George E. Collins

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All published works

Action	Title	Year	Authors
+	On the maximum computing time of the bisection method for real root isolation	2016	George E. Collins
+	Continued fraction real root isolation using the Hong root bound	2014	George E. Collins
+	Krandick's proof of Lagrange's real root bound claim	2014	George E. Collins
+	Single-factor coefficient bounds	2004	George E. Collins
+	A Fast Euclidean Algorithm for Gaussian Integers	2002	George E. Collins
+	Polynomial Minimum Root Separation	2001	George E. Collins
+	Cylindrical Algebraic Decomposition II: An Adjacency Algorithm for the Plane	1998	Dennis S. Arnon George E. Collins Scott A. McCallum
+	Application of Quantifier Elimination to Solotareff’s Approximation Problem	1996	George E. Collins
+	A tangent-secant method for polynomial complex root calculation	1996	George E. Collins Werner Krandick
+	The probability of relative primality of Gaussian integers	1989	George E. Collins Jeremy Johnson
+	An adjacency algorithm for cylindrical algebraic decompositions of three-dimenslonal space	1988	Dennis S. Arnon George E. Collins Scott McCallum
+	The Euclidean Algorithm for Gaussian Integers (Abstract)	1985	George E. Collins
+	Real zeroes of polynomials	1983	George E. Collins Rüdiger Loos
+	Arithmetic in Basic Algebraic Domains	1983	George E. Collins Max Mignotte Franz Winkler
+ PDF Chat	Algorithms for the Solution of Systems of Linear Diophantine Equations	1982	Tsu-Wu J. Chou George E. Collins
+	Factorization in Cylindrical Algebraic Decomposition	1982	George E. Collins
+	Factorization in cylindrical algebraic decomposition — Abstract	1982	George E. Collins
+	Real Zeros of Polynomials	1982	George E. Collins Rüdiger Loos
+	Arithmetic in Basic Algebraic Domains	1982	George E. Collins Max Mignotte Franz Winkler
+	Factoring univariate integral polynomials in polynomial average time	1979	George E. Collins
+	Infallible Calculation of Polynomial Zeros to Specified Precision	1977	George E. Collins
+	Polynomial real root isolation using Descarte's rule of signs	1976	George E. Collins Alkiviadis G. Akritas
+ PDF Chat	The Minimum Root Separation of a Polynomial	1974	George E. Collins Ellis Horowitz
+ PDF Chat	The minimum root separation of a polynomial	1974	George E. Collins Ellis Horowitz
+	Computer Algebra of Polynomials and Rational Functions	1973	George E. Collins
+ PDF Chat	The Calculation of Multivariate Polynomial Resultants	1971	George E. Collins
+	The SAC-1 system	1971	George E. Collins
+	The calculation of multivariate polynomial resultants	1971	George E. Collins
+	Computing Multiplicative Inverses in GF(p)	1969	George E. Collins
+ PDF Chat	Subresultants and Reduced Polynomial Remainder Sequences	1967	George E. Collins
+	Polynomial Remainder Sequences and Determinants	1966	George E. Collins

