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The Descartes method for polynomial real root isolation can be performed with respect to monomial bases and with respect to Bernstein bases. The first variant uses Taylor shift by 1 as its main subalgorithm, the second uses de Casteljau's algorithm. When applied to integer polynomials, the two variants have co-dominant, almost tight computing time bounds. Implementations of either variant can obtain speed-ups over previous state-of-the-art implementations by more than an order of magnitude ifdoi:10.1145/1145768.1145797 dblp:conf/issac/JohnsonKLRR06 fatcat:cho3mdcirraibi5bstuotb6pzu