Waldek, Thanks for looking at this.
On 8 September 2014 15:15, Waldek Hebisch <[email protected]> wrote: > Bill Page wrote: >> >> I would like to include: >> >> 2) my code for adding conjugate to special functions >> http://axiom-wiki.newsynthesis.org/SandBoxFunctionalSpecialFunction > > Definitions you gave are debatable. In particular > 'D(conjugate(x), x) = 0' may lead to troubles. For example, > 'D(conjugate(conjugate(x)), x)' should be equal to 'D(x, x) = 1' > regardless how we compute it. Consider: > > y := operator 'y > D(conjugate(y(x)), x) > > substituting 'conjugate(x)' for 'y(x)' and derivative of > 'conjugate(x)' for derivative of 'y(x)' should give derivative > of 'conjugate(conjugate(x))'. > The code that I wrote for conjugate assumes that operators always represent holomorphic functions, while conjugate itself is explicitly not holomorphic so a substitution such as you suggest does not make sense. The reason that I wanted D(conjugate(x), x) = 0 is to have D correspond to the first Wirtinger derivative that I mentioned in another email chain. It is not clear to me that this could result in nasty bugs. Maybe this is possible in the cases where the chain rule is applied since in that case the conjugate Wirtinger derivative would be required. > If what I wrote looks like nitpicking let me note that FriCAS > blindly applies rather complex transformations. For example > during integration internal form is quite different than > user input and final result. Inconsistency in derivative > rule will bring all kinds of nasty bugs. > > We probably can leave derivative of 'conjugate' unevaluated. Maybe only as a last resort. (This is what Maple does.) > But even that needs some thought to make sure there are > no inconsistency. Signaling error would be safe from > correctness point of view, but would significantly limit > usefulness -- code handling expressions assumes that it > can freely compute derivatives, so when dealing with > 'conjugate' we would routinely get errors deep inside > library code. > I would like to collect some examples of such errors. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
