fromDual -- ideal from inverse system

i1 : R = ZZ/32003[x_1..x_3];

i2 : g = random(R^1, R^{-4})

o2 = | 12167x_1^4+10922x_1^3x_2+9624x_1^2x_2^2+2575x_1x_2^3-15069x_2^4+12897x
     ------------------------------------------------------------------------
     _1^3x_3+4146x_1^2x_2x_3-7857x_1x_2^2x_3-3797x_2^3x_3-11390x_1^2x_3^2-
     ------------------------------------------------------------------------
     3298x_1x_2x_3^2+15473x_2^2x_3^2+826x_1x_3^3+1996x_2x_3^3-6482x_3^4 |

             1       1
o2 : Matrix R  <--- R

i3 : f = fromDual g

o3 = | x_2^2x_3+8698x_1x_3^2+5173x_2x_3^2+15575x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-8040x_1x_3^2+3292x_2x_3^2-14349x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+12219x_1x_3^2+6372x_2x_3^2-6120x_3^3
     ------------------------------------------------------------------------
     x_2^3-6766x_1x_3^2+8044x_2x_3^2+6270x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-15053x_1x_3^2-7990x_2x_3^2+15532x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+12120x_1x_3^2+1025x_2x_3^2-15775x_3^3
     ------------------------------------------------------------------------
     x_1^3-64x_1x_3^2+9099x_2x_3^2+2771x_3^3 |

             1       7
o3 : Matrix R  <--- R

i4 : res ideal f

      1      7      7      1
o4 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o4 : ChainComplex

i5 : betti oo

            0 1 2 3
o5 = total: 1 7 7 1
         0: 1 . . .
         1: . . . .
         2: . 7 7 .
         3: . . . .
         4: . . . 1

o5 : BettiTally