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1d
comment How to clear everything in Mathematica?
Another caution: if you sign in to Wolfram Cloud, then you may have objects in the context CloudObject.
1d
comment Colors on a 3D curve not working
Just a note that your Color1, Color2, Color3 are Blue, Red, Green, respectively.
1d
comment MatrixExp of a complex matrix of size about 10000 by 10000
For finding the trace of a matrix, including a sparse matrix, there's the built-in function Tr. (I don't understand the comment, "the algorithms are not built-in."
1d
comment Transform a vector DE into a set of scalar DEs
In recent versions of Mathematica, you do not have to transform the vector equation into a pair of scalar equations before using solving them. Thus DSolve[{{a, b}, {c, d}}.D[{x1[t], x2[t]}, t] == {{e, f}, {g, h}}.{u1[t], u2[t]}, {x1[t], x2[t]}, t] works just fine as is, whether with "abstract" functions u[t], u2[t] and symbolic coefficient matrices, or with specific functions and actual values in the coefficient matrices.
Jul
30
comment Mathematica 10, Show, and PlotRange
It's not immediately obvious to know that: Options[Show] yields an empty list of options; and the doc page for Show lists just a single option, namely, DisplayFunction. However the Details section of the page for Show does state, "Show allows any option that can be applied to graphics to be given."
Jul
24
answered How to make Mathematica to assemble components we already have like a regular input
Jul
24
revised Input Aliases in Mathematica 10
added 31 characters in body
Jul
22
awarded  Inquisitive
Jul
21
accepted How align Table column on decimal point yet use text styling?
Jul
21
comment How align Table column on decimal point yet use text styling?
Perfect! (And the one possibility I didn't think of.) I note that the same things works on an entire Grid, too (which is what I had originally wanted to use so as to better control the frame and dividers.
Jul
21
asked How align Table column on decimal point yet use text styling?
Jul
20
comment Function for the Second Derivative Test
@David: The issue in the original question was not the classification of critical points, but rather locating the critical points (for that nasty function).
Jul
20
comment Function for the Second Derivative Test
@Guess who it is: Stan Wagon's implementation where? Are you perhaps referring to function LowestCriticalPoint in Chapter 13 of his Mathematica in Action, 3rd edition?
Jul
19
comment Export rotate bug in Mathematica v10
Same bug no matter whether the exported PDF is viewed with Preview or Adobe Acrobat Reader under Mac OS X.
Jul
19
comment Function for the Second Derivative Test
Yep, 4 critical points indeed. Guided by your contour plot, they may be located by using FindRoot. Obtain all 4 as follows: FindRoot[Grad[f, {x, y}] == 0, {x, First@#}, {y, Last@#}] & /@ {{0, 0}, {-0.5, -1}, {0.25, 1}, {-0.5, 0.5}}.
Jul
19
comment Function for the Second Derivative Test
If you calculate Simplify[Grad[f, {x, y}]], you'll see that you have components that have factors of Exp[-(x^2 + y^2}. And if you look at that, or even do a Plot3D on the gradient, you'll see that the graph becomes very flat, close to the $xy$-axis, as you move away from the origin.
Jul
18
comment Why do I need to apply DiscretizeRegion to a derived region to visualize it?
But why DiscretizeRegion rather than RegionPlot in these two-dimensional examples?
Jul
17
comment Why do I need to apply DiscretizeRegion to a derived region to visualize it?
Still the whole situation doesn't yet fit together for me: Using RegionPlot to visualize RegionUnion[Disk[{0, 0}, 1], Disk[{2, 0}, 1]] makes perfect sense. However, RegionProduct[Disk[{0, 0}, 1], Line[{{0}, {1}}]] has head Cylinder, so just Graphics3D[RegionProduct[Disk[{0, 0}, 1], Line[{{0}, {1}}]]] works to see it. And RegionProduct[Disk[], Line[{{0}, {1}}]] has head Cylinder, but wrapping that with Graphics3D fails to display it whereas wrapping it with RegionPlot3D does display it.
Jul
17
accepted Why do I need to apply DiscretizeRegion to a derived region to visualize it?
Jul
16
asked Why do I need to apply DiscretizeRegion to a derived region to visualize it?