• Define two disc intervals with midpoints at 1 and -1+i and mulitply them using centered and area optimal multiplication.
   
• Enclose the range of the complex polynomial

  

  on the disc interval [-0.2,0.4,1] with midpoint at -0.2+0.4i and radius 1 using three different evaluation methods.

Here's the Maple Worksheet solving the task with intpakX.

> restart;

> libname:="/usr/maple/intpakX/lib", libname;

> with(intpakX);
 

> A1:=[1,0,1];

> B1:=[-1,1,1];

> C1:=A1 &cmult B1;

> D1:=A1 &cmult_opt B1;

> cmd1:=complex_disc_plot(A1,color=black):
cmd2:=complex_disc_plot(B1,color=black):
cmd3:=complex_disc_plot(C1,color=red):
cmd4:=complex_disc_plot(D1,color=blue):

> display([cmd1,cmd2,cmd3,cmd4],scaling=constrained);

> p1:=(0.1+0.1*I)*z^5+0.2*I*z^4-0.1*I*z^3+(-0.2-0.1*I)*z+2.0+1.0*I;

> Z:=[-0.2,0.4,1];

> pH:=horner_eval_cent(p1,Z);

> pO:=horner_eval_opt(p1,Z);

> pC:=centred_form_eval(p1,Z);

> cp:=complex_polynom_plot(p1,Z):
c1:=complex_disc_plot(pH,color=blue,linestyle=4):
c2:=complex_disc_plot(pO,color=green,linestyle=3):
c3:=complex_disc_plot(pC,color=black,linestyle=2):

> display([c1,c2,c3,cp],scaling=constrained);

>