[Numpy-discussion] Another suggestion for making numpy's functions generic

[Sebastian Walter]

On Tue, Oct 20, 2009 at 5:45 AM, Anne Archibald
<peridot.faceted at gmail.com> wrote:
> 2009/10/19 Sebastian Walter <sebastian.walter at gmail.com>:
>>
>> I'm all for generic (u)funcs since they might come handy for me since
>> I'm doing lots of operation on arrays of polynomials.
>
> Just as a side note, if you don't mind my asking, what sorts of
> operations do you do on arrays of polynomials? In a thread on
> scipy-dev we're discussing improving scipy's polynomial support, and
> we'd be happy to get some more feedback on what they need to be able
> to do.

I've been reading (and commenting) that thread ;)
 I'm doing algorithmic differentiation by computing on truncated
Taylor polynomials in the Powerbasis,
 i.e. always truncating all operation at degree D
z(t) = \sum_d=0^{D-1} z_d t^d =  x(t) * y(t) = \sum_{d=0}^{D-1}
\sum_{k=0}^d x_k * y_{d-k} + O(t^D)

Using other bases does not make sense in my case since the truncation
of all terms of higher degree than t^D
has afaik no good counterpart for bases like chebycheff.
On the other hand, I need to be generic in the coefficients, e.g.
z_d from above could be a tensor of any shape,  e.g.  a matrix.

Typical workcase when I need to perform operations on arrays of
polynomials is best explained in a talk I gave earlier this year:
http://github.com/b45ch1/pyadolc/raw/master/doc/walter_talk_algorithmic_differentiation_in_python_with_pyadolc_pycppad_algopy.pdf
on slide 7 and 8. (the class adouble "is" a Taylor polynomial).

>
> Thanks!
> Anne
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