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Jan
18
comment Using Solve to solve the equation $x^{1/3}=-1$
I don't think there is a solution. I believe that the image of the complex plane under $z\to z^{1/3}$ is $\{r e^{i\theta}: r\geq 0, -\pi/3 < \theta \leq \pi/3\}$, given the location of the branch cut.
Dec
24
comment Revolution of Koch Snowflake
@ubpdqn Thanks - and same to you!
Dec
11
comment Numerically evaluating an integral related to Cantor's staircase
@J.M. Glad you like it!
Dec
7
comment Basins of attraction of equilibrium points
For the system $x'=V_x,y'=V_y$, an equilibrium will be attractive iff it's a local minimum of the potential function. Before proceeding further, though, you should make sure that's the system you're interested in. Perhaps, you're really interested in a second order system, which is likely in celestial mechanics. That's a more complicated question, as you've got to deal with initial conditions on $x'$ and $y'$ as well.
Dec
7
comment Basins of attraction of equilibrium points
As you have shown, the algebraic system $V_x=0,V_y=0$ has four numeric solutions and, if we apply Newton's method to that system, each of those solutions has an interesting basin of attraction. But that is a different question from whether those equilibrium points are attractive under a system of differential equations like $x'=V_x,y'=V_y$.
Dec
7
comment Basins of attraction using Newton's method Part II
I agree with Quantum_Oli - it would be nice to know where this came from. It appears there might be an interesting question here but the image looks like the Julia set of a polynomial - I can't imagine how your non-differentiable function generated it.
Dec
7
comment Basins of attraction of equilibrium points
I'm quite sure that the basins of attraction of Newton's method in two real variables have been well studied; there's an elementary discussion on pages 486-487 of Gil Strang's calculus text. If you're interested in studying the basins of attraction of the smooth dynamical system with a given potential, however, that's quite a different thing. Only one of your equilibrium points is attractive for that system.
Dec
5
comment Basins of attraction using Newton's method
The first thing my answer to that question does is generalize the code to arbitrary functions. I guess that's what @Saurav is referring to.
Nov
11
comment Can Mathematica Handle Open Intervals? Interval complements?
@alancalvitti True - but, again, I don't think it's hard to roll your own depending on your needs.
Nov
11
comment Can Mathematica Handle Open Intervals? Interval complements?
@alancalvitti There is no such function that I know of, though it should be quite easy to create one using patterns. Something like toInequality[Interval[{a_,b_}], var_] := a<var<b. Then, for example, toInequality[Interval[{1, 2}], x] returns 1<x<2. Of course, you'd still need to decide whether you want open or closed intervals or some combination depending on the situation.
Oct
23
comment How to find all graph isomorphisms in FindGraphIsomorphism
Thanks for the info! I've not been using Mathematica of late but, if I find myself needing to study graph theory within Mathematica at some point, I'm sure I'll have a look.
Jul
1
comment Plotting iterated function system images
@AJY I've added the code defining the depth level version of ShowIFS to the response. It works fine in V9 on my mac. The package contains some other features as well. I don't know why you're having problems with it on your machine. I assume you unzipped the file, opened up the Installation.nb file and executed the commands in order - including the PrependTo command?
Jul
1
comment Plotting iterated function system images
@AJY Were you able to get my packages to work? I'd certainly be happy to help.
Jun
22
comment Plotting iterated function system images
Did you execute the PrependTo command in the Quick start section before the Needs command? If so, what OS and version of Mathematica are you running?
Jun
17
comment Mathematica vs Python - how does it compare to Python's scientific computing suite?
@halirutan While your question is a good one to ask, note that the original question as asked in the next to last paragraph specifies "other than in computer algebra". Probably, the OP is aware of sympy which is, frankly, vastly inferior to Mathematica. Sympy fails on your suggested integral, for example.
Jun
3
comment Möbius transformations revealed
Nice - and, it deals with the colors much better than I anticipated!
Feb
26
comment Ghost trails with Animate?
@Kuba Neat! I never noticed a function that actually declares itself as undocumented in its name before. I'm curious - how did you avoid the problem that I had with the misbehaving invisible characters after copy/paste? It looks like you used 4 space indentation; maybe that's it? My code was inline.
Feb
26
comment Ghost trails with Animate?
Sadly, the Import code I just wrote doesn't seem to survive a copy from the comment box. Hopefully, you get the idea.
Feb
26
comment Ghost trails with Animate?
@Kuba But then, you wouldn't have the joy of writing code to extract the code. :) code=StringJoin[Cases[First[Cases[Import["http://mathematica.stackexchange.com/‌​questions/75936/ghost-trails-with-animate","XMLObject"], XMLElement["td", {_, _, "class" -> "answercell"}, ___],Infinity]],XMLElement["pre", {}, {XMLElement["code", _, {code_}]}] :> code, Infinity]]
Dec
19
comment Module function corrupts string?
+1 @TraceKira This code is much more idiomatic and easily readable by anyone who is familiar with Mathematica. This style of programming is also much more efficient in Mathematica, as I've tried to illustrate in my edit.