Nisoli Isaia wrote:
> 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.
This is very interesting!
> I'm trying to understand which parent class could be the best for
> these objects for them
> to be compatible with Sage coercion model.
I think the most natural thing to do would be to implement new parents
similar to the rings of power series, but which would additionally track
bounds on the truncation errors. Some refactoring in the implementations
of polynomials and power series may be necessary to make it possible to
share code when that makes sense.
Note that in the case of a single variable, Sage already has very
efficient code for arithmetic on real and complex interval Taylor series
based on Arb. The available operations include composition of arbitrary
series as well as a number of specialized routines for composing with
elementary and special functions ("intrinsics" in Taylor model
parlance). See the methods *_trunc and _*_series of polynomials over RBF
and CBF. Arb provides a lot more functions of this kind that are not yet
exposed by Sage.
--
Marc
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