CoCoASchool2007

Tutorials of the Robbiano/Kreuzer track

Tutorial 1 (82kb)

the ideals for part c.)

Use Q[x[1..4]];
IsZeroDim(Ideal([x[1]x[3], x[1]x[4]-x[2]x[3], x[2]x[4]-x[3]^3, x[2]^2x[3]-x[1]x[3]^2]));

Use Q[x[1..3]];
IsZeroDim(Ideal([x[1]^3 - x[2]x[3]^2, x[1]^2x[2]x[3] - x[2]^2, x[1]^2 + x[2]^2 + x[3]^2]));

Use Q[x[1..4]];
IsZeroDim(Ideal([x[1]x[2]-x[3]^2,x[2]^2-x[3]x[4],x[1]x[3] - x[4]^3,x[2]x[4] - x[3]^2])); 

Use Q[x[1..3]];
IsZeroDim(Ideal([x[1]^2 - x[1]x[2],x[2]^2-x[2]x[3],x[3]^2-x[3]x[1],x[1]x[2] + x[2]x[3] + x[1]x[3]]));

the ideals for part f.)

Warning: Second ideal is NOT zero dimensional!

Use Q[x,y];
ZeroDimRadical(Ideal([x^3,x^2y,x,y^2]) );

Use Q[x,y,z];
ZeroDimRadical(Ideal([x^2 +2xy + y^2, xz+ yz, xy^2+y^3 + xy + y^2,y^4+2y^3 + y^2, y^2z + yz]));

Use Q[x,y,z];
ZeroDimRadical(Ideal([x^2 + y+z -1, x+y^2 + z -1, x+y+z^2 -1]));

the ideals for part h.)

Use Q[x,y];
[IsNormalPos(Ideal([x^2+y^2-1,4xy-2x-2y+1]),I) | I In 1..NumIndets()]; 

Use Q[x,y];
[IsNormalPos(Ideal([x^2-y,x^2-3x+2]),I) | I In 1..NumIndets()];

Use Q[x,y,z];
[IsNormalPos(Ideal([yz + z, y^2+y,x+y+z,z^2-z]),I) | I In 1..NumIndets()];

the ideals for part i.)

Use Q[x,y];
[NormalPosTrafo(Ideal([x^2 + y^2 +3, x^2 - y^2 +1]),I) | I In 1..NumIndets()];

Use Q[x,y];
[NormalPosTrafo(Ideal([xy,x^2+x,y^3+2y^2 + y]),I) | I In 1..NumIndets()];

Use Q[x,y,z];
[NormalPosTrafo(Ideal([x^3 - x, y^2 -y, z^2 - z]),I) | I In 1..NumIndets()];