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Re: [Axiom-developer] 20080505.02.tpd.patch (CATS Schams-Axiom branch cu

From: Raymond E. Rogers
Subject: Re: [Axiom-developer] 20080505.02.tpd.patch (CATS Schams-Axiom branch cut analysis)
Date: Tue, 06 May 2008 07:42:04 -0400
User-agent: Thunderbird (X11/20080226)

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.


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 ......


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