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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 = | 12771x_1^4+4571x_1^3x_2+1498x_1^2x_2^2+458x_1x_2^3+14376x_2^4+6687x_1^
     ------------------------------------------------------------------------
     3x_3-15343x_1^2x_2x_3+3747x_1x_2^2x_3-7359x_2^3x_3-12664x_1^2x_3^2+4490x
     ------------------------------------------------------------------------
     _1x_2x_3^2+8217x_2^2x_3^2+7994x_1x_3^3-3319x_2x_3^3+11080x_3^4 |

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

o3 = | x_2^2x_3-14071x_1x_3^2+8928x_2x_3^2-4571x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+3319x_1x_3^2+3372x_2x_3^2+15356x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+248x_1x_3^2-10721x_2x_3^2+6746x_3^3
     ------------------------------------------------------------------------
     x_2^3-258x_1x_3^2+742x_2x_3^2+11665x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-4482x_1x_3^2+4526x_2x_3^2-13622x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-5270x_1x_3^2+4302x_2x_3^2+10040x_3^3
     ------------------------------------------------------------------------
     x_1^3+3126x_1x_3^2+14894x_2x_3^2-8207x_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 :