implement symbolic Stieltjes constants

[rwst]

Probably just another symbolic function would suffice. This would be needed for zeta expansion and special values. The Sage side would be a new GinacFunction and numeric evaluation.

• https://en.wikipedia.org/wiki/Stieltjes_constants
• http://docs.sympy.org/dev/modules/mpmath/functions/zeta.html#stieltjes
• Section 4.2 of http://arxiv.org/abs/1309.2877

Depends on pynac/pynac#120
See also #18141.

Depends on #19948

CC: @behackl

Component: symbolics

Author: Ralf Stephan

Branch/Commit: 0e1162b

Reviewer: Benjamin Hackl

Issue created by migration from https://trac.sagemath.org/ticket/19834

[behackl]

comment:5

For the sake of representation: should there be two separate functions, say stieltjes(n) and generalized_stieltjes(n, a) represented as \gamma_n and \gamma_n(a), respectively?

Of course, like stieltjes(0) should return euler_gamma, generalized_stieltjes(n, 1) should return stieltjes(n) -- but I think this can be done easily, either still in pynac, or after registering the function in sage.

[behackl]

comment:6

... or just stieltjes(n, a=1) with adaptive representation. That's probably more elegant. ;-)

[rwst]

Branch: u/rws/implement_symbolic_stieltjes_constants

[rwst]

Author: Ralf Stephan

[rwst]

comment:8

This is what Sage needs to use the current pynac git master implementation of Stieltjes constants (not generalized).

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New commits:

bdac71f

19834: implement symbolic Stieltjes constants

[rwst]

Commit: bdac71f

[rwst]

Dependencies: pynac-0.6.1

[videlec]

comment:9

Why are you making cdef object py_stieltjes a cdef function? A cdef function that takes as input a Python object, returns a Python object would and only contains Python code would better be a def function.

[videlec]

comment:10

Ho I see. This is actually needed for the array of functions.

[rwst]

comment:11

Yes, everything symbolic is rooted through Pynac, so ex.n() calls Pynac's evalf functions which call (indirectly) Python functions which therefore must be cdef.

[rwst]

Changed dependencies from pynac-0.6.1 to #19448

[rwst]

Changed dependencies from #19448 to #19948

[behackl]

comment:14

I just resolved the merge conflict with 7.1.beta1.

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New commits:

0e1162b

Merge tag '7.1.beta1' into symbolics/stieltjes-constants

[behackl]

Changed commit from bdac71f to 0e1162b

[behackl]

Changed branch from u/rws/implement_symbolic_stieltjes_constants to u/behackl/symbolics/stieltjes-constants

[behackl]

Reviewer: Benjamin Hackl

[behackl]

comment:15

Implementation looks fine to me; doctests pass. I'd still like to see if the patchbot is satisfied, too. I'll set this to positive_review later---or you can do so directly, if you do not want to wait. ;-)

[rwst]

comment:17

Thanks!

[vbraun]

Changed branch from u/behackl/symbolics/stieltjes-constants to 0e1162b