You might be interested in this ..

https://people.eecs.berkeley.edu/~fateman/papers/ADIL.pdf

which is algorithm differentiation written in Lisp.
Sage includes Lisp (underneath Maxima, for example)

Manipulation of program source to produce other program source
is routinely supported in Lisp,  and there is a built-in compiler
to use when appropriate.  

I do not know about the particular difficulties one might face
in using Cython, which I have not used,  but in comparison to
some other code, the lisp included in that paper is about 10% of
the code size and considerably more extensive and extendable.

RJF


On Friday, April 19, 2019 at 5:48:09 AM UTC-7, Nisoli Isaia wrote:
>
> Dear all,
> I was planning in doing a Cython implementation of Forward automatic 
> differentiation and 
> Taylor arithmetics  as in
> https://press.princeton.edu/titles/9488.html
> to use to implement a library for Sage with rigorous quadrature and 
> integration of ODE.
>
> I'm trying to understand which parent class could be the best for these 
> objects for them 
> to be compatible with Sage coercion model.
>
> What is the usual procedure, I read through 
>
> http://doc.sagemath.org/html/en/reference/structure/sage/structure/element.html
> but I'm still confused.
>
> Best wishes
> Isaia
>

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