-- -*- M2-comint -*- {* hash: 655370177 *}

i1 : R = QQ[x,y,z]/ideal(x*y^2-z^9)

o1 = R

o1 : QuotientRing

i2 : J = ideal(x,y,z)

o2 = ideal (x, y, z)

o2 : Ideal of R

i3 : I = reesIdeal(J, Variable => p)

                                                             8       2  
o3 = ideal (z*p  - y*p , z*p  - x*p , y*p  - x*p , x*y*p  - z p , x*p  -
               1      2     0      2     0      1       1      2     1  
     ------------------------------------------------------------------------
      7 2     2    6 3
     z p , p p  - z p )
        2   0 1      2

o3 : Ideal of R[p , p , p ]
                 0   1   2

i4 : describe ring I

o4 = R[p , p , p , Degrees => {3:{1}}, Heft => {1, 0}, MonomialOrder =>
        0   1   2                {1}                                   
                                                                       
     ------------------------------------------------------------------------
     {MonomialSize => 32}, DegreeRank => 2]
     {GRevLex => {3:1}  }
     {Position => Up    }

i5 : I1 = first flattenRing I

               9      2                                              8   2   
o5 = ideal (- z  + x*y , p z - p y, p z - p x, p y - p x, p x*y - p z , p x -
                          1     2    0     2    0     1    1       2     1   
     ------------------------------------------------------------------------
      2 7     2    3 6
     p z , p p  - p z )
      2     0 1    2

o5 : Ideal of QQ[p , p , p , x, y, z]
                  0   1   2

i6 : describe ring oo

o6 = QQ[p , p , p , x..z, Degrees => {3:{1}, 3:{0}}, Heft => {0..1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 2]
         0   1   2                      {1}    {1}                                    {GRevLex => {3:1}  }
                                                                                      {Position => Up    }
                                                                                      {GRevLex => {3:1}  }

i7 : S = newRing(ring I1, Degrees=>{numgens ring I1:1})

o7 = S

o7 : PolynomialRing

i8 : describe S

o8 = QQ[p , p , p , x..z, Degrees => {6:1}, Heft => {1}, MonomialOrder => {MonomialSize => 32}, DegreeRank => 1]
         0   1   2                                                        {GRevLex => {3:1}  }
                                                                          {Position => Up    }
                                                                          {GRevLex => {3:1}  }

i9 : I2 = sub(I1,vars S)

               9      2                                              8   2   
o9 = ideal (- z  + x*y , p z - p y, p z - p x, p y - p x, p x*y - p z , p x -
                          1     2    0     2    0     1    1       2     1   
     ------------------------------------------------------------------------
      2 7     2    3 6
     p z , p p  - p z )
      2     0 1    2

o9 : Ideal of S

i10 : res I2

       1      7      11      6      1
o10 = S  <-- S  <-- S   <-- S  <-- S  <-- 0
                                           
      0      1      2       3      4      5

o10 : ChainComplex

i11 :