--| home | txt | code | teach | talks | specialfunctionswiki | timescalewiki | hyperspacewiki | links |--
timescalecalculus on GitHub
Arithmetical functions in Python
Haskell notes

Mathematica stuff
Jacobi elliptic function homotopies
Gamma function on time scales
Zero-divisor, nilradical, and non-nilradical graph generator (not my code; credit: Brendan Kelly, Oliver Pechenik, Elizabeth Wilson)
The mathematica code I use to generate domain colorings
ComplexGraph[f_, {xmin_, xmax_}, {ymin_, ymax_}, opts : OptionsPattern[]] := RegionPlot[True, {x, xmin, xmax}, {y, ymin, ymax}, opts, PlotPoints -> 200, ColorFunctionScaling -> False, ColorFunction -> Function[{x, y}, With[{ff = f[x + I y]}, ColorConvert[ Hue[(2. Pi)^-1 Mod[Arg[ff], 2 Pi], 1, 1 - (1.2 + 10 Log[Abs[ff] + 1])^-1], "LAB"]]]]
Plotting an animated gif:
R[x_, N_] := Sum[Sin[k^2*x]/k^2, {k, 1, N}] plotme = Table[ Plot[R[x, N], {x, -5, 5}, PlotLegends -> Placed[StringJoin["N=", ToString[N]], Bottom], PlotRange -> {-1.5, 1.5}, PlotStyle -> Thickness[0.001]], {N, 1, 25, 1}]; Export["riemannfunction.gif", plotme, "FrameRate" -> 0.5, ImageSize -> {1000, 1000}]

GPF conjecture
cycle finder
GPF graph creator (Mathematica notebook)
GPF graph creator (Python+SAGE)
various GPF conjecture stuff (mathematica notebook)

Time scale calculus in haskell
Time scale $\mathbb{T}=\mathbb{Z}$ exponential function $e_p(t,s)=\displaystyle\prod_{k=s}^{t-1}1+p(k)$ in ghci:
Prelude> let expP p t s = product[1+(p k) |k<-[s..(t-1)]]
So if we would like to calculate the value of $e_p(5,2)$ whenever $p(x)=x+\dfrac{22}{3}$, we can write
Prelude> let regP x = x + 22/3 Prelude> expP regP 5 2 1444.37037037037
Time scale $\mathbb{T}=\mathbb{Z}$ gamma function $\Gamma_{\mathbb{Z}}(x)=\displaystyle\sum_{k=0}^{\infty} \left( \displaystyle\prod_{j=1}^{k-1} \dfrac{j+x}{j+1} \right) \dfrac{1}{2^{k+1}}$ in ghci:
Prelude> let gammaProd x k = product [ (x+j)/(j+1) | j<-[0..(k-1)]] Prelude> let gammaZ x = (1/x)*sum[(gammaProd x k)/(2**(k+1)) |k<-[0..1000]]

Linux stuff
Start mysql server if it crashes:
sudo service mysql start
Remote mount a folder:
Unmount remote folder:
fusermount -u LOCAL_MOUNT_POINT
If remote mounted folder freezes, run the following and then unmount:
killall -9 sshfs
Convert flac to mp3:
ffmpeg -i input.flac -ab 196k -ac 2 -ar 48000 output.mp3
To halt a process, detach from shell, and run in background
ctrl+z to pause disown -h %1 bg 1
autossh command
autossh -M 20000 -f -N serverurl.com -R 19999:localhost:22 -C
To generate a video file from png's labelled 0000.png 0001.png, etc
ffmpeg -f image2 -i %04d.png -vb 20M FILENAME.mpg