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Solving zero-dimensional systems through the rational univariate representation. (English) Zbl 0932.12008
A Kronecker definition for a zero-dimensional system states that it is solved if each root is represented in sucha way that any arithmetical operation may be performed over the arithmetical expressions of its coordinates. The author introduces a new univariate representation and shows that each root of a zero-dimensional system may be expressed in a so-called Rational Univariate Representation. Moreover, the paper proposes efficient algorithms for computing such a representation, implements them and includes timings and comparisons with existing methods.

MSC:
12Y05 Computational aspects of field theory and polynomials (MSC2010)
65H10 Numerical computation of solutions to systems of equations
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Software:
ISOLATE
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