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fromDual -- ideal from inverse system

Synopsis

Description

For other examples, and a more precise definition, see inverse systems.
i1 : R = ZZ/32003[x_1..x_3];
i2 : g = random(R^1, R^{-4})

o2 = | 6905x_1^4-3409x_1^3x_2+7791x_1^2x_2^2+11670x_1x_2^3-15961x_2^4-14399x_
     ------------------------------------------------------------------------
     1^3x_3-4164x_1^2x_2x_3+2660x_1x_2^2x_3+6539x_2^3x_3-7781x_1^2x_3^2-
     ------------------------------------------------------------------------
     10804x_1x_2x_3^2+152x_2^2x_3^2+12652x_1x_3^3+6641x_2x_3^3-15368x_3^4 |

             1       1
o2 : Matrix R  <--- R
i3 : f = fromDual g

o3 = | x_2^2x_3+5652x_1x_3^2-2927x_2x_3^2-5914x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-15359x_1x_3^2+11097x_2x_3^2+4222x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-6234x_1x_3^2+3900x_2x_3^2+2323x_3^3
     ------------------------------------------------------------------------
     x_2^3+12197x_1x_3^2+8989x_2x_3^2-14320x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-4043x_1x_3^2+13542x_2x_3^2+11399x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+10257x_1x_3^2+13316x_2x_3^2-1570x_3^3
     ------------------------------------------------------------------------
     x_1^3+14385x_1x_3^2-12301x_2x_3^2+13873x_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

See also

Ways to use fromDual :