;; This is supposed to prove that the 3 altitudes of a triangle
;; intersect at a single point
(string-grobner-system
"[U1*Y-V1*X,-X2*Y+U2*Y+V2*X2-V2*X,X*Y3-U3*Y3-X3*Y+U3*Y+V3*X3-V3*X,V1*Y3+U1*X3-U1*X2,V2*Y3-X2*X3+U2*X3,U3*X2-X2*X3]"
'(x y u1 v1 u2 v2 u3 v3)
'(x2 x3 y3)
:main-order #'lex>
:parameter-order #'grevlex>)