number; early termination; sparse signal processing

TL;DR:
An algorithm is given that can be used to compute the sparsity and estimate the minimal number of samples needed in numerical sparse interpolation and the early termination strategy of polynomial interpolation has been incorporated in the algorithm.
(via Semantic Scholar)

Source: Crossref

Added: July 21, 2019

2016 journal article

Sparse multivariate function recovery with a small number of evaluations

*JOURNAL OF SYMBOLIC COMPUTATION*, *75*, 209–218.

author keywords: Error correcting coding; Fault tolerance; Cauchy interpolation; Multivariate rational function model

TL;DR:
Here it is proved that T + O ( 1 ) evaluations at random points indeed suffice, thus providing the missing proof to Theorem 2.1 in Section 2 of the ISSAC 2014 paper.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2015 conference paper

Error-Correcting Sparse Interpolation in the Chebyshev Basis

*Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15*. Presented at the the 2015 ACM.

Event: the 2015 ACM

author keywords: sparse polynomial interpolation; Prony's algorithm; Chebyshev polynomials; Descartes' rule of signs; orthogonal basis; error-correcting code

TL;DR:
The correctness of the list-decoder-based algorithm with a Descartes-rule-of-signs-like property for sparse polynomials in Chebyshev basis is proved and the many techniques for the sparse interpolation in power basis, for instance, supersparse (lacunary) interpolation over large finite fields, are made available to interpolation on Chebyshv basis.
(via Semantic Scholar)

Source: Crossref

Added: July 21, 2019

2015 book

PASCO '15 Proceedings of the 2015 International Workshop on Parallel Symbolic Computation

New York, NY: Association for Computing Machinery.

Ed(s): J. Dumas, & C. Pernet

Source: NC State University Libraries

Added: August 16, 2021

2014 conference paper

Cleaning-up data for sparse model synthesis

*Proceedings of the 2014 Symposium on Symbolic-Numeric Computation - SNC '14*. Presented at the the 2014 Symposium.

Event: the 2014 Symposium

Source: Crossref

Added: July 21, 2019

2014 conference paper

Essentially optimal interactive certificates in linear algebra

*Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14*. Presented at the the 39th International Symposium.

Event: the 39th International Symposium

Source: Crossref

Added: July 21, 2019

2014 conference paper

Numerical linear system solving with parametric entries by error correction

*Proceedings of the 2014 Symposium on Symbolic-Numeric Computation - SNC '14*. Presented at the the 2014 Symposium.

Event: the 2014 Symposium

Source: Crossref

Added: July 21, 2019

2014 chapter

Sparse Polynomial Interpolation by Variable Shift in the Presence of Noise and Outliers in the Evaluations

In *Computer Mathematics* (pp. 183–197).

Source: Crossref

Added: July 27, 2019

2014 conference paper

Sparse multivariate function recovery with a high error rate in the evaluations

*Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14*. Presented at the the 39th International Symposium.

Event: the 39th International Symposium

Source: Crossref

Added: July 21, 2019

2014 conference paper

Sparse polynomial interpolation codes and their decoding beyond half the minimum distance

*Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14*. Presented at the the 39th International Symposium.

Event: the 39th International Symposium

Source: Crossref

Added: July 21, 2019

2014 chapter

Symbolic Computation and Complexity Theory Transcript of My Talk

In *Computer Mathematics* (pp. 3–7).

Source: Crossref

Added: July 27, 2019

2013 journal article

A fraction free Matrix Berlekamp/Massey algorithm

*LINEAR ALGEBRA AND ITS APPLICATIONS*, *439*(9), 2515–2526.

author keywords: Exact division; Linear recurrences; Matrix recurrences; Block Hankel systems; Block Toeplitz systems; Integer sequences

TL;DR:
This new scalar algorithm has smaller intermediate values than the known fraction free Berlekamp/Massey algorithm and performs all operations in the integral domain, so all divisions performed are exact.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2013 chapter

Factorization of multivariate polynomials

In G. L. Mullen & D. Panario (Eds.), *Handbook of Finite Fields* (pp. 382–392). Boca Raton, Florida: CRC Press, Taylor & Francis Group.

Ed(s): G. Mullen & D. Panario

Source: NC State University Libraries

Added: March 26, 2022

2013 journal article

On the Matrix Berlekamp-Massey Algorithm

*ACM TRANSACTIONS ON ALGORITHMS*, *9*(4).

author keywords: Linear generated sequences; matrix polynomials; minimal generators; vector Berlekamp/Massey algorithm; multivariable linear control

TL;DR:
This work analyzes the Matrix Berlekamp/Massey algorithm and gives new proofs of correctness and complexity for the algorithm, which is based on self-contained loop invariants and includes an explicit termination criterion for a given determinantal degree bound of the minimal matrix generator.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2013 conference paper

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 - ISSAC '13*. Presented at the the 38th international symposium.

Event: the 38th international symposium

Source: Crossref

Added: July 27, 2019

2012 conference paper

Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions

*Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12*. Presented at the the 37th International Symposium.

Event: the 37th International Symposium

Source: Crossref

Added: July 27, 2019

2012 journal article

Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients

*Journal of Symbolic Computation*, *47*(1), 1–15.

author keywords: Semidefinite programming; Sum-of-squares; Validated output; Hybrid method

TL;DR:
This work presents a hybrid symbolic-numeric algorithm for certifying a polynomial or rational function with rational coefficients to be non-negative for all real values of the variables by computing a representation for it as a fraction of twoPolynomial sum-of-squares (SOS) with rational coefficient.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

4. Quality Education
(OpenAlex)

11. Sustainable Cities and Communities
(Web of Science)

Source: Crossref

Added: July 27, 2019

2012 journal article

On the Berlekamp/Massey algorithm and counting singular Hankel matrices over a finite field

*JOURNAL OF SYMBOLIC COMPUTATION*, *47*(4), 480–491.

author keywords: Toeplitz matrix; Hankel matrix; Block matrix; Finite field; Singularity counts; Fixed entry; Berlekamp/Massey algorithm

TL;DR:
An explicit count for the number of singular nxn Hankel (Toeplitz) matrices whose entries range over a finite field with q elements is derived by observing the execution of the Berlekamp/Massey algorithm on its elements.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

9. Industry, Innovation and Infrastructure
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2012 conference paper

Sparse polynomial interpolation and Berlekamp/Massey algorithms that correct outlier errors in input values

*Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12*. Presented at the the 37th International Symposium.

