Re: [Axiom-developer] 20080505.02.tpd.patch (CATS Schams-Axiom branch cut analysis)

[Raymond E. Rogers]

address@hidden wrote:
> Here we try to understand why we cannot find a simplification
> that makes these two expressions equal. If the expressions were
> equal then we could use them as functions, substitute floating
> point values and expect the same numeric results. So we try that here.
>
> The result is that for some of the inverse trigonometric functions,
> the branch cut chosen by Schaums and the branch cut chosen by Axiom
> differ outside the range of the chosen branch cut. Thus they are not
> the same function and cannot be simplified to a constant difference.
> Within the range of the cut, Schaums and Axiom agree.
>
> This is not a bug, but a choice that needs to be made, since the
> inverse functions are multi-valued.
>
> Tim
>
>   
Yes and no, if Axiom is really to support the future (versus present 
expediency) then the "problem" should be addressed explicitly.  
Providing an array covering the branch cuts together with descriptions 
of the branches?  Asking about the deciding choices (which I find 
annoying but possible)?   Requiring the choices to be made before 
invoking?   But certainly not a hidden irrevocable choice made for the user.
In addition these things need to explicitly documented; something that I 
am sure the Axiom community will do. 
In general I guess the invoking of an multivalued function could 
specialize acos->acos_1,acos_2, etc... to only refer to one inverse 
image region.  For instance acos could, upon some relevant evaluation, 
return
[[domain, [range]],[domain,[range]] as true results and then the user 
could pick and choose the element wanted.  Only a passing thought; 
cumbersome but ......


RayR