File:Gauss function.svg
Summary
| Description |
English: Gauss function f(x) = 1/x - floor(1/x) |
| Date | |
| Source | own work with help of Robert Dodier |
| Author | Adam majewski |
Licensing
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Maxima Cas src code
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 */
)$