Event: the 37th International Symposium

Source: Crossref

Added: July 27, 2019

2012 article

Special Issue on Symbolic and Algebraic Computation Foundations, Algorithmics and Applications: ISSAC 2009

Johnson, J. R., Kaltofen, E., & Park, H. (2012, July). *JOURNAL OF SYMBOLIC COMPUTATION*, Vol. 47, pp. 751–751.

Source: Web Of Science

Added: August 6, 2018

2011 conference paper

Fast estimates of Hankel matrix condition numbers and numeric sparse interpolation

*Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation - SNC '11*. Presented at the the 2011 International Workshop.

Event: the 2011 International Workshop

Source: Crossref

Added: July 27, 2019

2011 conference paper

Quadratic-time certificates in linear algebra

*Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11*. Presented at the the 36th international symposium.

Event: the 36th international symposium

Source: Crossref

Added: August 18, 2019

2011 conference paper

Supersparse black box rational function interpolation

*Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11*. Presented at the the 36th international symposium.

Event: the 36th international symposium

Source: Crossref

Added: July 27, 2019

2011 other

Symmetric determinantal representation of formulas and weakly skew circuits

Source: Crossref

Added: July 27, 2019

2011 conference paper

Symmetric determinantal representation of weakly skew circuits

In C. Dürr & T. Schwentick (Eds.), *Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS 2011)* (pp. 543–554). Germany.

Ed(s): C. Dürr & T. Schwentick

Event: Symposium on Theoretical Aspects of Computer Science (STACS 2011) at Dortmund, Germany

Source: NC State University Libraries

Added: March 26, 2022

2011 chapter

The “Seven Dwarfs” of Symbolic Computation

In *Texts & Monographs in Symbolic Computation* (pp. 95–104).

Source: Crossref

Added: July 27, 2019

2010 conference paper

Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of Seidenberg's method

*Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation - ISSAC '10*. Presented at the the 2010 International Symposium.

Event: the 2010 International Symposium

UN Sustainable Development Goal Categories

10. Reduced Inequalities
(OpenAlex)

Source: Crossref

Added: August 18, 2019

2010 journal article

Efficiently Certifying Non-Integer Powers

*COMPUTATIONAL COMPLEXITY*, *19*(3), 355–366.

author keywords: Integer roots; integer powers; linear-time algorithm; bit complexity; Chebotarev density theorem

TL;DR:
A randomized algorithm that, given an integer a, produces a certificate that the integer is not a pure power of an integer in expected (log a)1+o(1) bit operations under the assumption of the Generalized Riemann Hypothesis is described.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2010 conference paper

Fifteen years after DSC and WLSS2 what parallel computations I do today

*Proceedings of the 4th International Workshop on Parallel and Symbolic Computation - PASCO '10*. Presented at the the 4th International Workshop.

Event: the 4th International Workshop

Source: Crossref

Added: August 18, 2019

2010 report

The Role of Symbolic, Numeric and Algebraic Computation in Cyber-Enabled Discovery and Innovation (CDI)

In *Future Directions of Symbolic Computation Research And Their Applications to the Domain Sciences*. University of Rhode Island.

Source: NC State University Libraries

Added: March 26, 2022

2009 conference paper

A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions

*Proceedings of the 2009 conference on Symbolic numeric computation - SNC '09*. Presented at the the 2009 conference.

Event: the 2009 conference

Source: Crossref

Added: August 18, 2019

2008 journal article

Approximate factorization of multivariate polynomials using singular value decomposition

*JOURNAL OF SYMBOLIC COMPUTATION*, *43*(5), 359–376.

author keywords: multivariate polynomial factorization; approximate factorization; singular value decomposition; numerical algebra; Gauss-Newton optimization

TL;DR:
These algorithms are based on a generalization of the differential forms introduced by W. Ruppert and S. Gao to many variables, and use singular value decomposition or structured total least squares approximation and Gauss-Newton optimization to numerically compute the approximate multivariate factors.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2008 conference paper

Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars

*Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08*. Presented at the the twenty-first international symposium.

Event: the twenty-first international symposium

Source: Crossref

Added: August 18, 2019

2008 conference paper

Expressing a fraction of two determinants as a determinant

*Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08*. Presented at the the twenty-first international symposium.

Event: the twenty-first international symposium

Source: Crossref

Added: August 18, 2019

2007 journal article

Irreducible polynomials and barker sequences

*ACM Communications in Computer Algebra*, *41*(4), 118.

Source: Crossref

Added: August 18, 2019

2007 conference paper

Lower bounds for approximate factorizations via semidefinite programming

In J. Verschelde & S. M. Watt (Eds.), *Proceedings of the 2007 International Workshop on Symbolic-Numeric Computation (SNC '07)* (pp. 203–204). New York, NY: ACM Press.

Ed(s): J. Verschelde & S. Watt

Event: International Workshop on Symbolic-Numeric Computation at London, Ontario, Canada on July 25-27, 2007

Source: NC State University Libraries

Added: March 26, 2022

2007 conference paper

On exact and approximate interpolation of sparse rational functions

*ISSAC 2007: International Symposium for Symbolic and Algebraic Computation: Proceedings*.

Source: NC State University Libraries

Added: August 6, 2018

2007 conference paper

On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms

*International Workshop on Symbolic-Numeric Computation: Proceedings*. New York: ACM Press.

