Re: branch of (-1)^(1/3)
- To: mathgroup at smc.vnet.net
- Subject: [mg94502] Re: branch of (-1)^(1/3)
- From: "slawek" <human at site.pl>
- Date: Mon, 15 Dec 2008 07:43:47 -0500 (EST)
- References: <ghtjcj$r7f$1@smc.vnet.net> <gi2ufl$9pk$1@smc.vnet.net>
U¿ytkownik "Jean-Marc Gulliet" <jeanmarc.gulliet at gmail.com> napisa³ w wiadomo¶ci news:gi2ufl$9pk$1 at smc.vnet.net... > slawek wrote: > >> Is a simple way to choose the branch of (-1)^(1/3) ? > The tutorial "Functions That Do Not Have Unique Values" -- section 3.2.7 > of /The Mathematica Book/ 5th ed. -- might be worth reading. Jean, I REALLY known what is an analytic function. The question is not: "why, for the Good sake, the answer of (1)^4 is "-I" sometimes?" My question is quite simple one: "why the (-1)^(1/3) gives no way to pick up branch, what is sometimes needed for somebody. For example, because I exactly know which branch I need when I use complex numbers - but I have no control on Mathematica madness to pick up an arbitraty solution because somebody has got a misty vision which a branch is more basic and more primary than others." For example I have a simple real function z = Exp[-y^2 (3x + y)] of real x,y , obviously there are points where the function has zero derivative in a direction, but the Mathematica is unable to find them, because their coordinates are real (as anybody literate can easily see), whereas Mathematica prefer a complex solution and therefore Save gives a wrong - "unique" - solution. The Reduce work no better. Reduce generates an message "unable to solve". Ok, it was quite simple to request third power of solution before use Solve - and - supprise, supprise - the solution is real. And some tricks - and we have the real solutions (in requested domain). But I hate tricks - it is so simple to FORCE Mathematica to give quite other results - that the whole software is far less realiable than I needed. So your answer is the answer on the wrong question. First read my question again (and again) - then when you will be able to hadle the question your answer would be on the topic. Ad rem. slawek