🚀 go-pugleaf

Consider:  a*z^5+b*z^4+c*z^3+d*z^2+e*z+f

where  z=x+iy ;  a,b,c,d,e, f -   are real numbers.

Running the following MATLAB program for  particular values of a,b,c,d,e,f

the location of zeros is shown in a x,y -plane of an orthogonal coordinate
system.

x=-2:.02:2;
y=0:.01:2;           
[X,Y] = meshgrid(x,y);
a=0; b=0; c=1; d=0; e=1; f=1;

Z=sqrt((a*(X.^5-10*(X.^3).*(Y.^2)+5*X.*(Y.^4))+b*(X.^4-6*(X.^2).*(Y.^2)+Y.
^4)+c*(X.^3-3*X.*(Y.^2))+d*(X.^2-Y.^2)+e*X+f).^2+(a*(5*(X.^4).*Y-10*(X.^2).
*(Y.^3)+Y.^5)+b*(4*(X.^3).*Y-4*X.*(Y.^3))+c*(3*(X.^2).*Y-Y.^3)+d*(2*(X.*Y))
+e*Y).^2).*(+sin(atan((a*
(5*(X.^4).*Y-10*(X.^2).*(Y.^3)+Y.^5)+b*(4*(X.^3).*Y-4*X.*(Y.^3))+c*(3*(X.^
2).*Y-Y.^3)+d*(2*X.*Y)+e*Y)./(a*(X.^5-10*(X.^3).*(Y.^2)+5*X.*(Y.^4))+b*(X.^
4-6*(X.^2).*(Y.^2)+Y.^4)+c*(X.^3-3*X.*(Y.^2))+d*(X.^2-Y.^2)+e*X+f)))+cos(at
an((a*(5*(X.^4).*Y-10*(X.
^2).*(Y.^3)+Y.^5)+b*(4*(X.^3).*Y-4*X.*(Y.^3))+c*(3*(X.^2).*Y-Y.^3)+d*(2*X.
*Y)+e*Y)./(a*(X.^5-10*(X.^3).*(Y.^2)+5*X.*(Y.^4))+b*(X.^4-6*(X.^2).*(Y.^2)+
Y.^4)+c*(X.^3-3*X.*(Y.^2))+d*(X.^2-Y.^2)+e*X+f))));
c=contour(X,Y,Z,0:10:20);
clabel(c,'manual');

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