Source: NC State University Libraries

Added: August 6, 2018

2007 chapter

Structured Low Rank Approximation of a Sylvester Matrix

In *Trends in Mathematics* (pp. 69–83).

author keywords: Sylvester matrix; approximate greatest common divisor; structured total least norm; hybrid symbolic/numeric algorithm

TL;DR:
This work presents iterative algorithms that compute an approximate GCD and that can certify an approximate ∈-GCD when a tolerance ∈ is given on input and demonstrates the practical performance of these algorithms on a diverse set of univariate pairs of polynomials.
(via Semantic Scholar)

Source: Crossref

Added: August 18, 2019

2006 conference paper

Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials

*Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06*. Presented at the the 2006 international symposium.

Event: the 2006 international symposium

Source: Crossref

Added: August 18, 2019

2006 conference paper

Challenges in Symbolic Computation Software, number 06271

In *Dagstuhl Seminar Proceedings*. Germany: Schloss Dagstuhl.

Ed(s): W. Decker, M. Dewar, & S. Watt

Event: Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI) at Schloss Dagstuhl

Source: NC State University Libraries

Added: March 26, 2022

2006 conference paper

Finding small degree factors of multivariate supersparse (lacunary) polynomials over algebraic number fields

*Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06*. Presented at the the 2006 international symposium.

Event: the 2006 international symposium

Source: Crossref

Added: August 28, 2020

2006 conference paper

Hybrid symbolic-numeric computation

*Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06*. Presented at the the 2006 international symposium.

Event: the 2006 international symposium

Source: Crossref

Added: August 28, 2020

2005 chapter

Explicit construction of the hilbert class fields of imaginary quadratic fields with class numbers 7 and 11

In J. Fitch (Ed.), *EUROSAM 84* (pp. 310–320).

Ed(s): J. Fitch

Event: International Symposium on Symbolic and Algebraic Computation at Cambridge, England on July 9-11, 1984

Source: Crossref

Added: June 15, 2021

2005 conference paper

Generic matrix multiplication and memory management in linBox

*Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05*. Presented at the the 2005 international symposium.

Event: the 2005 international symposium

Source: Crossref

Added: August 28, 2020

2005 journal article

On the complexity of computing determinants

*COMPUTATIONAL COMPLEXITY*, *13*(3-4), 91–130.

author keywords: integer matrix; matrix determinant; characteristic polynomial; Smith normal form; bit complexity; division-free complexity; randomized algorithm; multivariable control theory; realization; matrix sequence; block Wiedemann algorithm; block Lanczos algorithm

TL;DR:
New baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems that deterministically compute the determinant, characteristic polynomial and adjoint of A with n3.2+o(1) and O(n2.697263) ring additions, subtractions and multiplications are presented.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2005 conference paper

On the complexity of factoring bivariate supersparse (Lacunary) polynomials

*Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05*. Presented at the the 2005 international symposium.

Event: the 2005 international symposium

Source: Crossref

Added: August 28, 2020

2004 conference paper

Approximate factorization of multivariate polynomials via differential equations

*Proceedings of the 2004 international symposium on Symbolic and algebraic computation - ISSAC '04*. Presented at the the 2004 international symposium.

Event: the 2004 international symposium

Source: Crossref

Added: August 28, 2020

2004 article

Computing the sign or the value of the determinant of an integer matrix, a complexity survey

Kaltofen, E., & Villard, G. (2004, January 1). *JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS*, Vol. 162, pp. 133–146.

author keywords: determinant; bit-complexity; integer matrix; approximate computation; exact computation; randomized algorithms

TL;DR:
This work surveys the complexity of existing methods to solve problems when the input is an n × n matrix A with integer entries and studies the bit-complexities of the algorithms asymptotically in n and the norm of A.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2004 journal article

Deterministic distinct-degree factorization of polynomials over finite fields

*JOURNAL OF SYMBOLIC COMPUTATION*, *38*(6), 1461–1470.

author keywords: multivariate polynomial; deterministic algorithm; distinct-degree factorization

Source: Web Of Science

Added: August 6, 2018

2004 journal article

Early termination in Shoup's algorithm for the minimum polynomial of an algebraic

Source: NC State University Libraries

Added: March 26, 2022

2003 chapter

Absolute factorization of polynomials

In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), *Computer Algebra Handbook* (p. 26). Heidelberg, Germany: Springer Verlag.

Ed(s): J. Grabmeier, & V. Weispfenning

Source: NC State University Libraries

Added: December 5, 2020

2003 article

Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases

*JOURNAL OF SYMBOLIC COMPUTATION*, Vol. 36, pp. 401–424.

author keywords: sparse shifts; early termination; sparse polynomial; sparse interpolation; Chebyshev basis; Pochhammer basis

TL;DR:
These algorithms are based on the early termination version of sparse interpolation algorithms: for a symbolic set of interpolation points, a sparsest shift must be a root of the first possible zero discrepancy that can be used as the earlytermination test.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2003 book

Computer Algebra Handbook

(J. Grabmeier, E. Kaltofen, & V. Weispfenning, Eds.). Heidelberg, Germany: Springer Verlag.

Ed(s): J. Grabmeier, & V. Weispfenning

Source: NC State University Libraries

Added: March 26, 2022

2003 chapter

Computer algebra - impact on research

In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), *Computer Algebra Handbook* (pp. 4–6). Heidelberg, Germany: Springer Verlag.

Ed(s): J. Grabmeier, & V. Weispfenning

Source: NC State University Libraries

Added: December 5, 2020

2003 book

Computer algebra handbook foundations, applications, systems

Source: NC State University Libraries

Added: August 6, 2018

2003 article

Early termination in sparse interpolation algorithms

*JOURNAL OF SYMBOLIC COMPUTATION*, Vol. 36, pp. 365–400.

author keywords: early termination; sparse polynomial; black box polynomial; interpolation; sparse interpolation; randomized algorithm

TL;DR:
Based on early termination, racing algorithms execute simultaneously dense and sparse algorithms that can be embedded as the univariate interpolation substep within Zippel's multivariate method.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2003 chapter

FoxBox and other blackbox systems

In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), *Computer Algebra Handbook* (pp. 383–385). Heidelberg, Germany: Springer Verlag.

