Puiseux expansions of algebraic functions
algeqtoseries(pol, x, y, order, pos_slopes)
polynomial equation in two variables x and y
name; variable name
positive integer order of the expansions
(optional) only branches tending to 0 are computed
The algeqtoseries(pol, x, y, order) command computes an expansion of all the branches at the origin. The equation pol⁡x,y=0 defines a multivalued function y(x).
If pos_slopes is specified, only those branches tending to 0 are computed. Note that this function is not designed to compute expansions to a large order. In this case, the differential equation should be used. For more information, see algeqtodiffeq.
P ≔ y−x2−x3⁢y2+x6⁢y5
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