# Rahul Narain

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 Jul12 comment 3D Plot from 3 Polynomial Equations You can do sol0 = Solve[f0[λ0, y0, y1, x, k] == 0, λ0] and sol0 = Solve[f0[λ0, y0, y1, x, k] == 0, λ0] to find the values of $λ_0$ and $λ_1$ that satisfy $f_0 = 0$ and $f_1 = 0$ respectively. Then substitute them into $f_2$ via sol2 = f2[λ0, λ1, x, k] /. sol0 /. sol1 // Flatten to get something that only depends on $x$, $k$, $y_0$, and $y_1$. However, there are apparently eight different solutions each to $f_0 = 0$ and $f_1 = 0$, so you'll end up with 64 possible values of $f_2$. Jul12 comment Why does FindFit seem to have trouble fitting exponential data? Is the only difference between FindFit and NonlinearModelFit the fact that the latter provides more statistical information, or is there anything deeper than that? Jul12 comment Why does FindFit seem to have trouble fitting exponential data? Try providing a reasonable initial guess: fit = FindFit[data, model, {{a, Last@Mean[data]}, {k, 1/First@Mean[data]}}, t] Jul12 comment Different colors when comparing Plot3D V9 and V10 Since this is the canonical solution, I'll delete my answer and leave this here: the previous default lighting settings. Jul12 comment Different colors when comparing Plot3D V9 and V10 Well, if you compare the first three images on the documentation page "Change the Lighting of Plots", which are supposed to look the same (and did in previous versions), it is clear that the default lighting has changed. Jul12 comment Different colors when comparing Plot3D V9 and V10 Ah! This is the better solution! Jul11 comment ParametricPlot - Problem with ColorFunction I meant the tendency of some people to start accusing everyone who comments "Are you the downvoter?" "Are you the downvoter?". Often if someone reveals that they downvoted, the OP then goes and downvotes or leaves negative comments on their other unrelated posts. I'm not suggesting you would do that, I'm simply saying that one should not be expected to reveal one's votes, and asking whether one has downvoted should be considered an intrusive question. Jul11 comment ParametricPlot - Problem with ColorFunction If you don't care then why call them a coward and ask for a reason? Jul11 comment ParametricPlot - Problem with ColorFunction ColorFunction -> (ColorData["DarkRainbow"][Abs[2 #3 - 1]] &) Jul11 comment Neural Network and New Mathematica version Summary of New Features in Mathematica 10, Ctrl+F "neural", no results. However, it does have a whole bunch of new machine learning functionality, so if you're not married to neural networks per se this might be useful. Jul11 revised Rough mesh lines in partially opaque 3D plots edited title to remove ambiguity: is it the mesh lines or the plot that is partially opaque? Jul11 comment Rough mesh lines in partially opaque 3D plots Works fine for me on Mathematica 9.0.1 on Mac. What's your version and platform? Jul10 comment Random numbers that sum up to specific value +1: This is the approach endorsed by whuber and the statistics StackExchange. It also runs in only $O(n\log n)$ time. Jul10 comment Can mathematica rearrange an equation and solve/plot it? You can also try ContourPlot3D[Sin[x + y + z] == x^2 y - z, {x, -5, 5}, {y, 0, 1}, {z, 0, 1}, ViewPoint -> {Infinity, 0, 0}, MeshFunctions -> {#1 &}, Mesh -> 20, ContourStyle -> None, Ticks -> {None, Automatic, Automatic}, AxesLabel -> {"", y, z}] Jul9 comment How can the opacity of a dense data set be automatically chosen? That's pretty cool! I wonder what happens if you have two different datasets in the same plot -- are their point sizes adapted independently or are they the same? I can see arguments in favour of either. Jul9 comment Limits explanation in doc Think of it as the direction you're going, not the direction you're coming from. (Although I do agree with you that it is a little inconsistent with the traditional mathematical notation. Perhaps they should have just used Above and Below for no chance of confusion.) Jul8 comment Implicitly differentiate an equation, then solve the resulting equation Funny, this gives Indeterminate for f = x + y and 1 for f = x + y + z, both of which are incorrect. Jul8 comment Horizontal shift in fitting data by a sinusoidal nonlinear model It helps to provide reasonable initial guesses for the parameters so that the solver is more likely to converge to the right answer. In your case, it makes sense to start b at $\pi/180$ and d at the mean of the data: NonlinearModelFit[data, d + a Sin[b (x - c)], {a, {b, π/180}, c, {d, Mean@data[[All, 2]]}}, x]["BestFit"]; this gives the desired fit. Jul8 answered Problem regarding 3D plot of a Moebius strip from a set of 2D points Jul8 comment Identifying the color in Image Simpler way to preserve the structure: Map[PixelValue[#, .5*ImageDimensions@#] &, p, {2}]