[Top][All Lists]
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: [Axiom-developer] Bug 215: sin asin(7.0::COMPLEX FLOAT)
From: |
Gabriel Dos Reis |
Subject: |
Re: [Axiom-developer] 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/p21-patton.pdf?key1=235703&key2=4812509611&coll=GUIDE&dl=GUIDE&CFID=11704206&CFTOKEN=10201516
http://delivery.acm.org/10.1145/240000/235704/p25-rich.pdf?key1=235704&key2=9722509611&coll=GUIDE&dl=GUIDE&CFID=9284552&CFTOKEN=77401299
-- Gaby