Am 07.07.2012 01:18, schrieb Aaron Meurer:
According to http://en.wikipedia.org/wiki/Elliptic_integral, every
elliptic integral can be reduced to an expression containing only the
three Legendre canonical forms.  So I wonder if that is algorithmic.

The article says you need to find the "appropriate reduction formula". Following that link game list of known structural patterns and a reduction formula for each.

So it seems heuristic, with a set of well-known heuristics.

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