We had a similar problem with the complex derivative of logarithms in combination with the complex conjugate, where I also the use of Wirtinger Operators would solve the problem: https://groups.google.com/forum/?hl=en#!topic/sage-support/bEMPMEYeZKU
Having them in Sage would be a great achievement! Although this has some sense in complex analysis one should be careful with 'deriving' the absolute value, since it results in the weak derivative ( http://en.wikipedia.org/wiki/Weak_derivative) , which is in a broader sense the derivative in the distribution sense. Thus we have infinite possible derivatives With this expression it is indirectly forbidden to asign a specific value to the unspecified value at zero: sage: f = abs(x).diff(x) sage: f(x=0) --------------------------------------------------------------------------- ValueError Traceback (most recent call last) <ipython-input-14-615bbebcb37c> in <module>() ----> 1 f(x=Integer(0)) /home/maldun/sage/sage-6.3/local/lib/python2.7/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.__call__ (build/cythonized/sage/symbolic/expression.cpp:21933)() /home/maldun/sage/sage-6.3/local/lib/python2.7/site-packages/sage/symbolic/ring.so in sage.symbolic.ring.SymbolicRing._call_element_ (build/cythonized/sage/symbolic/ring.cpp:8493)() /home/maldun/sage/sage-6.3/local/lib/python2.7/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.substitute (build/cythonized/sage/symbolic/expression.cpp:21183)() ValueError: power::eval(): division by zero This is in some sense good, since we don't have to care about the derivative at zero, but in an other sense it is not so good, since the subdifferential ∂abs(0) = [0,1] is a bounded and with this definition one could come to the false conclusion that abs(x) has a pole, althoug by taking limits one can easily see that it should be bounded at zero. For symbolic purposes, of course one could live on with this. -- 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.