Ed(s): J. Grabmeier, & V. Weispfenning

Source: NC State University Libraries

Added: December 5, 2020

2003 chapter

Hybrid methods

In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), *Computer Algebra Handbook* (pp. 112–125). Heidelberg, Germany: Springer Verlag.

Ed(s): J. Grabmeier, & V. Weispfenning

Source: NC State University Libraries

Added: December 5, 2020

2003 chapter

Linear systems

In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), *Computer algebra handbook: foundations, applications, systems* (pp. 36–38). Heidelberg, Germany: Springer Verlag.

Ed(s): J. Grabmeier, & V. Weispfenning

Source: NC State University Libraries

Added: December 5, 2020

2003 conference paper

On approximate irreducibility of polynomials in several variables

*Proceedings of the 2003 international symposium on Symbolic and algebraic computation - ISSAC '03*. Presented at the the 2003 international symposium.

Event: the 2003 international symposium

Source: Crossref

Added: August 28, 2020

2003 conference paper

Polynomial factorization

*Proceedings of the 2003 international symposium on Symbolic and algebraic computation - ISSAC '03*. Presented at the the 2003 international symposium.

Event: the 2003 international symposium

Source: Crossref

Added: August 28, 2020

2002 conference paper

'Using Maple to grade Maple' assessment software from North Carolina State University

*Proceedings 2002 Maple Workshop*. Waterloo, Canada: Waterloo Maple Inc. With Dmitriy Morozov, John May and William Turner.

Source: NC State University Libraries

Added: March 26, 2022

2002 conference paper

Algorithms for computing the sparsest shifts of polynomials via the Berlekamp/Massey algorithm

*Proceedings of the 2002 international symposium on Symbolic and algebraic computation - ISSAC '02*. Presented at the ISSAC 02: International symposium on symbolic and algebraic computation, Lille, France.

Event: ISSAC 02: International symposium on symbolic and algebraic computation at Lille, France

Source: Crossref

Added: May 18, 2021

2002 conference paper

An output-sensitive variant of the baby steps/giant steps determinant algorithm

*Proceedings of the 2002 international symposium on Symbolic and algebraic computation - ISSAC '02*. Presented at the the 2002 international symposium.

Event: the 2002 international symposium

Source: Crossref

Added: August 28, 2020

2002 journal article

Efficient matrix preconditioners for black box linear algebra

*LINEAR ALGEBRA AND ITS APPLICATIONS*, *343*, 119–146.

author keywords: black box matrix; sparse matrix; structured matrix; Toeplitz-like matrix; matrix preconditioner; exact arithmetic; finite field; symbolic computation; linear system solution; minimal polynomial; characteristic polynomial; rank; determinant; Wiedemann algorithm; randomized algorithm; butterfly network

TL;DR:
Improvements are offered for the efficiency and applicability of preconditioners on linear algebra problems over finite fields, but most results are valid for entries from arbitrary fields.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2002 conference paper

LINBOX: A GENERIC LIBRARY FOR EXACT LINEAR ALGEBRA

*Mathematical Software*. Presented at the Proceedings of the First International Congress of Mathematical Software.

Event: Proceedings of the First International Congress of Mathematical Software

Source: Crossref

Added: August 28, 2020

2001 conference paper

Algorithms for sparse and black box matrices over finite fields

Kaltofen, E. (2001, May 23). Presented at the International Conference on Finite Fields and Applications, Oaxaca, Mexico.

Event: International Conference on Finite Fields and Applications at Oaxaca, Mexico

Source: NC State University Libraries

Added: March 26, 2022

2000 review

Challenges of symbolic computation: My favorite open problems

[Review of ]. *JOURNAL OF SYMBOLIC COMPUTATION*, *29*(6), 891–919.

Source: Web Of Science

Added: August 6, 2018

2000 conference paper

Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm

*Proceedings of the 2000 international symposium on Symbolic and algebraic computation symbolic and algebraic computation - ISSAC '00*. Presented at the the 2000 international symposium.

Event: the 2000 international symposium

Source: Crossref

Added: August 28, 2020

1999 journal article

Distributed matrix-free solution of large sparse linear systems over finite fields

*ALGORITHMICA*, *24*(3-4), 331–348.

author keywords: distributed symbolic computation; sparse linear systems; block Wiedemann; outer loop parallelization

TL;DR:
An outer loop parallelization that works well in conjunction with a black box abstraction for the coefficient matrix is performed that can be run on a network cluster of UNIX workstations as well as on an SP-2 multiprocessor.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

1999 journal article

East Coast Computer Algebra Day '99 (April 24, 1999): Abstracts of invited talks and presented posters

*Association for Computing Machinery SIGSAM Bulletin*, *33*(2), 43–52.

Ed(s): H. Hong ^{ n}, ^{ n} & M. Singer^{ n}

Event: East Coast Computer Algebra Day on April 24, 1999

Source: NC State University Libraries

Added: March 26, 2022

1999 conference paper

Efficient algorithms for computing the nearest polynomial with a real root and related problems

*Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99*. Presented at the the 1999 international symposium.

Event: the 1999 international symposium

Source: Crossref

Added: August 28, 2020

1999 conference paper

On the genericity of the modular polynomial GCD algorithm

*Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99*. Presented at the the 1999 international symposium.

Event: the 1999 international symposium

Source: Crossref

Added: August 28, 2020

1999 conference paper

Symbolic computation in Java

*Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99*. Presented at the the 1999 international symposium.

