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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 = | -15052x_1^4+14919x_1^3x_2+9531x_1^2x_2^2-2138x_1x_2^3-14124x_2^4+9861x
     ------------------------------------------------------------------------
     _1^3x_3-15406x_1^2x_2x_3+4694x_1x_2^2x_3-6624x_2^3x_3+4156x_1^2x_3^2+
     ------------------------------------------------------------------------
     4570x_1x_2x_3^2+15634x_2^2x_3^2+12536x_1x_3^3+8292x_2x_3^3+10556x_3^4 |

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

o3 = | x_2^2x_3-10310x_1x_3^2+14098x_2x_3^2-3422x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+10594x_1x_3^2+12260x_2x_3^2+5310x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-129x_1x_3^2+126x_2x_3^2+5038x_3^3
     ------------------------------------------------------------------------
     x_2^3+8602x_1x_3^2-8083x_2x_3^2-8789x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+8801x_1x_3^2-12011x_2x_3^2+12292x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+3300x_1x_3^2+299x_2x_3^2+4961x_3^3
     ------------------------------------------------------------------------
     x_1^3+694x_1x_3^2+1852x_2x_3^2+3538x_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 :