arctanh vs. artanh

[a.simpl...@gmail.com]

Hi all,

Sage has built-in inverses of hyperbolic functions

arcsinh,

arccosh,

arctanh,

arccoth,

arcsech,

arccsch.

But according to wikipedia,

the initial should be ar- that stands for area.

Perhaps for educational purpose we should use the correct name?

Best,

Hsin-Po

[Samuel Lelievre]

Note that Sage also provides aliases with `a-`

(the display is still with `arc-`):

```

sage: asinh, acosh, atanh, acoth, asech, acsch
(arcsinh, arccosh, arctanh, arccoth, arcsech, arccsch)

```

[kcrisman]

In terms of the missions statement, apparently we aren't the only ones, so consistency might be more important in any case: https://reference.wolfram.com/language/ref/ArcTanh.html

Note e.g. sympy uses atanh as the "ordinary": https://docs.sympy.org/latest/modules/functions/elementary.html#atanh

[Martin R]

I'd be in favor of the change (keeping arc- as an alias, of course).  It is not a good experience to explain in the course how the function is defined, and then see sage print it wrong.

[Nathan Dunfield]

Mathematica, Maple, and numpy all use "arctanh"; MATLAB uses "atanh".  It's "arctanh" in the NIST Digital Library of Mathematical Functions as well:

https://dlmf.nist.gov/4.37

It is the case that "ar-" prefix is the current ISO standard, and per the Wikipedia talk page the "ar-" prefix is more common in the non-English literature, but I'm not aware of any computer algebra system that uses it.  So I would not support changing away from "arc-" as the default.

Best wishes,

Nathan

[Dima Pasechnik]

On Wed, 23 Mar 2022, 13:57 Nathan Dunfield, <nat...@dunfield.info> wrote:

Mathematica, Maple, and numpy all use "arctanh"; MATLAB uses "atanh". 

atanh, etc., i.e. just "a-"-prefix is well in line with the tradition of Fortran libraries,

as well as C libm's.

It's "arctanh" in the NIST Digital Library of Mathematical Functions as well:

https://dlmf.nist.gov/4.37

It is the case that "ar-" prefix is the current ISO standard, and per the Wikipedia talk page the "ar-" prefix is more common in the non-English literature, but I'm not aware of any computer algebra system that uses it.  So I would not support changing away from "arc-" as the default.

Best wishes,

Nathan

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[Martin R]

fricas also uses atanh (and yes, I agree that the a- prefix would be better than arc- and ar-)

[Adarsh Kishore]

I would suggest keeping all three 'a-', 'ar-', 'arc-' as aliases for the same function (we could keep the 'a-' as the default as it is the shortest to type). This is because I have seen all three versions being used across Computer Science and Mathematics, and restricting anyone of them would be equally unfair.