Concerning what minimal_approximant_basis returns: this is specified in the
documentation,
http://doc.sagemath.org/html/en/reference/matrices/sage/matrix/matrix_polynomial_dense.html#sage.matrix.matrix_polynomial_dense.Matrix_polynomial_dense.minimal_approximant_basis
but in formal (hence
A big thank you for your help, which was absolutely necessary. Synthesis:
1) Vincent Neiger's proposal works ; I have been able to obtain acceptable
duplications of Maxima's pade results in a small sample of test cases
(mostly by treating the "shifts" symmetrically).
However, the overall
Dear Dima,
I'm trying to offer a tool for "engineering" problems, similar to (and
along the lines of) our taylor() and series() functions for symbolic
expressions. Therefore, few assumptions can be made. Accordingly, we can
accept some failures (as we accept failures of taylor() or series() as
In the multivariate case a lot depends on input.
E.g., do you know something about zeros of your function?
E.g. do you have derivatives easily available?
If derivates are hard, you probably would like to avoid them all together,
using something known as Newton-Pade
approximation:
For the univariate case, to compare speed etc., you could also call FriCAS
and do something like
sage: fricas.pade(3,2, fricas.taylor(atan(x), x=0)).sage()
(4/9*x^3 + 5/3*x)/(x^2 + 5/3)
In fact, there is also Hermite-Padé in FriCAS, but I cannot remember the
details.
--
You received this
Le mardi 12 novembre 2019 20:42:16 UTC+1, rjf a écrit :
>
> Since Maxima is free and open source and gpl, why not just read the
> algorithm implemented there
> and rewrite it in Python?
>
That can be done. But I had other interest in mind:
- multivariate case (my solution of iterative
Since Maxima is free and open source and gpl, why not just read the
algorithm implemented there
and rewrite it in Python?
RJF
\
On Monday, November 11, 2019 at 1:29:56 AM UTC-8, Emmanuel Charpentier
wrote:
>
> Dear Vincent,
>
> a very quick answer (limbic system level. :-). Thank you for this
Dear Vincent,
a very quick answer (limbic system level. :-). Thank you for this hint. It
seems really interesting. But I'll need time to explore it and find my way.
Of course, I will have to work on PolynomialRing(SR) in order to be able to
work on one variable while ignoring the rest...
I'll
Dear Emmanuel,
You may be interested in taking a look at the following function:
Matrix_polynomial_dense.minimal_approximant_basis
This only supports the univariate case. This solves a problem which
generalizes Padé approximation (the documentation gives a precise
description of what it
