On Wed, 17 Jan 2007, Waldek Hebisch wrote: | Gabriel Dos Reis wrote: | > Waldek Hebisch <[EMAIL PROTECTED]> 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 _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer
