/*

Batch file for Maxima CAS
save as a o.mac
run maxima :
       
 maxima
 
and then : 

batch("a.mac");

*/
kill(all);
remvalue(all);
ratprint:false; /*  It doesn't change the computing, just the warnings. */
display2d:false;
numer: true;





/* 

http://mathworld.wolfram.com/Rose.html

r = a* sin(n*t)

If n is odd, the rose is n-petalled. 
If n is even, the rose is 2n-petalled.


If n=r/s is a rational number, then the curve closes at a polar angle of theta=pi*s*p, where  
p=1 if r*s is odd 
p=2 if r*s is even.

 
If n is irrational, then there are an infinite number of petals.


*/

RoseCurve_Polar(n, a):= 
	/* polar(radius, ang, minang, maxang) */
	polar(a*sin(n*t),t,0,2*%pi)$
	
	
	
/*
 https://commons.wikimedia.org/wiki/File:Two_3_Petal_roses.png
 
*/	

RoseCurves_Polar(n, aMin, aMax, aStep):= block(

	[a,l, ll],
	ll:[],
	for a:aMin step aStep thru aMax do (
		l:RoseCurve_Polar(n,a),
		ll: cons(l,ll),
		l:RoseCurve_Polar(n,-a), /* mirror symmmetry  */
		ll: cons(l,ll)
	),
	
	return (ll)


)$










n:3;
ll:RoseCurves_Polar(n, 1, 20,0.5)$


load(draw);

/* strings */
path:"~/c/julia/parabolic/hawaian/6/"$ /*  if empty then file is in a home dir , path should end with "/" */ 
FileName:  string(n)$


draw2d(
	terminal      = svg,
	file_name = sconcat(path, FileName,""),
	title = "",
	dimensions = [1000, 1000],
	nticks=300,
	ll)$


/*  https://math.stackexchange.com/questions/104163/writing-a-polar-equation-for-the-graph-of-an-implicit-cartesian-equation 
l:polar(abs(sin(2*t))^(1/3),t,0,2*%pi);
ll: cons(l,ll);
l:polar(abs(sin(2*t)),t,0,2*%pi);
ll: cons(l,ll);

ll:[];
draw2d(nticks=300,ll);

*/