547 reputation
39
bio website alfe.de
location Berlin, Germany
age
visits member for 2 years, 2 months
seen Nov 20 at 8:45

Sep
30
awarded  Explainer
Sep
12
awarded  Yearling
Dec
9
accepted Is it valid to write $\displaystyle \lim_{x \to 0} \frac{1}{x^2} = \infty$?
Dec
9
comment Is it valid to write $\displaystyle \lim_{x \to 0} \frac{1}{x^2} = \infty$?
Just for completeness: What about $\lim_{x \to 0} \frac{1}{x} = ±\infty$?
Dec
9
comment Is it valid to write $\displaystyle \lim_{x \to 0} \frac{1}{x^2} = \infty$?
That $+\infty$ thing is interesting. Does it mean that $\infty$ without the $+$ can mean positive as well as negative? In particular, can one write $\lim_{x \to 0} \frac{1}{x} = \infty$ even if that can be positive or negative?
Dec
9
comment Is it valid to write $\displaystyle \lim_{x \to 0} \frac{1}{x^2} = \infty$?
No problem, since I'm not so fluent in English mathematics, questions like these point out things to me I didn't know yet. So the case here with limes vs. limit. Thanks to @Daniel Fischer. :)
Dec
9
comment Is it valid to write $\displaystyle \lim_{x \to 0} \frac{1}{x^2} = \infty$?
No …? Your question baffles me.
Dec
9
asked Is it valid to write $\displaystyle \lim_{x \to 0} \frac{1}{x^2} = \infty$?
Dec
4
awarded  Scholar
Dec
4
accepted Non-iterative solution for $(a + nb)\mod c < d$
Dec
4
accepted How to solve $y = \frac{1}{x-1} +\frac {1}{x-5}$ for $x$
Dec
4
comment How to solve $y = \frac{1}{x-1} +\frac {1}{x-5}$ for $x$
Right. Thanks a lot, now it seems too simple ;-) (will accept as soon as possible).
Dec
4
asked How to solve $y = \frac{1}{x-1} +\frac {1}{x-5}$ for $x$
Nov
28
comment Non-iterative solution for $(a + nb)\mod c < d$
That's a whole different approach, basically switching from raytracing to standard triangle rendering as video games do it today. I find that rather boring. I chose raytracing because I viewed the resulting image from the same perspective as a Mandelbrot set in which zooming into the minutest details is possible. (I can do that as well of course.) I also rendered a high-res image in size A0 with 300 dpi (i. e. ≈ 15000 × 10000 pixels), so I would be hard pressed to find a true upper limit for $n$. Also, in raytracing I can easily combine such a grid with various other objects.
Nov
28
comment Non-iterative solution for $(a + nb)\mod c < d$
That's what I do. I hoped to speed it up by some fancy one-liner without looping.
Nov
28
comment Non-iterative solution for $(a + nb)\mod c < d$
I'm considering using well-chosen ratios of $d$ and $c$; since this is a design issue, I can choose those rather freely, so maybe I can speed up things by ensuring that $\gcd(d, c) = d$. Also, I can iterate for, say, twenty times, and then switch to your algorithm to find results for the points farther away. Btw, in case you're interested: this is used for creating Escher-inspired pictures. See is.gd/KBJ4eC and i.imgur.com/bsW6k9h.png .
Nov
28
comment Non-iterative solution for $(a + nb)\mod c < d$
I found the "strage" thing, it was about negative $b$, so I could fix that with taking it mod $c$, now the results always match the original. But the performance still is an issue. I hoped for fastening up things by getting a simpler version without the need to loop, and now only got a better but slower version (depending on usecase of course, but this is mine). I will leave this answer unaccepted for a week or so (and will accept eventually if nothing better shows up); but maybe someone else has an idea which actually speeds up my algorithm.
Nov
27
comment Non-iterative solution for $(a + nb)\mod c < d$
Now I get useful results! (There's something strange, sometimes the results don't seem to match my original ones, but I didn't investigate on that any further.) But, of course, now you've blown up the computation massively (I have to compute each $k_i$ now). Because I typically limit my dumb computation to at most some hundred cycles, your current version is way slower than the dumb one then. For much higher results your solution of course is better but for my situation unfortunately this doesn't help :-( Any (maybe different) idea on how to speed up things?
Nov
27
comment Non-iterative solution for $(a + nb)\mod c < d$
Maybe I'm misunderstanding something; my Python code for computing this can be found at pastebin.com/6FW6sAE6 .
Nov
27
comment Non-iterative solution for $(a + nb)\mod c < d$
Examining your answer in more detail I saw that the value $d$ does not appear anymore within the implementation at all; it only appears in the existence restriction (which I do not use because for my unround values a solution always should exist). But at least when computing it, the value $d$ should be part of the computation, shouldn't it?