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Aug
30
comment How to implement this simple product rule in mathematica
The σ are exactly the matrices PauliMatrix[i], so it's easiest to realize this algebra using them explicitly. You can always re-express results of explicit matrix algebra in terms of the Pauli matrices because the latter (together with IdentityMatrix[2] or PauliMatrix[0]) form a basis of the space of $2\times 2$ matrices.
Aug
30
awarded  equation-solving
Aug
29
comment Alternate parameterization of a line
@Mr.Wizard Regarding localization: that's fine, but what I did instead also works. I put $\rho$ into a Clear just for completeness now, but actually that isn't even needed, I believe.
Aug
29
revised Alternate parameterization of a line
added 3 characters in body
Aug
29
comment Alternate parameterization of a line
@Mr.Wizard I double-checked with the same test you did, and mine is consistently faster on version 9: Set r = RandomReal[9, 150000]; and then lineFromPolar2[1.4, 0.3] /@ r // Timing // First. It yields 0.021555 for your function and 0.018534 for mine.
Aug
29
comment Alternate parameterization of a line
@bills OK, I've changed lineToPolar so that angles of Pi or 0 are now describing vertical lines, which is what lineFromPolar was already assuming.
Aug
29
revised Alternate parameterization of a line
Changed angle definition in inverse
Aug
29
comment Alternate parameterization of a line
@bills Oh sorry, I used different definitions of $\theta$ for the two functions. What do you prefer: is $\theta$ the angle of the actual line with the horizontal? Or is it the angle of the normal to the line with the horizontal, as in the article you linked here? I have to change one or the other, but I'll wait until you let me know which you like better...
Aug
29
revised Alternate parameterization of a line
Component form simplified
Aug
29
revised Alternate parameterization of a line
More efficient inverse
Aug
29
comment Alternate parameterization of a line
@Mr.Wizard You're right, I didn't think about efficiency in the inverse. The version in my edit is even faster than yours now.
Aug
29
revised Alternate parameterization of a line
More efficient inverse
Aug
29
revised Alternate parameterization of a line
added 198 characters in body
Aug
29
answered Alternate parameterization of a line
Aug
21
comment Symbolic Integration of Special Functions
Maybe worth adding: if you apply FunctionExpand to this, you can also get rid of the Pochhammer symbol.
Aug
19
awarded  Nice Answer
Aug
17
comment Identifying when two graphic objects overlap
I think the tip sharpness should affect the collision detection, but it doesn't do that here.
Aug
17
answered Identifying when two graphic objects overlap
Aug
17
comment What is the best way to produce a symmetric semi-definite matrix using as few variables as possible?
@EdenHarder It seems very fast to me. What do you mean by "not direct?"
Aug
17
comment Resources on Mathematica and strong AI (a.k.a. AGI)
@Murta Agree with the first part (read only the first paragraph in Wikipedia and knew I can stop right there), but if Mr. Wizard were AGI he wouldn't need Mathematica, would he? Or is he implemented in Mathematica -- version 7??