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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 = | 11753x_1^4-8489x_1^3x_2-10263x_1^2x_2^2-8210x_1x_2^3-5170x_2^4+13283x_
     ------------------------------------------------------------------------
     1^3x_3-2835x_1^2x_2x_3+9906x_1x_2^2x_3-5725x_2^3x_3+15330x_1^2x_3^2-
     ------------------------------------------------------------------------
     7474x_1x_2x_3^2-14761x_2^2x_3^2-916x_1x_3^3-9677x_2x_3^3-3824x_3^4 |

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

o3 = | x_2^2x_3-694x_1x_3^2+2504x_2x_3^2+8982x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-14272x_1x_3^2-2492x_2x_3^2-5927x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+13693x_1x_3^2+15219x_2x_3^2+9655x_3^3
     ------------------------------------------------------------------------
     x_2^3-10837x_1x_3^2+12813x_2x_3^2+6508x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+6284x_1x_3^2-11086x_2x_3^2-564x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-6733x_1x_3^2-5392x_2x_3^2+8202x_3^3
     ------------------------------------------------------------------------
     x_1^3-1347x_1x_3^2+7635x_2x_3^2-14777x_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 :