My point was that information on branch cuts should either A) be publicly available or B) preferably available as an export option. Mathematica and Maple both do A. Perhaps B is the better answer for open systems. In any event I stand by my point that this is only an issue because people have a tendency to ignore branch cuts; it is not actually a flaw inherent in aggregating many systems, and there are no technical reasons it couldn't be handled better.
On Wed, Apr 30, 2008 at 6:39 PM, root <[EMAIL PROTECTED]> wrote: > > >> - It suffers from the "OpenMath" communication issue (e.g. if you > >> take an Axiom expression, export it to maple, compute with it, > >> and re-import it to Axiom you have violated a lot of type > >> assumptions in Axiom, possibly violated branch cut assumptions > >> (e.g. acosh), done invalid simplifications, and any number of > >> violent mathematical mistakes) > > > >If merely by exporting the data and re-importing it you have violated > >assumptions, then Axiom is broken and needs a better exporting system. > > Well, that's something of the issue, actually. > > Suppose we're looking at an inverse function that uses branch cuts. > System A uses "cut 1", say $-\pi < x < \pi$ > System B uses "cut 2", say $0 < x < 2\pi$ > > Suppose you take a result from System A: > > x=A.getResult() > > simplify it with System B > > y=B.simplify() > > and hand it back to System A > > A.compute(y) > > Trigonometric simplification formulas depend on the branch cuts. > Thus, the simplification performed in B, while perfectly valid under > the branch cut assumptions in System B, may not be valid under the > branch cut assumptions in System A. > > You get a final answer (assuming a LONG chain of using a lot of > available systems in Sage). Is the answer correct? > > Do all of the subsystems in Sage that use transcendental functions > use the same choice of branch cuts in all their routines? Frankly, > I'm not sure how to begin to answer the question because (a) most > (all?) of the systems do NOT document their branch cut assumptions > and (b) I'd likely not be able to follow the logic of so many > systems through their simplifier. > > Is this important? Only if you want a correct answer. > > > > Tim > > > > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
