fromDual -- ideal from inverse system

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

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

o2 = | 1785x_1^4-5324x_1^3x_2-468x_1^2x_2^2+244x_1x_2^3+12122x_2^4+15261x_1^
     ------------------------------------------------------------------------
     3x_3-12782x_1^2x_2x_3+3681x_1x_2^2x_3-13407x_2^3x_3-11754x_1^2x_3^2-
     ------------------------------------------------------------------------
     4285x_1x_2x_3^2+3393x_2^2x_3^2+13231x_1x_3^3+15014x_2x_3^3-2981x_3^4 |

             1       1
o2 : Matrix R  <--- R

i3 : f = fromDual g

o3 = | x_2^2x_3+4504x_1x_3^2-7898x_2x_3^2+686x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+735x_1x_3^2-3776x_2x_3^2-7523x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-8043x_1x_3^2+12458x_2x_3^2+9587x_3^3
     ------------------------------------------------------------------------
     x_2^3-970x_1x_3^2+3407x_2x_3^2-12948x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+2231x_1x_3^2-12706x_2x_3^2+12953x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+5689x_1x_3^2+9230x_2x_3^2-8172x_3^3
     ------------------------------------------------------------------------
     x_1^3+730x_1x_3^2+6588x_2x_3^2+7472x_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