>> - 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 -~----------~----~----~----~------~----~------~--~---