Common Coauthors

Coauthor	Papers Together
Dennis S. Arnon	2
Franz Winkler	2
Max Mignotte	2
Rüdiger Loos	2
Ellis Horowitz	2
Tsu-Wu J. Chou	1
Scott McCallum	1
Alkiviadis G. Akritas	1
Scott A. McCallum	1
Werner Krandick	1
Jeremy Johnson	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Subresultants and Reduced Polynomial Remainder Sequences	1967	George E. Collins	6
+ PDF Chat	The Calculation of Multivariate Polynomial Resultants	1971	George E. Collins	5
+ PDF Chat	The minimum root separation of a polynomial	1974	George E. Collins Ellis Horowitz	4
+	Polynomial real root isolation using Descarte's rule of signs	1976	George E. Collins Alkiviadis G. Akritas	4
+	An Introduction to the Theory of Numbers. By G. H. Hardy and E. M. Wright. 2nd edition. Pp. xvi, 407 25s. 1945. (Oxford)	1946	T. A. A. B.	3
+ PDF Chat	Multiple precision arithmetic	1960	David Pope Marvin L. Stein	3
+	Algebraic algorithms for computing the complex zeros of gaussian polynomials.	1973	James R. Pinkert	3
+ PDF Chat	On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors	1971	Warren S. Brown	3
+ PDF Chat	An Exact Method for Finding the Roots of a Complex Polynomial	1976	James R. Pinkert	2
+	Approximate rational arithmetic systems: Analysis of recovery of simple fractions during expression evaluation	1979	David W. Matula Peter Kornerup	2
+	Schnelle Berechnung von Kettenbruchentwicklungen	1971	Arnold Schönhage	2
+	On the Computation of Powers of Sparse Polynomials	1974	Richard J. Fateman	2
+	Lectures in Abstract Algebra : vol. III, Theory of Fields and Galois Theory. By N. Jacobson. Pp. xi, 323. 76s. (Van Nostrand)	1966	Walter Ledermann	2
+	Euclid's Algorithm for Large Numbers	1938	D. H. Lehmer	2
+	Fixed-slash and floating-slash rational arithmetic	1975	David W. Matula	2
+ PDF Chat	An introduction to the theory of numbers	1960	G. H. Hardy	2
+ PDF Chat	Algorithms for partial fraction decomposition and rational function integration	1971	Ellis Horowitz	2
+	Euclid's Algorithm for Large Numbers	1938	D. H. Lehmer	2
+	A Decision Method for Elementary Algebra and Geometry	1951	Alfred Tarski J. C. C. McKinsey	2
+ PDF Chat	An Introduction To The Theory Of Numbers	2008	G. H. Hardy E. M. Wright	2
+ PDF Chat	On the Number of Multiplications for the Evaluation of a Polynomial and Some of Its Derivatives	1974	Mary Shaw J. F. Traub	2
+	Bounds for Absolute Positiveness of Multivariate Polynomials	1998	Hanpyo Hong	2
+	Introduction to P-Adic Numbers and their Functions	1973	Kurt Mahler Henry A. Hansen	2
+	The SAC-1 system	1971	George E. Collins	2
+	Numerical Solution of Initial Value Problems	1967	Thomas E. Hull F. Ceschino Jean Küntzmann D. Boyanovitch	2
+	Computer Algebra of Polynomials and Rational Functions	1973	George E. Collins	2
+ PDF Chat	A Sorting Algorithm for Polynomial Multiplication	1975	Ellis Horowitz	2
+ PDF Chat	On Runge-Kutta processes of high order	1964	J. C. Butcher	2
+ PDF Chat	Fast Multiple-Precision Evaluation of Elementary Functions	1976	Richard P. Brent	2
+	Quantifier Elimination and Cylindrical Algebraic Decomposition	1998	B. F. Caviness Jeremy Johnson	2
+	Some inequalities about univariate polynomials	1981	Maurice Mignotte	1
+ PDF Chat	Algorithm 288: solution of simultaneous linear Diophantine equations [F4]	1966	W. A. Blankinship	1
+	Randbemerkungen zu Hauptproblemen der Mathematik	1924	H Weyl	1
+ PDF Chat	Recherches sur la méthode de graeffe et les zéros des polynomes et des séries de laurent	1940	Alexandre Ostrowski	1
+	On the Coefficients of the Cyclotomic Polynomials	1968	D. M. Bloom	1
+	Computing Multiplicative Inverses in GF(p)	1969	George E. Collins	1
+	Über die obere Schranke des absoluten Betrages der Wurzeln einer algebraischen Gleichung	1916	Matsusaburô Fujiwara	1
+ PDF Chat	The efficient calculation of powers of polynomials	1972	Ellis Horowitz	1
+ PDF Chat	The exact solution of systems of linear equations with polynomial coefficients	1971	Michael T. McClellan	1
+	The calculation of multivariate polynomial resultants	1971	George E. Collins	1
+	Homology and cohomology theory	1978	William S. Massey	1
+ PDF Chat	Algebraic number theory	1999	Kazuya Katô Nobushige Kurokawa Takeshi Saito	1
+	Ueber den Zahlbegriff.	1887	L. Kronecker	1
+	A Note on the Linear Diophantine Equation	1941	Barkley Rosser	1
+	Moderne Algebra	1930	B. L. Waerden	1
+	The Theory of Fields and Galois Theory	2021	D. J. H. Garling	1
+	Traité de la Résolution des Équations Numériques de Tous les Degrés	1981	Joseph Louis Lagrange	1
+	Fundamental Problems of Algorithmic Algebra	1999	Chee Yap	1
+	Algebraic Number Fields	1995	Gerald J. Janusz	1
+	Solution of equations in Euclidean and Banach spaces	1973	Alexander Ostrowski	1