fromDual -- ideal from inverse system

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

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

o2 = | -3619x_1^4-7243x_1^3x_2+1927x_1^2x_2^2+6902x_1x_2^3-7898x_2^4+9722x_1^
     ------------------------------------------------------------------------
     3x_3-12785x_1^2x_2x_3-3624x_1x_2^2x_3-13396x_2^3x_3-13963x_1^2x_3^2+
     ------------------------------------------------------------------------
     10683x_1x_2x_3^2-5224x_2^2x_3^2-2588x_1x_3^3+6221x_2x_3^3-12764x_3^4 |

             1       1
o2 : Matrix R  <--- R

i3 : f = fromDual g

o3 = | x_2^2x_3+5853x_1x_3^2+11185x_2x_3^2+11227x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-10589x_1x_3^2+7148x_2x_3^2+3162x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-12690x_1x_3^2+3132x_2x_3^2+3790x_3^3
     ------------------------------------------------------------------------
     x_2^3-4635x_1x_3^2+5926x_2x_3^2-11653x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+13040x_1x_3^2-2402x_2x_3^2-3489x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+1802x_1x_3^2+7718x_2x_3^2+15172x_3^3
     ------------------------------------------------------------------------
     x_1^3-2573x_1x_3^2+6751x_2x_3^2-6615x_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