computational geometry - Prove Theorem with Groebner Basis -


i'm trying prove theorems using groebner basis (as described in cox, little , o'shea link )

the mentioned book gives excercise prove pappus theorem using given methodology, can't make work. i've tried usign sage, mathematica , singular, grobner basis computation doesn't terminate.

any idea of can do? else have done excersise before? thanks.

this singular code:

ring r= (0,u1,u2,u3,u4,u5,u6,u7),(y,x1,x2,x3,x4,x5,x6,x7),dp; poly h1=(u3 - u5)*(u4 - u6) - (u5 - u7)*(u6 - x1); poly h2=-(u1 - u4)*u3 + (u1 - x3)*x2; poly h3=-(u5 - x2)*(u6 - x3) + u5*u6; poly h4=-(u2 - u4)*u3 + (u2 - x5)*x4; poly h5=-(u7 - x4)*(x1 - x5) + u7*x1; poly h6=-(u2 - u6)*u5 + (u2 - x7)*x6; poly h7=-(u1 - x1)*u7 - (u7 - x6)*(x1 - x7); poly g=(x2 - x4)*(x3 - x5) - (x4 - x6)*(x5 - x7); poly g2=1-y*g; ideal v=h1,h2,h3,h4,h5,h6,h7,g2; std(v);


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