On Thu, Nov 20, 2014 at 9:59 AM, Bill Page <bill.p...@newsynthesis.org> wrote: > Perhaps this is more or less where Richardson's theorem enters. > > http://en.wikipedia.org/wiki/Richardson%27s_theorem > > We badly want a reliable way to determine when an expression is > identically zero. In general this is not possible, but if we restrict > our selves to a subset of "elementary" functions, in particular if we > can avoid 'abs', then it is in principle decidable (not withstanding > the possible undecidability of equality of constants). As I understand > it FriCAS effectively relies on this as part of the machinery for > integration, e.g. in 'rischNormalize'. Waldek's challenge to me on > the FriCAS list in regards to my proposals related to conjugate and > this thread was to show that it is possible to include 'conjugate' and > still have a decidable system given the complex equivalent of > Richardson's theorem. > > So far I have not been able to meet this challenge or even to find any > specific relevant related publications. Perhaps it is obvious that > this is not possible given the definition of abs in terms of conjugate > and sqrt. I would be interested in anyone here has considered this > issue or might suggest some leads. Of course this is likely not of > too much interest in computer algebra systems that take a more > pragmatic approach than FriCAS/Axiom.
Can you give an example of an expression that cannot be decided by the Richardson's theorem? How does FriCAS do the zero testing? I.e. if you give it f(x) = sin(x)^2 + cos(x)^2-1 how does it decide that it is equal to 0? Are we talking about functions of just one variable (f(x)) or more (f(x, y, z, ...))? Why cannot you just use the probabilistic testing, where you plug in various (complex) numbers into f(x) and test that it is equal to zero, numerically. Ondrej -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