Event: the 1999 international symposium

Source: Crossref

Added: August 28, 2020

1998 chapter

Algebraic Algorithms

In *Algorithms and Theory of Computation Handbook*.

Source: Crossref

Added: January 21, 2021

1998 conference paper

Efficient algorithms for computing the nearest polynomial with constrained roots

*Proceedings of the 1998 international symposium on Symbolic and algebraic computation - ISSAC '98*. Presented at the the 1998 international symposium.

Event: the 1998 international symposium

Source: Crossref

Added: August 28, 2020

1998 conference paper

FOXBOX

*Proceedings of the 1998 international symposium on Symbolic and algebraic computation - ISSAC '98*. Presented at the the 1998 international symposium.

Event: the 1998 international symposium

Source: Crossref

Added: August 28, 2020

1998 journal article

Subquadratic-time factoring of polynomials over finite fields

*MATHEMATICS OF COMPUTATION*, *67*(223), 1179–1197.

author keywords: factoring; polynomials; finite fields; randomized algorithms; normal bases

Source: Web Of Science

Added: August 6, 2018

1997 chapter

Algebraic algorithms

In A. B. Tucker (Ed.), *The computer science and engineering handbook* (pp. 226–248). Boca Raton, Florida: CRC Press.

Ed(s): A. Tucker

Source: NC State University Libraries

Added: March 26, 2022

1997 conference paper

Fast polynomial factorization over high algebraic extensions of finite fields

*Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97*. Presented at the the 1997 international symposium.

Event: the 1997 international symposium

Source: Crossref

Added: August 28, 2020

1997 conference paper

On randomized Lanczos algorithms

*Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97*. Presented at the the 1997 international symposium.

Event: the 1997 international symposium

Source: Crossref

Added: August 28, 2020

1997 book

PASCO '97: Proceedings of the second international symposium on Parallel symbolic computation

Ed(s): H. Hong, & M. Hitz

Event: PASCO97: International Symposium on Parallel Symbolic Computation at Maui, Hawaii on July 20-22, 1997

Source: Crossref

Added: June 15, 2021

1997 journal article

Teaching computational abstract algebra

*JOURNAL OF SYMBOLIC COMPUTATION*, *23*(5-6), 503–515.

UN Sustainable Development Goal Categories

4. Quality Education
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

1996 conference paper

Blocked iterative sparse linear system solvers for finite fields

In C. Roucairol (Ed.), *Proceedings of the Symposium of Parallel Computing Solving Large Scale Irregular Applications (Stratagem '96)* (pp. 91–95). Sophia Antipolis, France: INRIA.

Ed(s): C. Roucairol

Source: NC State University Libraries

Added: March 26, 2022

1996 conference paper

Generic Gram-Schmidt orthogonalization by exact division

*Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96*. Presented at the the 1996 international symposium.

Event: the 1996 international symposium

Source: Crossref

Added: August 28, 2020

1996 conference paper

On rank properties of Toeplitz matrices over finite fields

*Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96*. Presented at the the 1996 international symposium.

Event: the 1996 international symposium

Source: Crossref

Added: August 28, 2020

1996 chapter

Prediction Based Task Scheduling in Distributed Computing

In *Languages, Compilers and Run-Time Systems for Scalable Computers* (pp. 317–320).

Source: Crossref

Added: August 28, 2020

1995 journal article

Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems

*Mathematics of Computation*, *64*(210), 777–777.

Source: Crossref

Added: August 28, 2020

1995 journal article

Effective Noether Irreducibility Forms and Applications

*Journal of Computer and System Sciences*, *50*(2), 274–295.

Source: Crossref

Added: August 28, 2020

1995 journal article

Integer division in residue number systems

*IEEE Transactions on Computers*, *44*(8), 983–989.

author keywords: INTEGER DIVISION; RECIPROCAL; NEWTON ITERATION; EXTENDED RESIDUE NUMBER SYSTEM; MIXED RADIX CONVERSION; BASE EXTENSION

TL;DR:
This contribution to the ongoing discussion of division algorithm for residue number systems (RNS) is based on Newton iteration for computing the reciprocal, and an extended RNS with twice the number of moduli provides the range required for multiplication and scaling.
(via Semantic Scholar)

Source: Crossref

Added: August 28, 2020

1995 conference paper

On computing greatest common divisors with polynomials given by black boxes for their evaluations

In A. H. M. Levelt (Ed.), *Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95*.

Ed(s): A. Levelt

Event: ISSAC95: International Symposium on Symbolic and Algebraic Computation at Montreal Quebec Canada on July 10-12, 1995

Source: Crossref

Added: June 15, 2021

1995 journal article

Process Scheduling in DSC and the Large Sparse Linear Systems Challenge

*Journal of Symbolic Computation*, *19*(1-3), 269–282.

Source: Crossref

Added: August 28, 2020

1994 chapter

A Distributed Approach to Problem Solving in Maple

In *Maple V: Mathematics and its Applications* (pp. 13–21).

Source: Crossref

Added: August 28, 2020

1994 conference paper

Asymptotically fast solution of Toeplitz-like singular linear systems

*Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94*. Presented at the the international symposium.

Event: the international symposium

Source: Crossref

Added: August 28, 2020

1994 conference paper

Factoring high-degree polynomials by the black box Berlekamp algorithm

*Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94*. Presented at the the international symposium.

Event: the international symposium

Source: Crossref

Added: August 28, 2020

1994 conference paper

Parallel solution of Toeplitz and Toeplitz-like linear systems over fields of small positive characteristic

In H. Hong (Ed.), *Proceedings of the First International Symposium of Parallel Symbolic Computation* (pp. 225–233). Singapore: World Scientific Publishing Co.

Ed(s): H. Hong

Source: NC State University Libraries

Added: March 26, 2022

1993 chapter

Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems

In *Applied Algebra, Algebraic Algorithms and Error-Correcting Codes* (pp. 195–212).

