Fig7.mw

> restart;with(plots):interface(showassumed=0):assume(x,real);assume(y,real);

> #A degenerate parabolic CR singularity

> z1*conjugate(z1)+(1/2)*(z1^2+conjugate(z1)^2)+z1*conjugate(z1)*(z1^2+conjugate(z1)^2);

z1*conjugate(z1)+1/2*z1^2+1/2*conjugate(z1)^2+z1*conjugate(z1)*(z1^2+conjugate(z1)^2)

> eval(%,z1=x+I*y);

(x+I*y)*(x-I*y)+1/2*(x+I*y)^2+1/2*(x-I*y)^2+(x+I*y)*(x-I*y)*((x+I*y)^2+(x-I*y)^2)

> h2:=expand(%);

h2 := 2*x^2+2*x^4-2*y^4

> plot3d(h2,x=-0.5..0.5,y=-0.5..0.5,contours=27,axes=boxed,style=patchcontour,shading=zgrayscale,tickmarks=[0,0,0],transparency=0.9,labels=["","",""]);

[Plot]