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Re: [Axiom-developer] 20080505.02.tpd.patch (CATS Schams-Axiom branch cu
Raymond E. Rogers
Re: [Axiom-developer] 20080505.02.tpd.patch (CATS Schams-Axiom branch cut analysis)
Tue, 06 May 2008 07:42:04 -0400
Thunderbird 188.8.131.52 (X11/20080226)
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,
[[domain, [range]],[domain,[range]] as true results and then the user
could pick and choose the element wanted. Only a passing thought;
cumbersome but ......
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.