Examples 3.17 and 18 (A Prototypical Amoeba and Contour) 

>	# Define H H := 1-x-y;

 

(1)

 

>	# Plot the amoeba X := solve(H,x); pt := subs(y=r*exp(I*t),[log(abs(X)),log(abs(y))]): PTS := seq(plot([op(subs(t=k*Pi/90,pt)),r=-40..40],thickness=7),k=0..89): plots[display](PTS, view=[-3.5..3.5,-3.5..3.5]);

 

>	# Plot contour sbs := solve([diff(H,x)*x-diff(H,y)*y*t,H],[x,y])[1]: cc := subs(sbs,[log(abs(x)),log(abs(y))]); plot([op(cc),t=-100..100], view=[-4..4,-4..4]);