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visits member for 2 years, 10 months
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Apr
21
comment Sqrt — how to get negative branch?
To get the negative branch correctly, you'd have to make it work for complex numbers, too. Without trying it (I don't like to modify the built-in function Power), it seems that your method with /; a < 0 can't do this.
Apr
21
comment Sqrt — how to get negative branch?
Your edited question asks why Sqrt[x] doesn't return Abs[x]. The simple reason is that this isn't true unless x is real. But the default assumption for symbols without numerical value is that they are complex.
Apr
21
comment Optimizing a Numerical Laplace Equation Solver
Oh yes, that should be doable in Mathematica. I was more thinking about a really big electrostatic problem (as in the many components of a particle accelerators on the large-scale side, or molecular fields on the small-scale end of the spectrum). But I've only needed the 2D Cartesian version so far.
Apr
20
comment 3D plot of two 2D functions
@pauleck, if this answers your question you should click on the check mark and the up-arrow next to the answer (to up-vote it - as I just did...) If you still want to wait for other answers, it's OK to leave the check mark unchecked until a day or so later.
Apr
20
revised 3D plot of two 2D functions
more coherent description not referring to sum
Apr
20
comment 3D plot of two 2D functions
What do you mean by zy layer? Why do you refer to a sum in the text of the question?
Apr
20
reviewed Reject 3D plot of two 2D functions
Apr
20
comment Optimizing a Numerical Laplace Equation Solver
What you consider optimization also depends on what limits you in any particular application: memory or speed...
Apr
20
comment Optimizing a Numerical Laplace Equation Solver
I haven't extended it to three dimensions. The first thing one might try is to do a cylindrically symmetric 3D problem in cylinder coordinates, where the radial derivative is modified to $\frac{1}{r}\frac{\partial}{\partial r}\left(r\,\frac{\partial f}{\partial r}\right)$ but can still be discretized. But fully 3D calculations aren't just tricky, they may quickly become impractical for Mathematica. It depends on the application, I guess, but I'd go straight to FORTRAN.
Apr
20
comment 3D plot of two 2D functions
Then what's wrong with Plot3D[x^2+y^2,{x,-1,1},{y,-1,1}] ?
Apr
20
answered How to make traditional output for derivatives
Apr
20
comment How to make traditional output for derivatives
I posted a solution to this problem as part of my answer here. Its advantage is that it is more compact and that it automatically uses straight derivative symbols (instead of curly ones) when you're not doing partial derivatives.
Apr
19
comment Optimizing a Numerical Laplace Equation Solver
I posted a pretty flexible relaxation solver for the Poisson equation here. The Laplace equation is a special case of that. Maybe you can use it for your problem.
Apr
17
revised Method used by FindFit
formatting, title
Apr
17
awarded  Enlightened
Apr
17
awarded  Nice Answer
Apr
16
comment How do I simplify a vector expression?
I already anticipated this comment in my answer, and mentioned that it opens up a wide field of additional definitions one could add. I may come back to that when I have time.
Apr
15
comment Symbolic evaluation fails because it exceeds $RecursionLimit
Yes, that's a way around the problem (+1). And if you have other cases where Subscript needs its arguments evaluated, you just have to wrap those in Evaluate.
Apr
15
answered Upper bound for x
Apr
14
comment Series expansion in terms of Hermite polynomials
@belisarius For that general case, at least I can allow a larger basis than necessary, with the latest edit. Then basis can be kept fixed as some list with a number of polynomials that is expected to be large enough for all purposes.