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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 = | 11967x_1^4-3317x_1^3x_2+1878x_1^2x_2^2+14234x_1x_2^3-9235x_2^4+761x_1^
     ------------------------------------------------------------------------
     3x_3+2925x_1^2x_2x_3-14838x_1x_2^2x_3+13403x_2^3x_3+12649x_1^2x_3^2+
     ------------------------------------------------------------------------
     1957x_1x_2x_3^2-2491x_2^2x_3^2+9472x_1x_3^3+496x_2x_3^3+9591x_3^4 |

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

o3 = | x_2^2x_3-2310x_1x_3^2-4301x_2x_3^2-9158x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+13739x_1x_3^2+6813x_2x_3^2-5122x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+12218x_1x_3^2-5907x_2x_3^2+8839x_3^3
     ------------------------------------------------------------------------
     x_2^3-9553x_1x_3^2+874x_2x_3^2+13065x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+7452x_1x_3^2-3418x_2x_3^2+14054x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-9186x_1x_3^2+6333x_2x_3^2+15331x_3^3
     ------------------------------------------------------------------------
     x_1^3-673x_1x_3^2-11596x_2x_3^2+43x_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 :