Exact real arithmetic formulating real numbers as functions
Research topics in functional programming
Analysis of PSLQ, an integer relation finding algorithm
Mathematics of Computation
Exact real arithmetic: a case study in higher order programming
LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
Applications of integer relation algorithms
Discrete Mathematics
Pseudofactors of multivariate polynomials
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Towards factoring bivariate approximate polynomials
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Integer Relations Among Algebraic Numbers
MFCS '89 Proceedings on Mathematical Foundations of Computer Science 1989
Factorization of Polynominals by Transcendental Evaluation
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
A geometric-numeric algorithm for absolute factorization of multivariate polynomials
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
From an approximate to an exact absolute polynomial factorization
Journal of Symbolic Computation
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We present a new algorithm for reconstructing an exact algebraic number from its approximate value by using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on obtaining an exact rational number from its approximation. The algorithm is applicable for finding exact minimal polynomial of an algebraic number by its approximate root. This also enables us to provide an efficient method of converting the rational approximation representation to the minimal polynomial representation, and devise a simple algorithm to factor multivariate polynomials with rational coefficients. Compared with the subsistent methods, our method combines advantage of high efficiency in numerical computation, and exact, stable results in symbolic computation. The experimental results show that the method is more efficient than identify in Maple for obtaining an exact algebraic number from its approximation. Moreover, the Digits of our algorithm is far less than the LLL-lattice basis reduction technique in theory. In this paper, we completely implement how to obtain exact results by numerical approximate computations.