There are even simpler examples.  For instance, some systems multiply
polynomials by some evaluation/interpolation scheme in finite fields. Or by 
FFT
or by so-called Karatsuba   or Cooke-Toom methods or a Kronecker method
evaluating a polynomial to a single huge integer...

Risch integration is certainly another one.


On Wednesday, October 29, 2014 3:40:58 AM UTC-7, Christophe Bal wrote:
>
> Hello.
>
> I'm looking for formal outputs that are not calculated as a human can do 
> (this is for a free french "book"). Do you know such kind of examples ?
>
> Christophe BAL
>
> PS : this questions has been posted on both Sage and Sympy lists.
>

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