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Mar
25
revised Proof a formula of the Fibonacci sequence with induction
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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
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Mar
15
revised How can I calculate $\sum_{k=1}^{n-1}\binom{n-1}{n-k}$?
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Mar
15
revised Find the minimum and maximum of $f(x) = \sum\limits_{k=0}^n (x-a_k)^2$
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Mar
14
revised Circular Helicoid
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Mar
14
revised How to prove the result of this definite integral?
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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.