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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 = | 7918x_1^4-12499x_1^3x_2+6849x_1^2x_2^2-12376x_1x_2^3+15953x_2^4-12640x
     ------------------------------------------------------------------------
     _1^3x_3-9768x_1^2x_2x_3-14116x_1x_2^2x_3+7943x_2^3x_3-5993x_1^2x_3^2+
     ------------------------------------------------------------------------
     14485x_1x_2x_3^2-11606x_2^2x_3^2+11742x_1x_3^3-6229x_2x_3^3-11315x_3^4 |

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

o3 = | x_2^2x_3+12095x_1x_3^2-2414x_2x_3^2+586x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-5841x_1x_3^2+6193x_2x_3^2-12855x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+6434x_1x_3^2+6181x_2x_3^2-13773x_3^3
     ------------------------------------------------------------------------
     x_2^3+1452x_1x_3^2+7452x_2x_3^2-5856x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-6494x_1x_3^2+1596x_2x_3^2-14984x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+1472x_1x_3^2-6853x_2x_3^2+163x_3^3
     ------------------------------------------------------------------------
     x_1^3-3916x_1x_3^2+15128x_2x_3^2+2620x_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 :