/* examples by Prof. Kimura for groebner basis computation */

F=9*(2*y*(u-x)+3)*v^2+18*y*v-72*y*(u-x)*(u^3-x^3)
	-108*(u+2*x)*(u-x)^2-36*t*y*(u-x)^2-2*y^3*(u-x)+3*y^2$
G=(u-x)*(9*v^2-36*(u^3-x^3)-18*t*(u-x)-y^2)^2+6*(3*v+y)
	*(9*v^2-36*(u^3-x^3)-18*t*(u-x)-y^2)+324*(u-x)^2$
D=(diff(F,x)*diff(G,y)-diff(F,y)*diff(G,x))
	-(diff(F,u)*diff(G,v)-diff(F,v)*diff(G,u))$

Kimura1 = [F,G,D]$

A1=(9*(u-x)*v^2-9*(u-x)*(2*u^2+s)*v+9*v-18*r*(u-x)^2-y*(y-6*x^2-3*s)*(u-x)-3*y)*w
-(9*v^2-9*(2*u^2+s)*v-18*r*(u-x)-y^2+(6*x^2+3*s)*y)$

A2=(((3*(u-x)*v-6*(u^2-x^2)*(u-x)-y*(u-x)+6)*(3*v+y-6*x^2-3*s))
+(6*(u-3*x)*(u-x)*((y-6*x^2-3*s)*(u-x)+3)+18*r*(u-x)^2))*w
-2*(3*v+y-6*x^2-3*s)*(3*v-3*(u+3*x)*(u-x)+y-6*x^2-3*s)
+18*((u-x)^2)*v-6*(y-6*x^2-3*s)*(u-x)^2-18*(u-x)$

A3=(3*(u-x)*v-6*(u^2-x^2)*(u-x)-y*(u-x)+6)*w^2
-2*(3*v-6*u*(u-x)+y-6*x^2-3*s)*w - 6*(u-x)$

F=res(w,A1,A2)$
P=res(w,A1,A3)$
Dxy=diff(F,x)*diff(P,y)-diff(F,y)*diff(P,x)$
Duv=diff(F,u)*diff(P,v)-diff(F,v)*diff(P,u)$
D=Dxy-Duv$

Kimura2 = [F,P,D]$

end$
