Re: Function Typing

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Thu, Oct 11, 2018 at 12:19:10PM -0500, Brad Klee wrote:
> Hi Pari users,
> 
> Typing "?" lists: "8: TRANSCENDENTAL functions", and
> typing "?8" lists: "... hypergeom ... sqrt ..." ( on v2.12 ).
> 
> Of course f(x) = sqrt(x) satisfies x - f^2 = 0, so it is algebraic
> rather than transcendental. The type of "hypergeom" depends
> on parameter values. Ex. g(x) = hypergeom([1,1],[1],x), then
> (1-x)*g(x) - 1 = 0, also see "Schwarz's list" ( awesome! ).
> 
> We could change many of these TRANSCENDENTAL
> functions to HOLONOMIC or D-FINITE. This is not just an
> organizational question.

The list index is just the corresponding section of the manual. Most
users would not know what an holonomic or d-finite function is.
TRANSCENDENTAL is used a bit abusively for some functions,
but it is a decriptive name for such a section, and there is not enough
algebraic functions to justify a dedicated section.

> This is not much extra data, and actually more helpful than
> current implementation of "?". In the end "def" can even be
> computed at runtime. For "?besselk" or "?besselj", it would
> be more clear to have a "def" function, rather than having to
> compare with Mathworld or Wikipedia or the Source.

The short help is meant to be short, but we also provide a long help
('?? besselk') that is normally more descriptive.

Suggestions for improving the long help are quite welcome.

Cheers,
Bill.