Caprasse’s system

                                                    caprasse [1]

Equations:

y^{2}z + 2 xyt − 2 x − z; 2 yzt + xt^{2} − x − 2 z; −x^{3}z + 4 xy^{2}z + 4 x^{2}yt + 2 y^{3}t + 4 x^{2} − 10 y^{2} + 4 xz − 10 yt + 2; −xz^{3} + 4 yz^{2}t + 4 xzt^{2} + 2 yt^{3} + 4 xz + 4 z^{2} − 10 yt − 10 t^{2} + 2;

Also in the PoSSo Tests suite. Characteristics:

• Dimension 0.

• Degree 56. Number of different complex solutions: 32. Number of different real solutions: 18.

• Component at infinity of dimension 1. Example 1:

[y**2*z+2*x*y*t-2*x-z,
-x**3*z+4*x*y**2*z+4*x**2*y*t+2*y**3*t+4*x**2-10*y**2+4*x*z-10*y*t+2,
2*y*z*t+x*t**2-x-2*z,
-x*z**3+4*y*z**2*t+4*x*z*t**2+2*y*t**3+4*x*z+4*z**2-10*y*t-10*t**2+2];

References

[1] D. Bini and B. Mourrain. Polynomial test suite. 1996.