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]);