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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 = | -14788x_1^4+15540x_1^3x_2-13296x_1^2x_2^2+8852x_1x_2^3+14623x_2^4+
     ------------------------------------------------------------------------
     1851x_1^3x_3+12538x_1^2x_2x_3+1190x_1x_2^2x_3+6498x_2^3x_3+15771x_1^2x_3
     ------------------------------------------------------------------------
     ^2-4450x_1x_2x_3^2-5133x_2^2x_3^2+7694x_1x_3^3+12093x_2x_3^3+14218x_3^4
     ------------------------------------------------------------------------
     |

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

o3 = | x_2^2x_3+14246x_1x_3^2+7886x_2x_3^2-15922x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+15717x_1x_3^2+12939x_2x_3^2-9856x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-11160x_1x_3^2-3330x_2x_3^2+5996x_3^3
     ------------------------------------------------------------------------
     x_2^3-12803x_1x_3^2+14663x_2x_3^2-5753x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-2323x_1x_3^2-4575x_2x_3^2+3935x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+7131x_1x_3^2+1066x_2x_3^2-7418x_3^3
     ------------------------------------------------------------------------
     x_1^3-3683x_1x_3^2-11762x_2x_3^2-11626x_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 :