. We describe an efficient method for deriving such a D (2007)
Christopher W. Brown, George E. Collins, For F
Given a prenex formula F of elementary real algebra having k free variables, the CAD method of quantifier elimination produces a truth invariant CAD, D, for F, that is, a CAD of k-dimensional real...
George E. Collins, Werner Krandick
Let a rectangle be given which contains exactly one complex root of a given univariate polynomial. Let the edges of the rectangle be parallel to the coordinate axes. We present a hybrid...
Stefan Ratschan, Dennis S. Arnon, George E. Collins, Scott Mccallum Cylindrical
[4] Frédéric Benhamou and W. J. Older. Applying interval arithmetic to real, integer and Boolean constraints. Journal of Logic Programming,
Local box adjacency algorithms for cylindrical algebraic decompositions (2002)
McCallum, Scott, Collins, George E
We describe new algorithms for determining the adjacencies between zero-dimensional cells and those one-dimensional cells that are sections (not sectors) in cylindrical algebraic decompositions...
Local box adjacency algorithms for cylindrical algebraic decompositions (2002)
McCallum, Scott, Collins, George E
We describe new algorithms for determining the adjacencies between zero-dimensional cells and those one-dimensional cells that are sections (not sectors) in cylindrical algebraic decompositions...
Local box adjacency algorithms for cylindrical algebraic decompositions (2002)
McCallum, Scott, Collins, George E
We describe new algorithms for determining the adjacencies between zero-dimensional cells and those one-dimensional cells that are sections (not sectors) in cylindrical algebraic decompositions...
Local box adjacency algorithms for cylindrical algebraic decompositions (2002)
McCallum, Scott, Collins, George E
We describe new algorithms for determining the adjacencies between zero-dimensional cells and those one-dimensional cells that are sections (not sectors) in cylindrical algebraic decompositions...
The Minimum Root Separation of a Polynomial, (1998)
Collins,George E., Horowitz,Ellis
The minimum root separation of a complex polynomial A is defined as the minimum of the distances between distinct roots of A. For polynomials with Gaussian integer coefficients and no multiple roots,...
A rational number in SACLIB is represented by a numerator and a denominator, which are relatively prime. To make the representation unique, the denominator is required to be positive. The rational...
The SACLIB program IPRODA uses the classical method to multiply any two non-negative integers that are stored in arrays, producing the product in a third array supplied by the user. This is a simple...
Orge E. Collins, George E. Collins, Scott Mccallum
Let A be a set of trivariate irreducible integral polynomials and let D be an A-invariant cylindrical algebraic decomposition (cad) of threedimensional space. This paper presents a new algorithm for...
Application of Quantifier Elimination to Solotareff's Approximation Problem (1997)
Solotareff's approximation problem is that of obtaining the best uniform approximation on the interval [-1,+1] of a real polynomial of degree n by one of degree n \Gamma 2 or less. Without loss...
A tangent-secant method for polynomial complex root calculation (1996)
George E. Collins, Werner Krandick
Let a rectangle be given which contains exactly one complex root of a given univariate polynomial. Let the edges of the rectangle be parallel to the coordinate axes. We present a hybrid...
Improved Techniques for Factoring Univariate Polynomials (1995)
George E. Collins, Mark J. Encarnación
this paper. References
Efficient Rational Number Reconstruction (1994)
George E. Collins, Mark J. Encarnación
this paper we describe how a variant of the algorithm in Jebelean [6] can be so adapted. In Section 2 we review the problem of rational reconstruction and the solution proposed by Wang, while fixing...
A Hybrid Method for High Precision Calculation of Polynomial Real Roots (1993)
A straightforward implementation of Newton's method for polynomial real root calculation using exact arithmetic is inefficient. In each step the length of the iterate multiplies by the degree of...
An Efficient Algorithm for Infallible Polynomial Complex Root Isolation (1992)
George E. Collins, Werner Krandick
Applying the principle of the argument to rectangles provides an efficient algorithm for polynomial complex root isolation. For example, the roots of a real integral polynomial of degree 10 (with...
The use of a police records system for developing trends in drug abuse /--George E. Collins. (1970)
P.B. Weston, Chairperson.
Subresultants and reduced polynomial remainder sequences (1967)
ABSTRACT. Let 9 be an integral domain, (9(9) the integral domain of polynomials over 9. L~ P, Q E (P(9) with m = deg (P) _> n = deg (Q)> 0. Let M be the matrix whose determina~ defines the...