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We give new algorithms for the computation of square roots and reciprocals ofpower series in C[[x]]. If M(n) denotes the cost of multiplying polynomials ofdegree n, the square root to order n costs (1.333... + o(1)) M(n) and thereciprocal costs (1.444... + o(1)) M(n). These improve on the previous bestresults, respectively (1.8333... + o(1)) M(n) and (1.5 + o(1)) M(n).

Faster algorithms for the square root and reciprocal of power series