Source: Crossref

Added: August 28, 2020

1993 report

Computational differentiation and algebraic complexity theory

In C. H. Bischof, A. Griewank, & P. M. Khademi (Eds.), *Workshop Report on First Theory Institute on Computational Differentiation* (Technical Report No. ANL/MCS-TM-183; pp. 28–30). Argonne, Illinois: Argonne National Laboratory.

Ed(s): C. Bischof, A. Griewank & P. Khademi

Source: NC State University Libraries

Added: March 26, 2022

1993 journal article

Direct proof of a theorem by Kalkbrener, Sweedler, and Taylor

*ACM SIGSAM Bulletin*, *27*(4), 2.

Source: Crossref

Added: August 28, 2020

1993 chapter

Dynamic parallel evaluation of computation DAGs

In J. Reif (Ed.), *Synthesis of Parallel Algorithms* (pp. 723–758). San Mateo, California: Morgan Kaufmann Publishers.

Ed(s): J. Reif

Source: NC State University Libraries

Added: March 26, 2022

1993 conference paper

Process scheduling in DSC and the large sparse linear systems challenge

*Design and Implementation of Symbolic Computation Systems (DISCO 1993)*, 66–80.

Event: Design and Implementation of Symbolic Computation Systems International Symposium, DISCO '93 at Gmunden, Austria on September 15-17, 1993

Source: Crossref

Added: June 15, 2021

1992 report

Efficient solution of sparse linear systems

[Lecture Notes]. Troy, New York: Rensselaer Polytechnic Institute, Department of Computer Science.

Source: NC State University Libraries

Added: March 26, 2022

1992 conference paper

On computing determinants of matrices without divisions

*Papers from the international symposium on Symbolic and algebraic computation - ISSAC '92*. Presented at the Papers from the international symposium.

Event: Papers from the international symposium

Source: Crossref

Added: August 28, 2020

1992 chapter

Polynomial factorization 1987–1991

In *Lecture Notes in Computer Science*: *Vol.* *583*. *LATIN '92* (pp. 294–313).

Event: 1st Latin American Symposium on Theoretical Informatics at São Paulo, Brazil on April 6-10, 1992

Source: Crossref

Added: June 15, 2021

1992 conference paper

Processor-efficient parallel solution of linear systems. II. The positive characteristic and singular cases

*Proceedings., 33rd Annual Symposium on Foundations of Computer Science*. Presented at the Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

Event: Proceedings., 33rd Annual Symposium on Foundations of Computer Science

Source: Crossref

Added: August 28, 2020

1991 conference paper

DSC: a system for distributed symbolic computation

In S. M. Watt (Ed.), *Proceedings of the 1991 international symposium on Symbolic and algebraic computation - ISSAC '91* (pp. 323–332).

Ed(s): S. Watt

Event: ISSAC 91: International Symposium on Symbolic Algebraic Computation at Bonn, West Germany on July 15-17, 1991

Source: Crossref

Added: June 15, 2021

1991 conference paper

Effective Noether irreducibility forms and applications

*Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91*. Presented at the the twenty-third annual ACM symposium.

Event: the twenty-third annual ACM symposium

Source: Crossref

Added: August 28, 2020

1991 chapter

Explicit Construction of the Hilbert Class Fields of Imaginary Quadratic Fields by Integer Lattice Reduction

In D. V. Chudnovsky, G. V. Chudnovsky, H. Cohn, & M. B. Nathanson (Eds.), *Number Theory* (pp. 149–202).

Ed(s): D. Chudnovsky, G. Chudnovsky, H. Cohn & M. Nathanson

Source: Crossref

Added: June 15, 2021

1991 journal article

On fast multiplication of polynomials over arbitrary algebras

*Acta Informatica*, *28*(7), 693–701.

Source: Crossref

Added: August 28, 2020

1991 chapter

On wiedemann's method of solving sparse linear systems

In H. F. Mattson, T. Mora, & T. R. N. Rao (Eds.), *Applied Algebra, Algebraic Algorithms and Error-Correcting Codes* (pp. 29–38).

Ed(s): H. Mattson, T. Mora & T. Rao

Event: 9th International Symposium, AAECC-9 at New Orleans, LA on October 7-11, 1991

Source: Crossref

Added: June 15, 2021

1991 conference paper

Processor efficient parallel solution of linear systems over an abstract field

*Proceedings of the third annual ACM symposium on Parallel algorithms and architectures - SPAA '91*. Presented at the the third annual ACM symposium.

Event: the third annual ACM symposium

Source: Crossref

Added: August 28, 2020

1991 conference paper

Size efficient parallel algebraic circuits for partial derivatives

In D. V. Shirkov, V. A. Rostovtsev, & V. P. Gerdt (Eds.), *IV International Conference on Computer Algebra in Physical Research* (pp. 133–145). Singapore: World Scientific Publishing Co.

Ed(s): D. Shirkov, V. Rostovtsev & V. Gerdt

Source: NC State University Libraries

Added: March 26, 2022

1990 journal article

Algebraic Computational Complexity

*Journal of Symbolic Computation*, *9*(3).

Ed(s):

Source: NC State University Libraries

Added: March 26, 2022

1990 conference paper

Computer mathematics systems and a trilateral approach to human resource development in technical occupations

In N. Estes, J. Heene, & D. Leclercq (Eds.), *Proceedings of the 7th International Conference on Technology and Education* (Vol. 1, pp. 251–253). Edinburgh, United Kingdom: CEP Consultants Ltd.

Ed(s): N. Estes, J. Heene & D. Leclercq

Source: NC State University Libraries

Added: March 26, 2022

1990 journal article

Computing the irreducible real factors and components of an algebraic curve

*Applicable Algebra in Engineering, Communication and Computing*, *1*(2), 135–148.

Source: Crossref

Added: August 28, 2020

1990 journal article

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

*Journal of Symbolic Computation*, *9*(3), 301–320.

