add numerical integration to reference manual

[Karl-Dieter Crisman]

Somewhat surprisingly, this function (numerical_integral) is not in the reference manual! Let's clean up its documentation and put it there.

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Note: this ticket would be superseded by #8321 or #7763 addressing this, though it's not clear that either of them do at this time.

[Paul Zimmermann]

what do you mean by "not in the reference manual"? It is documented:

sage: numerical_integral?
String Form:    <built-in function numerical_integral>
Namespace:      Interactive
Definition:     numerical_integral(func, a, b=None, algorithm='qag', max_points=87, params=[], eps_abs=9.9999999999999995e-07, eps_rel=9.9999999999999995e-07, rule=6)
Docstring:
    
       Returns the numerical integral of the function on the interval from
       a to b and an error bound.
...

Paul

[Karl-Dieter Crisman]

Replying to zimmerma:

what do you mean by "not in the reference manual"?

I mean it is not in the HTML/PDF document generated by Sphinx, because we haven't added it to that. See ​http://www.sagemath.org/doc/reference/genindex-N.html and search for this command.

[Paul Zimmermann]

isn't the HTML/PDF document automatically generated from the on-line documentation?

Paul

[Karl-Dieter Crisman]

The documentation from the command line is NOT the same as the HTML/PDF documentation. You may have noticed, after a Sage build completes, that it spends some time generating doc; but only modules which are up to snuff in terms of formatting and which someone bothered to add to it gets added. That is a lot of them! But not all. And they do need to be formatted pretty well for that to happen.

Anyway, this is probably a fairly trivial patch to make, looking at examples of how other modules are included, so I'm putting 'beginner' on it. An ideal patch for this would also put in some hyperlink cross-references in the calculus documentation, e.g. at ​http://www.sagemath.org/doc/reference/sage/calculus/functional.html.

[Jeroen Demeyer]

See #12047 where I do this (I had to edit that file anyway and decided to clean up the documentation while I was at it).