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One can draw using simple command :

   f(x):= 1/x - floor(1/x);  plot2d(f(x),[x,0,1]);

For more precise drawing

• split curve into segments
• add end points

/*


https://stackoverflow.com/questions/49587741/how-to-draw-graph-of-gauss-function


Batch file for Maxima CAS
save as a g.mac
run maxima : 
 maxima
and then : 
batch("g.mac");

*/



kill(all);
remvalue(all);
ratprint:false;


/* ---------- functions ---------------------------------------------------- */


/* 
Gauss function
https://en.wikipedia.org/wiki/Gauss%E2%80%93Kuzmin%E2%80%93Wirsing_operator#The_Gaus_map 

f: x -> y

*/
f(x):= 1/x - floor(1/x)$

/* 

g : x -> x+y*i 

*/

g(x):= x+f(x)*%i$



/* 
converts complex number z = x*y*%i 
to the list in a draw format:  
[x,y] 
*/
draw_f(z):=[float(realpart(z)), float(imagpart(z))]$

/* give Draw List from one point*/
dl(z):=points([draw_f(z)])$

ToPoints(myList):= points(map(draw_f , myList))$







/* gives part of graph */
GivePart(n):=(
	[Part,  xMax, xMin, dx, iMax],
	
	if (n>20) then iMax:10
	  else iMax : 250,
	xMax : 1/n,
	xMin : 1/(n+1),
	dx : (xMax - xMin)/iMax,
	Part : makelist(xMin + i*dx, i, 0, iMax),
	 
	Part : map(g, Part), 
	Part[1] : xMin + %i, /* lower semi-continuous function */
	Part
	
)$





GiveClosedPoint(z):=

	[point_type = filled_circle,
	points_joined    =  false,
	point_size    =  0.8,
	dl(z)]$





GiveOpenPoint(z):=

	[point_type = circle,
	points_joined    =  false,
	point_size    =  0.9,
	dl(z)]$


/* 

*/
AddEndPoints(MyList):=(
	[zLeft, zRight],
	zLeft : first(MyList),
	if (realpart(zLeft)>0.07) then MyList: delete(zLeft, MyList ), 
	zRight : last(MyList),
	MyList :ToPoints(MyList),
	MyList : [GiveOpenPoint(zLeft),point_type = filled_circle, points_joined =true, point_size    =  0.1, MyList, points_joined = false, GiveClosedPoint(zRight)]	


)$



GiveList(i_Max):=(
	[Part, PartList ],
	PartList:[],
	for i:1 thru i_Max step 1 do (
		Part:  GivePart(i),
		Part : AddEndPoints(Part),
		PartList : cons(Part, PartList)
	
	),
	PartList



)$


compile(all);

nMax:60;


/* computations */


pp:GiveList(nMax)$


/* draw */

path:"~/maxima/batch/gauss/test/slim/"$ /*  pwd, if empty then file is in a home dir , path should end with "/" */

/* draw it using draw package by */

 load(draw); 
/* if graphic  file is empty (= 0 bytes) then run draw2d command again */

 draw2d(
  user_preamble="set key top right; unset mouse",
  terminal  = 'svg,
  file_name = sconcat(path,"gauss", string(nMax), "a"),
  font = "Liberation Sans", /* https://commons.wikimedia.org/wiki/Help:SVG#Font_substitution_and_fallback_fonts */
  title= "Gauss function  g(x)= 1/x - floor(1/x)",
    /*  */
  dimensions = [1000, 1000],
   
  yrange = [-0.1,1.1],
  xrange = [-0.1,1.1],
  
  
  xlabel     = "x ",
  ylabel     = "y",
  
  color         = blue,
  key = "",
  pp /* draw accepts list of parameters and data */
  
   )$
  

iThe source code of this SVG is valid.

 

This plot was created with Gnuplot by v.