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