SymPy conversions for symbolic functions that are missing them

[eviatarbach]

Some symbolic functions are missing SymPy? conversions.

[eviatarbach]

The patch adds conversions for all the symbolic functions in Sage that I could find that have a SymPy? equivalent.

Patchbot apply trac15057.patch​

[asmeurer]

You must be using an old version of SymPy?. KroneckerDelta? is just KroneckerDelta?. The rest look fine.

[eviatarbach]

Ah, alright. I was using 0.7.1, which is the version currently in Sage. This should be merged after #14694 then. I also added doctests in case the names change again in the future.

[asmeurer]

A bunch of new special functions have been added since then too, so this is probably not complete.

[eviatarbach]

I think I checked fairly thoroughly (I believe that I automatically ran through all the functions in sage/functions and tried to call their _sympy_ method, and if it failed I checked if there was a SymPy? equivalent), and with the current SymPy? documentation. I may have missed a few though.

[asmeurer]

Can you provide the list of functions without equivalents?

[eviatarbach]

Actually, I didn't include the conversions for the exponential integrals and lambert_w. Patch for that coming up.

Here are the functions in Sage that are not in SymPy? as far as I can tell. I haven't checked the ones in sage/rings/arith.py yet, and of course there are tons of combinatorial functions.

• Dickman's function (dickman_rho in Sage)
• Heaviside step function and unit step function (heaviside and unit_step in Sage; they only seem to differ in that heaviside is undefined at 0)
• Inverse Jacobi functions (inverse_jacobi in Sage)
• Jacobi amplitude function (to be added in #14996 as jacobi_am)
• Spherical Bessel and spherical Hankel functions (spherical_bessel_J, spherical_bessel_Y, spherical_hankel1, and spherical_hankel2 in Sage)
• Symmetric zeta function (zeta_symmetric in Sage)
• Derivatives of the zeta function (zetaderiv in Sage)

Note that some SymPy? conversions are going to be added in pending tickets that transition functions to use Sage's BuiltinFunction instead of being simple Maxima wrappers. For example, #15046 and #14996.

[asmeurer]

SymPy? has Heaviside, which gives 1/2 at 0. It also has (I believe all) the bessel functions (I don't remember, but some of them may be new in the most recent version).

I opened ​https://code.google.com/p/sympy/issues/detail?id=3992 to implement the rest :)

[eviatarbach]

Right, the spherical Bessel functions are implemented, but not the spherical Hankel functions. They're not in mpmath, but numeric evaluation is quite trivial to implement; see the function spherical_bessel_f at ​http://trac.sagemath.org/attachment/ticket/15024/trac15024.patch.

[eviatarbach]

This patch adds conversions for exponential integrals as well. I didn't add a Lambert W conversion since it has a different number of arguments in SymPy? (Sage allows you to choose the branch), and there doesn't seem to be a good way of doing more complicated conversions yet. It should be easy to add functionality for doing so, however.

[eviatarbach]

Apparently SymPy? doesn't have Jacobi elliptic functions at all. That's another one to add to the list.

[rws]

See also #14723

[rws]

It's all straightforward addition of conversions. Long doctests pass in functions.

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New commits:

​2c7174f	15057: Adding SymPy conversions, with reviewer's additions
​341de9a	15057: fix typo

[vbraun]

My release management script doesn't understand dependencies that predate the git transition ;-)