Plot Examples 8 and 9 from GroebnerIntro 

Example 8: Plot 

>

restart;

 

>	p1 := x^2 + y*z - 2:

 

>	p2 := y^2 + x*z - 3:

 

>	p3 := x*y + z^2 - 5:

 

>	F := [p1, p2, p3];

 

>	with(plots):

 

>	implicitplot3d(p1, x=-5..5, y=-5..5, z=-5..5, axes=boxed);

 

>	implicitplot3d(p2, x=-5..5, y=-5..5, z=-5..5, axes=boxed);

 

>	implicitplot3d(p3, x=-5..5, y=-5..5, z=-5..5, axes=boxed);

 

>	implicitplot3d([p1,p2,p3], x=-5..5, y=-5..5, z=-5..5,   axes=boxed, color=[red,blue,yellow]);

 

>

 

Example 9: Plot 

>

restart;

 

>	f1 := 4*x^2 + x*y^2 - z + 1/4:

 

>	f2 := 2*x + y^2*z + 1/2:

 

>	f3 := x^2*z - 1/2*x - y^2:

 

>	F := [f1, f2, f3];

 

>	with(plots):

 

>	implicitplot3d(f1, x=-10..10, y=-10..10, z=-10..10, axes=boxed);

 

>	implicitplot3d(f2, x=-10..10, y=-10..10, z=-10..10, axes=boxed);

 

>	implicitplot3d(f3, x=-10..10, y=-10..10, z=-10..10, axes=boxed);

 

>	implicitplot3d([f1,f2,f3], x=-10..10, y=-10..10, z=-10..10,   axes=boxed, color=[red,blue,yellow]);

 

>

 

The first subsystem G1 

>	G1 := [z-1, 2*y^2-1, 2*x+1];

 

>	implicitplot3d(G1, x=-2..2, y=-2..2, z=-2..2,   axes=boxed, color=[red,blue,yellow]);

 

>

 

The second subsystem G2 

>	G2 := [16*z^6+8*z^5+9*z^4+61*z^3+136*z^2-206*z+60, 284*y^2+5664*z^5+5568*z^4+5866*z^3+24365*z^2+59937*z-43978, 568*x-2736*z^5-2680*z^4-2771*z^3-11793*z^2-28946*z+21382];

 

>	implicitplot3d(G2, x=-10..10, y=-10..10, z=0..1,   axes=boxed, color=[red,blue,yellow]);

 

>