-- -*- M2-comint -*- {* hash: -879584816 *}

i1 : loadPackage "Elimination";

i2 : A = QQ[t,x,y,z];

i3 : I = ideal"t2+x2+y2+z2,t2+2x2-xy-z2,t+y3-z3";

o3 : Ideal of A

i4 : eliminate(I,t)

             2          2     2   6     3 3    6           2     2
o4 = ideal (x  - x*y - y  - 2z , y  - 2y z  + z  + x*y + 2y  + 3z )

o4 : Ideal of A

i5 : A1 = QQ[t,x,y,z,MonomialOrder=>{1,3}];

i6 : I = substitute(I,A1);

o6 : Ideal of A1

i7 : transpose gens gb I

o7 = {-2} | x2-xy-y2-2z2           |
     {-6} | y6-2y3z3+z6+xy+2y2+3z2 |
     {-3} | t+y3-z3                |

              3        1
o7 : Matrix A1  <--- A1

i8 : A2 = QQ[t,x,y,z,MonomialOrder=>Weights=>{1}];

i9 : I = substitute(I,A2);

o9 : Ideal of A2

i10 : transpose gens gb I

o10 = {-2} | x2-xy-y2-2z2           |
      {-6} | y6-2y3z3+z6+xy+2y2+3z2 |
      {-3} | t+y3-z3                |

               3        1
o10 : Matrix A2  <--- A2

i11 : A3 = QQ[t,x,y,z,MonomialOrder=>Eliminate 1];

i12 : I = substitute(I,A3);

o12 : Ideal of A3

i13 : transpose gens gb I

o13 = {-2} | x2-xy-y2-2z2           |
      {-6} | y6-2y3z3+z6+xy+2y2+3z2 |
      {-3} | t+y3-z3                |

               3        1
o13 : Matrix A3  <--- A3

i14 :