[IVA] Chapter 2, Section 8, Exercise 1,7

Mac版のAsirで計算しました

Exersise 1

$ /Applications/cfep.app/OpenXM/bin/openxm asir
[2189] G=gr([-x^3+y, x^2*y-z], [x,y,z], 0);
[-z*x+y^2,y*x^2-z,-x^3+y]
[2190] p_nf(x*y^3-z^2+y^5-z^3, G, [x,y,z], 0);
0

Exersise 7

$ /Applications/cfep.app/OpenXM/bin/openxm asir
[1891] load("gr");
[1998] load("noro_pd.rr");
[2182] B=[u*t-x, 1-u-y, u+t-u*t-z];
[-x+t*u,-y-u+1,-z+(-t+1)*u+t]
[2183] V=[u,t,x,y,z];
[u,t,x,y,z]
[2184] G=gr(B,V,2);
[y*x+y^2+(z-2)*y-z+1,-x-y-z+t+1,-y-u+1]
[2185] noro_pd.elimination(G,[x,y,z]);
[y*x+y^2+(z-2)*y-z+1]