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Macaulay2Doc :: fromDual

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 = | -4729x_1^4-10226x_1^3x_2-10744x_1^2x_2^2-13356x_1x_2^3+4372x_2^4-
     ------------------------------------------------------------------------
     10972x_1^3x_3+7598x_1^2x_2x_3+9279x_1x_2^2x_3-9818x_2^3x_3-2833x_1^2x_3^
     ------------------------------------------------------------------------
     2+8959x_1x_2x_3^2-4184x_2^2x_3^2-2486x_1x_3^3-14085x_2x_3^3-13253x_3^4 |

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

o3 = | x_2^2x_3+3045x_1x_3^2+5508x_2x_3^2-3699x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+3067x_1x_3^2-6460x_2x_3^2-4875x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+11317x_1x_3^2+1298x_2x_3^2-15574x_3^3
     ------------------------------------------------------------------------
     x_2^3+8520x_1x_3^2+13875x_2x_3^2-5039x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-952x_1x_3^2+14186x_2x_3^2-3898x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-4040x_1x_3^2+8623x_2x_3^2+6131x_3^3
     ------------------------------------------------------------------------
     x_1^3+854x_1x_3^2-3915x_2x_3^2+4432x_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 :