Singular

LIB "polybori.lib";
ring r0=2,x(1..4),lp;
poly f1=x(1)^2+2*x(2)*(x(3))-x(4)^3;
poly f2=x(1)^2-x(3)*x(1);
poly f3=x(2)+5-2*x(1);
poly f4=x(1)*x(2)-x(3);
ideal I=f1,f2,f3,f4;
boolean_ideal(I);
==> _[1] = x(1) + x(4)
==> _[2] = x(1)*x(3) + x(1)
==> _[3] = x(2) + 1
==> _[4] = x(1)*x(2) + x(3)
==> 
ring r1=0,x,Dp;
poly f1=x3+2*x+1;
poly f2=x10-x5+2x;
poly f3=19;
ideal I=f1,f2,f3;
boolean_ideal(I);
==> _[1] = x + 1
==> _[2] = 0
==> _[3] = 1
==> 
ring r2=32003,(x,y,z),Dp;
bring bbr2=r2;
poly f1=xyz+20*x^2*y-3*xz+15;
poly f2=32002*xy+z2;
poly f3=19;
ideal I=f1,f2,f3;
boolean_ideal(I);
==> _[1] = x*y*z + x*z + 1
==> _[2] = x*y + z
==> _[3] = 1
==> 
boolean_ideal(I,bbr2);
==> _[1] = x*y*z + x*z + 1
==> _[2] = x*y + z
==> _[3] = 1
==>