Complex analysis. Compute bar derivative

Can sage do complex analysis? I was unable to find documentation upon a quick web search.

For instance, I would like to define $f(z) = z \bar{z}$ and ask sage to compute $\displaystyle \frac{\partial f}{\partial \bar{z}}$, is that possible?

Of course I could treat $z$ and $\bar{z}$ as independent variables, but that is not what I'm asking.

edit retag close merge delete

Sort by ยป oldest newest most voted

See this discussion for some of the problems that currently arise when trying to do this with non-analytic functions.

more

I'm not going to read the discussion in detail, sorry. I'm not sure it's relevant. I don't see how there could be a problem with defining the z-derivative and zbar-derivative, who are simple combinations of the usual partial derivatives. So I'm simply understanding that these are not implemented in sage, oh well.

( 2015-03-25 01:01:23 +0200 )edit

I think the point is that one would first have to know that z is not a single variable, but really to be treated as a two-variable setup in the first place, as opposed to a single (possibly complex) variable. In which case one is basically doing independent variables anyway.

( 2015-03-25 02:08:33 +0200 )edit

http://en.wikipedia.org/wiki/Wirtinge...

I would agree that this is not implemented in Sage but I would disagree that it can be defined as a "simple combination of the usual derivatives". In particular it is necessary to consider the chain-rule. I have a prototype implementation in FriCAS (Axiom) that does this. In that context I am interested in collaboration and critical review.

http://axiom-wiki.newsynthesis.org/Sa...

From the point of view of complex analysis you might also want to look up references to polygenic functions, e.g. Kasner

http://www.ncbi.nlm.nih.gov/pmc/artic...

more