Source: Crossref

Added: January 24, 2021

1990 conference paper

Modular rational sparse multivariate polynomial interpolation

*Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '90*. Presented at the the international symposium.

Event: the international symposium

Source: Crossref

Added: August 28, 2020

1990 journal article

Parallel algorithms for matrix normal forms

*Linear Algebra and Its Applications*, *136*, 189–208.

Source: Crossref

Added: June 15, 2021

1990 chapter

Polynomial factorization 1982-1986

In D. V. Chudnovsky & R. D. Jenks (Eds.), *Computers in Mathematics, Lecture Notes in Pure and Applied Mathematics* (Vol. 125, pp. 285–309). New York, NY: Marcel Dekker, Inc.

Ed(s): D. Chudnovsky & R. Jenks

Source: NC State University Libraries

Added: March 26, 2022

1989 conference paper

An improved Las Vegas primality test

*Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89*. Presented at the the ACM-SIGSAM 1989 international symposium.

Event: the ACM-SIGSAM 1989 international symposium

Source: Crossref

Added: August 28, 2020

1989 book

Computers and Mathematics

Ed(s): ^{*} & S. Watt

Source: Crossref

Added: June 15, 2021

1989 journal article

Computing greatest common divisors and factorizations in quadratic number fields

*Mathematics of Computation*, *53*(188), 697–697.

Source: Crossref

Added: August 28, 2020

1989 conference paper

Computing the irreducible real factors and components of an algebraicf curve

In K. Mehlhorn (Ed.), *Proceedings of the fifth annual symposium on Computational geometry - SCG '89* (pp. 79–87).

Ed(s): K. Mehlhorn

Event: Fifth annual symposium on Computational geometry

Source: Crossref

Added: June 15, 2021

1989 chapter

Factorization of polynomials given by straight-line programs

In S. Micali (Ed.), *Randomness and Computation, Advances in Computing Research* (Vol. 5, pp. 375–412). Greenwhich, Connecticut: JAI Press Inc.

Ed(s): S. Micali

Source: NC State University Libraries

Added: March 26, 2022

1989 chapter

Improved sparse multivariate polynomial interpolation algorithms

In *Symbolic and Algebraic Computation* (pp. 467–474).

Event: International Symposium ISSAC '88 at Rome, Italy on July 4-8, 1988

Source: Crossref

Added: June 15, 2021

1989 chapter

Mr. Smith goes to Las Vegas: Randomized parallel computation of the Smith Normal form of polynomial matrices

In *Lecture Notes in Computer Science* (pp. 317–322).

Source: Crossref

Added: August 28, 2020

1989 conference paper

Parallel algebraic algorithm design

Kaltofen, E. (1989, July). Presented at the 1989 International Symposium on Symbolic and Algebraic Computation, Portland, Oregon.

Event: 1989 International Symposium on Symbolic and Algebraic Computation at Portland, Oregon

Source: NC State University Libraries

Added: March 26, 2022

1989 conference paper

Solving systems of nonlinear polynomial equations faster

*Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89*. Presented at the the ACM-SIGSAM 1989 international symposium.

Event: the ACM-SIGSAM 1989 international symposium

Source: Crossref

Added: January 24, 2021

1988 journal article

Analysis of the binary complexity of asymptotically fast algorithms for linear system solving

*ACM SIGSAM Bulletin*, *22*(2), 41–49.

Source: Crossref

Added: August 28, 2020

1988 conference paper

Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators

*[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science*. Presented at the [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

Event: [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science

UN Sustainable Development Goal Categories

4. Quality Education
(OpenAlex)

Source: Crossref

Added: August 28, 2020

1988 journal article

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

*ACM Transactions on Mathematical Software*, *14*(3), 218–240.

Source: Crossref

Added: August 28, 2020

1988 journal article

Efficient Parallel Evaluation of Straight-Line Code and Arithmetic Circuits

*SIAM Journal on Computing*, *17*(4), 687–695.

Source: Crossref

Added: August 28, 2020

1988 journal article

Greatest common divisors of polynomials given by straight-line programs

*Journal of the ACM*, *35*(1), 231–264.

Source: Crossref

Added: August 28, 2020

1987 journal article

Computer Algebra Algorithms

*Annual Review of Computer Science*, *2*(1), 91–118.

Source: Crossref

Added: August 28, 2020

1987 journal article

Deterministic irreducibility testing of polynomials over large finite fields

*Journal of Symbolic Computation*, *4*(1), 77–82.

Source: Crossref

Added: August 28, 2020

1987 journal article

Fast Parallel Computation of Hermite and Smith Forms of Polynomial Matrices

*SIAM Journal on Algebraic Discrete Methods*, *8*(4), 683–690.

Source: Crossref

Added: August 28, 2020

1987 report

Fast multiplication of polynomials over arbitrary rings

(Technical Report No. 87-35). Troy, NY: Rensselaer Polytechnic Institute, Department of Computer Science.

Source: NC State University Libraries

Added: March 26, 2022

1987 conference paper

Single-factor Hensel lifting and its application to the straight-line complexity of certain polynomials

*Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87*. Presented at the the nineteenth annual ACM conference.

Event: the nineteenth annual ACM conference

Source: Crossref

Added: August 28, 2020

1986 conference paper

A system for manipulating polynomials given by straight-line programs

*Proceedings of the fifth ACM symposium on Symbolic and algebraic computation - SYMSAC '86*. Presented at the the fifth ACM symposium.

Event: the fifth ACM symposium

Source: Crossref

Added: August 28, 2020

1986 chapter

Efficient parallel evaluation of straight-line code and arithmetic circuits

In *VLSI Algorithms and Architectures* (pp. 236–245).

Source: Crossref

Added: August 28, 2020

1986 conference paper

Fast parallel algorithms for similarity of matrices

*Proceedings of the fifth ACM symposium on Symbolic and algebraic computation - SYMSAC '86*. Presented at the the fifth ACM symposium.

