Challenges of Symbolic Computation -- My Favorite Open Problems

Challenges of Symbolic Computation -- My Favorite Open Problems (1999)

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by Erich Kaltofen , Robert M. Corless , David J. Jeffrey

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@MISC{Kaltofen99challengesof,
    author = {Erich Kaltofen and Robert M. Corless and David J. Jeffrey},
    title = {Challenges of Symbolic Computation -- My Favorite Open Problems},
    year = {1999}
}

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553	Factoring Polynomials with Rational Coefficients - Lenstra, Lovàsz - 1982
323	Gr"obner Bases: An algorithmic method in polynomial ideal theory - Buchberger - 1985
299	Gröbner bases: A computational approach to commutative algebra GTM 141 - Becker, Weispfenning, et al. - 1993
216	Shift-register synthesis and BCH decoding - Massey - 1969
189	Ein Algorithmus zum Auffinden der Basiselemente des Restklassenrings nach einem nulldimensionalen Polynomideal” Universität - Buchberger - 1965
184	Ideals, Varieties and Algorithms - Cox, Little, et al. - 1992
177	On Lovász’ lattice reduction and the nearest lattice point problem - Babai - 1986
163	A Public-Key Cryptosystem with Worst-Case/Average-Case Equivalence - Ajtai, Dwork - 1997
152	Algebraic complexity theory - BÜRGISSER, CLAUSEN, et al. - 1997
138	Elliptic curves and primality proving - Atkin, Morain - 1993
131	Factoring polynomials over large finite fields - Berlekamp - 1970
121	Seminumerical Algorithms, volume 2 of The Art of Computer Programming - Knuth - 1997
116	Modern Computer Algebra - Gathen, Gerhard, et al. - 1999
112	Fast solution of Toeplitz systems of equations and computation of Padé approximations - Brent, Gustavson, et al. - 1980
110	A Method for Overlapping and Erasure of Lists - Collins - 1960
103	STL Tutorial and Reference Guide: C++ Programming with the Standard Template Library - Musser, Saini - 1996
100	Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation - Griewank - 1992
88	editors. axiom The Scientific Computation System - Jenks, Sutor - 1992
85	On the rapid computation of various polylogarithmic constants - Bailey, Borwein, et al. - 1997
67	Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems - Buchberger - 1970
61	Generalized characteristic polynomials - Canny - 1990
61	A new polynomial factorization algorithm and its implementation - Shoup - 1995
59	Analysis of PSLQ, an integer relation finding algorithm - Ferguson, Bailey, et al. - 1999
57	Computing with polynomials given by black boxes for their evaluations: Greatest common divisors, factorization, separation of numerators and denominators - Kaltofen, Trager - 1990
56	Subquadratic-time factoring of polynomials over finite fields - Kaltofen, Shoup - 1998
56	editors. Quantifier elimination and cylindrical algebraic decomposition - Caviness, Johnson - 2004
53	On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors - Brown - 1971
53	The problem of integration in finite terms - Risch - 1969
45	Approximate polynomial greatest common divisors and nearest singular polynomials - Karmarka, Lakshman
44	Improved sparse multivariate polynomial interpolation algorithms - Kaltofen, Lakshman
44	Résolution des systèmes d’équations algébriques, Theor - Lazard - 1981
43	Polynomial factorization 1987-1991 - Kaltofen - 1992
43	Solving systems of nonlinear polynomial equations faster - F, Kaltofen, et al. - 1989
42	Polynomial Time Algorithms for Finding Integer Relations among Real Numbers - Hastad, Helfrich, et al. - 1986
40	Fast construction of irreducible polynomials over finite fields - Shoup
40	Algebraic Factoring and Rational Function Integration - Trager - 1976
39	Checking robust nonsingularity is NP-hard - Poljak, Rohn - 1993
33	Symbolic Integration I: Transcendental Functions. Algorithms and Computation in Mathematics - Bronstein - 1996
33	An OpenMath 1.0 Implementation - Dalmas, Gaëtano, et al.
32	Numerical linear algebra - Kahan - 1966
32	Further analysis of Coppersmith’s block Wiedemann algorithm for the solution of sparse linear systems - Villard - 1997
31	Efficient algorithms for computing the nearest polynomial with a real root and related problems - Hitz, Kaltofen, et al. - 1999
28	Efficient computation of minimal polynomials in algebraic extensions of finite fields - Shoup - 1999
27	FoxBox: A System for Manipulating Symbolic Objects in Black Box Representation - Diaz, Kaltofen - 1998
27	The Theory of Matrices, Volume 2 - Gantmacher - 1959
27	Effective Noether irreducibility forms and applications - Kaltofen - 1995
27	Computing in Algebraic Extensions - Loos - 1982
26	On Randomized Lanczos Algorithms - Eberly, Kaltofen - 1997
26	A Library for doing Number Theory. version 5.5.2 - Shoup
26	A first report on the A # compiler - Watt, Broadbery, et al. - 1994