affineResultant -- affine resultant

i1 : ZZ[t,u][y,z]

o1 = ZZ[t..u][y..z]

o1 : PolynomialRing

i2 : f = {3*t*y*z-u*z^2+1, -y+t+3*u-1, u*z^4-t*y^3+t*y*z}

                  2                           4      3
o2 = {3t*y*z - u*z  + 1, - y + t + 3u - 1, u*z  - t*y  + t*y*z}

o2 : List

i3 : affineResultant f

          12         11 2         10 3         9 4          8 5          7 6
o3 = - 81t  u - 1701t  u  - 15309t  u  - 76545t u  - 229635t u  - 413343t u 
     ------------------------------------------------------------------------
              6 7          5 8       11          10 2         9 3  
     - 413343t u  - 177147t u  + 567t  u + 10206t  u  + 76545t u  +
     ------------------------------------------------------------------------
            8 4          7 5          6 6          5 7        4 8        3 9
     306181t u  + 688923t u  + 826821t u  + 413883t u  + 1215t u  + 1458t u 
     ------------------------------------------------------------------------
           2 10        10          9 2          8 3          7 4          6 5
     + 729t u   - 1701t  u - 25515t u  - 153093t u  - 459321t u  - 689265t u 
     ------------------------------------------------------------------------
              5 6        4 7        3 8        2 9        9          8 2  
     - 414693t u  - 2835t u  - 3159t u  - 1458t u  + 2835t u + 33984t u  +
     ------------------------------------------------------------------------
            7 3          6 4          5 5         4 6        3 7        2 8  
     152565t u  + 303135t u  + 220905t u  - 12150t u  - 5913t u  + 1215t u  -
     ------------------------------------------------------------------------
          8          7 2         6 3         5 4         4 5         3 6  
     2862t u - 25659t u  - 75873t u  - 70031t u  + 16263t u  + 13230t u  -
     ------------------------------------------------------------------------
         2 7        7          6 2         5 3        4 4        3 5  
     540t u  + 1809t u + 10818t u  + 15015t u  - 6609t u  - 9360t u  +
     ------------------------------------------------------------------------
         2 6       6         5 2       4 3        3 4      2 5        6  
     135t u  - 729t u - 2313t u  + 684t u  + 3165t u  - 81t u  - 54t*u  +
     ------------------------------------------------------------------------
         5        4 2       3 3      2 4        5      4       3 2      2 3  
     189t u + 135t u  - 583t u  - 38t u  + 54t*u  - 27t u + 54t u  + 47t u  -
     ------------------------------------------------------------------------
          4     2 2       3    2
     18t*u  - 9t u  + 2t*u  + u

o3 : ZZ[t..u]