deprecate taylor() in favor of series()

[robertwb]

Symbolic expressions have two methods to obtain series expansions. The taylor() method is a wrapper around maxima's taylor command. The result of this is not always a Taylor series, which leads to confusions.

The series() method was introduced in the pynac-based symbolics. ATM, it is a thin wrapper around GiNaC series expansions. This also plays well with the symbolic functions, etc. introduced based on Pynac/GiNaC.

We should deprecate the taylor() method and add an algorith= argument to series(). The default behavior can be to call GiNaC and fall back to maxima if that fails.

Dependencies: pynac-0.7.4

CC: @kcrisman @rwst

Component: calculus

Author: Ralf Stephan

Branch/Commit: u/rws/deprecate_taylor___in_favor_of_series__ @ 46c8e43

Issue created by migration from https://trac.sagemath.org/ticket/6119

[burcin]

comment:2

From #9555 comment:6:

The taylor() method is cruft left over from pre-pynac symbolics. We should deprecate it in favor of the series() method. It's perfectly acceptable to give Puiseux series as a result of a call to .series(). I expect this to be done in #6119, where we add an algorithm= option to .series(). The default behavior can be to call pynac and fall back to maxima if that returns an error.

In short, we should change this ticket to cover this transition. Series expansions in Pynac need more work to match what maxima does. That should be tracked on the pynac issue tracker:

https://bitbucket.org/burcin/pynac/issues

[burcin]

Description changed:

--- 
+++ 
@@ -1 +1,5 @@
-Ginac has series about zero, it should be easy to shift to get the series about any point.
+Symbolic expressions have two methods to obtain series expansions. The `taylor()` method is a wrapper around maxima's `taylor` command. The result of this is not always a Taylor series, which leads to confusions.
+
+The `series()` method was introduced in the pynac-based symbolics. ATM, it is a thin wrapper around GiNaC series expansions. This also plays well with the symbolic functions, etc. introduced based on Pynac/GiNaC.
+
+We should deprecate the `taylor()` method and add an `algorith=` argument to `series()`. The default behavior can be to call GiNaC and fall back to maxima if that fails.

[kcrisman]

comment:3

As I say in #9555, I think that changing the .taylor() method so that it calls a suitably Taylor-only version of the .series() method is preferable, especially since the global name taylor() should really be kept.