ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 22 Mar 2015 08:10:44 -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.SeubSun, 22 Mar 2015 08:10:44 -0500http://ask.sagemath.org/question/26279/Why is diff(conjugate(x),x) unevaluated?http://ask.sagemath.org/question/24027/why-is-diffconjugatexx-unevaluated/Or, can we differentiate holomorphic functions only?
Wirtinger defined two derivations in complex analysis for which we have:
diff(x,conjugate(x)) = 0
and
diff(conjugate(x),x) = 0.
http://en.wikipedia.org/wiki/Wirtinger_derivatives
Wirtinger calculus has important applications in optimization and has been extended to quaternion functions.
Is there any situation in which leaving diff(conjugate(x),x) unevaluated is an advantage?Bill Page _ againTue, 02 Sep 2014 20:25:09 -0500http://ask.sagemath.org/question/24027/