File:Gauss function.svg

Summary[edit]

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:

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You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue

Maxima Cas src code[edit]

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.