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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 = | 10644x_1^4-15225x_1^3x_2+11351x_1^2x_2^2+5648x_1x_2^3-5419x_2^4-7051x_
     ------------------------------------------------------------------------
     1^3x_3-1154x_1^2x_2x_3-3287x_1x_2^2x_3-78x_2^3x_3+9825x_1^2x_3^2+7219x_
     ------------------------------------------------------------------------
     1x_2x_3^2+13960x_2^2x_3^2-4626x_1x_3^3+661x_2x_3^3+2518x_3^4 |

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

o3 = | x_2^2x_3+9013x_1x_3^2+13827x_2x_3^2+8640x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+12488x_1x_3^2-10209x_2x_3^2-2062x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-9532x_1x_3^2+10025x_2x_3^2-13208x_3^3
     ------------------------------------------------------------------------
     x_2^3+3629x_1x_3^2-7004x_2x_3^2+1490x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+5172x_1x_3^2-5996x_2x_3^2+2066x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+15274x_1x_3^2+10744x_2x_3^2+3177x_3^3
     ------------------------------------------------------------------------
     x_1^3-10172x_1x_3^2-4499x_2x_3^2-3752x_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 :