File:Brjuno function.png
Summary
| Description |
English: Brjuno function. It has the asymmetric logarithmic singularities at rational points.[1] |
| Date | |
| Source | own work. Maxima CAS code by user slitvinov[2] |
| Author | Adam majewski |
| Other versions |
|
![[1]](./File:Brjuno_function.png#cite_note-1){kind=link}
![[2]](./File:Brjuno_function.png#cite_note-2){kind=link}
Licensing
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Maxima CAS src code
/*
https://stackoverflow.com/questions/69289026/how-to-compute-brjuno-function-in-maxima-cas/69369529#69369529
slitvinov : I used an equation from wikipedia and a continued fraction approximation:
*/
kill(all);
remvalue(all);
cflength: 20 $ /* Default value: 1 */
cf2num(e):=ev(cfdisrep(e), numer, infeval) $
B(x):= if length(x)=1
then 0
else (x[1]: 0, -log(cf2num(x))+cf2num(x)*B(rest(x)));
iMax: 10000; /* number of points to compute */
a: 0.997865394128713086 / iMax; /* it should be 1/iMax */
/* list of points x ( real values ) in [0.0 , 1.0 ] range */
x: makelist(i*a, i, 1, iMax)$
/* list of continued fractions of points x */
c: map(cf, x) $
/* list of Brjuno function values */
y: map(B, c) $
/*-----------------------------------------------------------------------*/
path:"~/Dokumenty/brjuno/"$ /* if empty then file is in a home dir */
/* draw = ( interface to gnuplot ) by Mario Rodriguez Riotorto http://www.telefonica.net/web2/biomates */
draw2d(
title = "Brjuno function",
terminal = png,
dimensions = [1000,1000], /* Since Maxima 5.23, pic_width and pic_height are deprecated. */
xrange = [0.0, 1.0],
yrange = [0.0, 8.0],
user_preamble = "", /* */
file_name = concat(path ,"bb"),
point_type = filled_circle,
points_joined = false,
point_size = 0.5,
key="",
color = blue,
xlabel = "x",
ylabel = "B(x)",
points(x, y)
)$
references
- ↑ Regularity properties of k-Brjuno and Wilton functions by Seul Bee Lee, Stefano Marmi, Izabela Petrykiewicz, Tanja I. Schindler
- ↑ stackoverflow question : how-to-compute-brjuno-function-in-maxima-cas
