Fig1.mw

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

> #A generic elliptic CR singularity.

> z1*conjugate(z1)+(1/4)*(z1^2+conjugate(z1)^2);

z1*conjugate(z1)+1/4*z1^2+1/4*conjugate(z1)^2

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

(x+I*y)*(x-I*y)+1/4*(x+I*y)^2+1/4*(x-I*y)^2

> h2:=expand(%);

h2 := 3/2*x^2+1/2*y^2

> plot3d(h2,x=-1..1,y=-1..1,style=patchcontour,axes=boxed,shading=zgrayscale,tickmarks=[0,0,0],transparency=0.7,labels=["x1","y1","x2"]);

[Plot]