Algorithms for computer algebra
Algorithms for computer algebra
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Fraction-free algorithms for linear and polynomial equations
ACM SIGSAM Bulletin
Fraction-Free RNS Algorithms for Solving Linear Systems
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
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In this paper, we present the basic ideas of the residue polynomial system (RPS), a polynomial analog of the familiar residue number systems (RNS) of integer arithmetic. Many of the properties of the RNS are shared by the RPS. The main exception is that division of polynomials in the RPS is much more tractable than its integer counterpart. Examples are included throughout. The underlying field of coefficients for polynomials under consideration can be the reals or the rationals, though extension to the complex field will be needed for division by irreducible quadratic factors.