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Re: [Axiomdeveloper] Bug 215: sin asin(7.0::COMPLEX FLOAT)
From: 
Gabriel Dos Reis 
Subject: 
Re: [Axiomdeveloper] Bug 215: sin asin(7.0::COMPLEX FLOAT) 
Date: 
Wed, 17 Jan 2007 10:51:16 0600 (CST) 
On Wed, 17 Jan 2007, Waldek Hebisch wrote:
 Gabriel Dos Reis wrote:
 > Waldek Hebisch <address@hidden> writes:
 >  However, the problem with asin is just one special case. We
 >  would like to support many multivalued special functions (which in
 >  numerical version require branch cuts). Tracking that we get
 >  "correct" values on cuts may well take significant portion of
 >  effert to implements those functions. OTOH computing with
 >  values on branch cuts does not seem very useful. So I am tempted
 >  to declare that arguments branch cuts are errors (like divison
 >  by 0).
 >
 > I'm concerned with that approach.
 >
 > After all, this is a mathematical computational platform. If we go
 > that way, how else can we expect other people to take branch cuts
 > seriously?
 >

 1)
 What can be more serious than signaling error?

 2)
 I am mathematician and I do not "take branch cuts seriously".
I'm a computational mathematician  even though I ended up corrupted by
computer scientists  and I do take branch cuts seriously.
[ In my PhD thesis work on Constant Mean Curvature surfaces, where
I did lot of numerical simulation and "construction", Riemann
surfaces were my benchwork. ]
 Serious math works with arbitrary branches, multivalued functions
 or Riemennian surfaces.
Which is why just signaling an error is not an option, from my perspective.
We must do better. See links below.
 Branch cuts are an artifical convention
 which pretends that multivalued functions can be used naively in
 numerical computations. In some sense it is an ideal field for
 standarisation: many choices are arbitrary, but for effective
 shortcut communication everybody should use the same choices.
 However, standarizing branch cuts produces a formal structure
 which has little to do with original functions. Once such structure
 is available there is good chance that somebody will abuse it to
 archive some good effect. But in most cases it would be better to
 use another mechanizm. More specifically, serious complex numerical
 computation can not depend on values on branch cuts
But, they do. And that is a matter of life Axiom has to take into
account if it ever has to be serious about "computational platform"
Somewhere we should record relevant literature on Axiom website.
http://www.cs.berkeley.edu/~fateman/papers/ding.ps
http://delivery.acm.org/10.1145/240000/235703/p21patton.pdf?key1=235703&key2=4812509611&coll=GUIDE&dl=GUIDE&CFID=11704206&CFTOKEN=10201516
http://delivery.acm.org/10.1145/240000/235704/p25rich.pdf?key1=235704&key2=9722509611&coll=GUIDE&dl=GUIDE&CFID=9284552&CFTOKEN=77401299
 Gaby