J. M.
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 Mar 25 revised Proof a formula of the Fibonacci sequence with induction edited tags Mar 25 comment Can partition be defined for numbers other than positive integers? @night, you might be interested in Egyptian fraction decomposition. Mar 24 comment Why is it more efficient to compute the modular exponentiation by calculating to the power of two and not three for example? @Ian, yes, as I had been obliquely stating, bit twiddling (when bit operation functions are available) is the most efficient way of going about it, but one then has to explain this to other people (or to yourself when you're reading code many moons later). So, probably a well-named subroutine that just hides the bit stuff behind the scenes. Mar 24 comment Why is it more efficient to compute the modular exponentiation by calculating to the power of two and not three for example? @Ian, one does hope for more straightforward routes instead of resorting to bit twiddling... ;) Mar 24 comment Why is it more efficient to compute the modular exponentiation by calculating to the power of two and not three for example? As @Yves notes, this really is one of those things you could have answered yourself by actually doing the experiment. Don't be afraid to try stuff and make wrong turns! Mar 18 comment Arc Length of Bézier Curves @user, yes, the formula is certainly not intended for collinear control points; the expectation is that anybody programming would have already recognized that case beforehand. Mar 17 comment Arc Length of Bézier Curves Here's a better idea than plotting, @user: try differentiating the two expressions you have and see what they return. ;) Mar 17 comment Quintillion bytes to terabytes It should be noted that sometimes one tries to distinguish the $1024$ conversion from the $1000$ conversion using "kibibytes", "gibibytes", etc. Not that I approve of the chosen terms for the units... :) Mar 17 comment Is the angle of a line from the bottom-right to the top-left of a graph always $45$ degrees? This is related to the fact that $\tan 45^\circ=1$. Mar 17 comment How to make analytic continuation and compute imaginary part You're in too much of a hurry. :) Anyway, do what I said earlier, and then you can apply the formulae here. Mar 17 comment How to make analytic continuation and compute imaginary part To start you out: $K$ becomes complex for real moduli $>1$, so you need to figure out when $k(x)>1$. Mar 17 comment How to make analytic continuation and compute imaginary part Is the argument of your elliptic integral the modulus or the parameter? Mar 16 comment The arithmetic-geometric mean for symmetric positive definite matrices Yes, I'm quite familiar with the matrix functions. :) I admittedly haven't visited this topic in quite a while, but this makes me wonder if this is related to evaluating the complete elliptic integral of the first kind for matrix arguments. Mar 16 awarded Favorite Question Mar 15 revised How can I calculate $\sum_{k=1}^{n-1}\binom{n-1}{n-k}$? edited tags Mar 15 revised Find the minimum and maximum of $f(x) = \sum\limits_{k=0}^n (x-a_k)^2$ edited title Mar 14 revised Circular Helicoid edited tags Mar 14 revised How to prove the result of this definite integral? added 1 character in body Mar 14 comment Is linear algebra laying the foundation for something important? Put another way: we approximate a nonlinear reality with a more easily imagined linear simulacrum. Mar 14 comment Is linear algebra laying the foundation for something important? @lisyarus, probably not "often", unless you deal with a lot of PDEs or networks. There's still much demand for dense methods, especially those that exploit structure. Nevertheless, linear algebra is one of the very handy tools in the box of a numericist.