fromDual -- ideal from inverse system

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

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

o2 = | -13289x_1^4-7905x_1^3x_2+2241x_1^2x_2^2+5063x_1x_2^3+14428x_2^4+10651x
     ------------------------------------------------------------------------
     _1^3x_3-7369x_1^2x_2x_3+3248x_1x_2^2x_3+13696x_2^3x_3+11849x_1^2x_3^2+
     ------------------------------------------------------------------------
     4346x_1x_2x_3^2+11804x_2^2x_3^2-11701x_1x_3^3-3842x_2x_3^3-8592x_3^4 |

             1       1
o2 : Matrix R  <--- R

i3 : f = fromDual g

o3 = | x_2^2x_3-593x_1x_3^2+9861x_2x_3^2-2457x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-10714x_1x_3^2-6944x_2x_3^2+10828x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-14610x_1x_3^2-51x_2x_3^2+5547x_3^3
     ------------------------------------------------------------------------
     x_2^3+218x_1x_3^2+12299x_2x_3^2+12948x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-3123x_1x_3^2+1097x_2x_3^2-13397x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-8601x_1x_3^2-14227x_2x_3^2-13981x_3^3
     ------------------------------------------------------------------------
     x_1^3+12106x_1x_3^2+11033x_2x_3^2-13243x_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