ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 24 Mar 2015 21:31:09 -0500Complex analysis. Compute bar derivativehttp://ask.sagemath.org/question/26279/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.Sun, 22 Mar 2015 08:10:44 -0500http://ask.sagemath.org/question/26279/complex-analysis-compute-bar-derivative/Answer by Bill Page _ again for <p>Can sage do complex analysis? I was unable to find documentation upon a quick web search.</p>
<p>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?</p>
<p>Of course I could treat $z$ and $\bar{z}$ as independent variables, but that is not what I'm asking.</p>
http://ask.sagemath.org/question/26279/complex-analysis-compute-bar-derivative/?answer=26323#post-id-26323 http://en.wikipedia.org/wiki/Wirtinger_derivatives
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/SandBoxWirtinger
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/articles/PMC1076732/Tue, 24 Mar 2015 21:31:09 -0500http://ask.sagemath.org/question/26279/complex-analysis-compute-bar-derivative/?answer=26323#post-id-26323Answer by kcrisman for <p>Can sage do complex analysis? I was unable to find documentation upon a quick web search.</p>
<p>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?</p>
<p>Of course I could treat $z$ and $\bar{z}$ as independent variables, but that is not what I'm asking.</p>
http://ask.sagemath.org/question/26279/complex-analysis-compute-bar-derivative/?answer=26284#post-id-26284See [this discussion](https://groups.google.com/forum/#!topic/sage-devel/6j-LcC6tpkE/overview) for some of the problems that currently arise when trying to do this with non-analytic functions.Mon, 23 Mar 2015 10:11:21 -0500http://ask.sagemath.org/question/26279/complex-analysis-compute-bar-derivative/?answer=26284#post-id-26284Comment by kcrisman for <p>See <a href="https://groups.google.com/forum/#!topic/sage-devel/6j-LcC6tpkE/overview">this discussion</a> for some of the problems that currently arise when trying to do this with non-analytic functions.</p>
http://ask.sagemath.org/question/26279/complex-analysis-compute-bar-derivative/?comment=26319#post-id-26319I 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.Tue, 24 Mar 2015 20:08:33 -0500http://ask.sagemath.org/question/26279/complex-analysis-compute-bar-derivative/?comment=26319#post-id-26319Comment by Seub for <p>See <a href="https://groups.google.com/forum/#!topic/sage-devel/6j-LcC6tpkE/overview">this discussion</a> for some of the problems that currently arise when trying to do this with non-analytic functions.</p>
http://ask.sagemath.org/question/26279/complex-analysis-compute-bar-derivative/?comment=26317#post-id-26317I'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.Tue, 24 Mar 2015 19:01:23 -0500http://ask.sagemath.org/question/26279/complex-analysis-compute-bar-derivative/?comment=26317#post-id-26317