File:Brjuno function.png

Summary[edit]

Licensing[edit]

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Maxima CAS src code[edit]

/*

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[edit]

1. ↑ Regularity properties of k-Brjuno and Wilton functions by Seul Bee Lee, Stefano Marmi, Izabela Petrykiewicz, Tanja I. Schindler
2. ↑ stackoverflow question : how-to-compute-brjuno-function-in-maxima-cas