Event: the fifth ACM symposium

Source: Crossref

Added: August 28, 2020

1986 conference paper

Uniform closure properties of P-computable functions

*Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86*. Presented at the the eighteenth annual ACM symposium.

Event: the eighteenth annual ACM symposium

Source: Crossref

Added: August 28, 2020

1985 conference paper

Computing with polynomials given by straight-line programs I: greatest common divisors

*Proceedings of the seventeenth annual ACM symposium on Theory of computing - STOC '85*. Presented at the the seventeenth annual ACM symposium.

Event: the seventeenth annual ACM symposium

Source: Crossref

Added: August 28, 2020

1985 conference paper

Computing with polynomials given by straight-line programs II sparse factorization

*26th Annual Symposium on Foundations of Computer Science (sfcs 1985)*. Presented at the 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

Event: 26th Annual Symposium on Foundations of Computer Science (sfcs 1985)

Source: Crossref

Added: August 28, 2020

1985 journal article

Effective Hilbert irreducibility

*Information and Control*, *66*(3), 123–137.

Source: Crossref

Added: August 28, 2020

1985 journal article

Factoring sparse multivariate polynomials

*Journal of Computer and System Sciences*, *31*(2), 265–287.

Source: Crossref

Added: August 28, 2020

1985 journal article

Factorization of multivariate polynomials over finite fields

*Mathematics of Computation*, *45*(171), 251–251.

Source: Crossref

Added: June 15, 2021

1985 journal article

Fast parallel absolute irreducibility testing

*Journal of Symbolic Computation*, *1*(1), 57–67.

Source: Crossref

Added: August 28, 2020

1985 journal article

Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization

*SIAM Journal on Computing*, *14*(2), 469–489.

Source: Crossref

Added: August 28, 2020

1985 chapter

Sparse hensel lifting

In *EUROCAL '85* (pp. 4–17).

Source: Crossref

Added: August 28, 2020

1985 report

The integer manipulation techniques can compete with the linear algebra methods for solving sparse linear systems

(Technical Report No. 85-6). State University of New York at Albany, Computer Science Department.

Source: NC State University Libraries

Added: March 26, 2022

1984 chapter

A note on the Risch differential equation

In J. Fitch (Ed.), *EUROSAM 84* (pp. 359–366).

Ed(s): J. Fitch

Source: Crossref

Added: June 15, 2021

1984 chapter

Effective Hilbert irreducibility

In *EUROSAM 84* (pp. 277–284).

Source: Crossref

Added: June 15, 2021

1984 chapter

On a theorem by R. Dedekind

In H. W. Lenstra Jr., J. K. Lenstra, & P. van Emde Boas (Eds.), *DOPO LE PAROLE, Album in Honor of A. K. Lenstra's Doctorate*. Amsterdam.

Ed(s): H. Lenstra, J. Lenstra & P. van Emde Boas

Source: NC State University Libraries

Added: March 26, 2022

1984 report

The algebraic theory of integration

[Lecture Notes]. Troy, New York: Rensselaer Polytechnic Institute, Department of Computer Science.

Source: NC State University Libraries

Added: March 26, 2022

1984 conference paper

The modular equation of order 11

*Third Macsyma Users' Conference*, 472–485. General Electric.

Source: NC State University Libraries

Added: March 26, 2022

1983 journal article

A Generalized Class of Polynomials that are Hard to Factor

*SIAM Journal on Computing*, *12*(3), 473–483.

Source: Crossref

Added: August 28, 2020

1983 chapter

On the complexity of finding short vectors in integer lattices

In *Lecture Notes in Computer Science* (pp. 236–244).

Source: Crossref

Added: August 28, 2020

1983 chapter

Polynomial-time factorization of multivariate polynomials over finite fields

In *Lecture Notes in Computer Science*: *Vol.* *154*. *Automata, Languages and Programming* (pp. 250–263).

Event: 10th Colloquium at Barcelona, Spain on July 18-22, 1983

Source: Crossref

Added: June 15, 2021

1982 conference paper

A polynomial reduction from multivariate to bivariate integral polynomial factorization.

*Proceedings of the fourteenth annual ACM symposium on Theory of computing - STOC '82*. Presented at the the fourteenth annual ACM symposium.

Event: the fourteenth annual ACM symposium

Source: Crossref

Added: August 28, 2020

1982 conference paper

A polynomial-time reduction from bivariate to univariate integral polynomial factorization

*23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)*. Presented at the 23rd Annual Symposium on Foundations of Computer Science.

Event: 23rd Annual Symposium on Foundations of Computer Science

Source: Crossref

Added: August 28, 2020

1982 chapter

Factorization of Polynomials

In B. Buchberger, G. E. Collins, & R. Loos (Eds.), *Computing Supplementum* (pp. 95–113).

Ed(s): B. Buchberger, G. Collins & R. Loos

Source: Crossref

Added: June 15, 2021

1982 thesis

On the complexity of factoring polynomials with integer coefficients

(PhD thesis). Rensselaer Polytechnic Institute, Troy, NY.

Source: NC State University Libraries

Added: March 26, 2022

1981 conference paper

A generalized class of polynomials that are hard to factor

*Proceedings of the fourth ACM symposium on Symbolic and algebraic computation - SYMSAC '81*. Presented at the the fourth ACM symposium.

Event: the fourth ACM symposium

Source: Crossref

Added: August 28, 2020

1981 report

An attributed LL(1) compilation of Pascal into the lambda-calculus

(Technical Report No. CS-8103). Troy, NY: Rensselaer Polytechnic Institute Mathematical Sciences Department.

Source: NC State University Libraries

Added: March 26, 2022

1980 report

LISP/370 under the Michigan Terminal System

Troy, NY: Rensselaer Polytechnic Institute, Mathematical Sciences Department.

Source: NC State University Libraries

Added: March 26, 2022

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