# Classifier Instance:

Anchor text: SymPy
Target Entity: SymPy
Preceding Context: The algorithm for isolating the roots, using Descartes' rule of signs and Vincent's theorem, had been originally called modified Uspensky's algorithm by its inventors Collins and Akritas. After going through names like "Collins-Akritas method" and "Descartes' method" (too confusing if ones considers Fourier's article), it was finally François Boulier, of Lille University, who gave it the name Vincent-Collins-Akritas (VCA) method, p. 24, based on the fact that "Uspensky's method" does not exist and neither does "Descartes' method". This algorithm has been improved by Rouillier and Zimmerman, and the resulting implementation is, to the date, the fastest bisection method. It has the same worst case complexity as Sturm algorithm, but is almost always much faster. It is the default algorithm of Maple root-finding function fsolve. Another method based on Vincent's theorem is the Vincent-Akritas-Strzeboński (VAS) method; it has been shown that the VAS (continued fractions) method is faster than the fastest implementation of the VCA (bisection) method, a fact that was independently confirmed elsewhere; more precisely, for the Mignotte polynomials of high degree VAS is about 50,000 times faster than the fastest implementation of VCA. VAS is the default algorithm for root isolation in Mathematica, Sage,
Succeeding Context: , Xcas. See Budan's theorem for a description of the historical background of these methods. For a comparison between Sturm's method and VAS use the functions realroot(poly) and time(realroot(poly)) of Xcas. By default, to isolate the real roots of poly realroot uses the VAS method; to use Sturm's method write realroot(sturm, poly). See also the External links for a pointer to an iPhone/iPod/iPad application that does the same thing.
Paragraph Title: null
Source Page: Root-finding algorithm

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