fromDual -- ideal from inverse system

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

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

o2 = | -9985x_1^4+612x_1^3x_2-14030x_1^2x_2^2-9578x_1x_2^3-10141x_2^4-5568x_1
     ------------------------------------------------------------------------
     ^3x_3-2013x_1^2x_2x_3-5038x_1x_2^2x_3+13897x_2^3x_3-15989x_1^2x_3^2-
     ------------------------------------------------------------------------
     8980x_1x_2x_3^2+12700x_2^2x_3^2+8563x_1x_3^3+13092x_2x_3^3+14697x_3^4 |

             1       1
o2 : Matrix R  <--- R

i3 : f = fromDual g

o3 = | x_2^2x_3+4848x_1x_3^2+4914x_2x_3^2+3835x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+5043x_1x_3^2+7417x_2x_3^2+9010x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-931x_1x_3^2-6637x_2x_3^2-11045x_3^3
     ------------------------------------------------------------------------
     x_2^3-2829x_1x_3^2+7007x_2x_3^2-9986x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+5649x_1x_3^2-5755x_2x_3^2-4930x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+2533x_1x_3^2-8908x_2x_3^2-10364x_3^3
     ------------------------------------------------------------------------
     x_1^3-3962x_1x_3^2+8797x_2x_3^2+12069x_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