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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 = | 8814x_1^4-2212x_1^3x_2-6952x_1^2x_2^2+15554x_1x_2^3+3339x_2^4-3220x_1^
     ------------------------------------------------------------------------
     3x_3+5589x_1^2x_2x_3-7234x_1x_2^2x_3+11557x_2^3x_3+12406x_1^2x_3^2+1950x
     ------------------------------------------------------------------------
     _1x_2x_3^2+13808x_2^2x_3^2+3170x_1x_3^3-6359x_2x_3^3+13683x_3^4 |

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

o3 = | x_2^2x_3-7089x_1x_3^2-6415x_2x_3^2+2152x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+6289x_1x_3^2-9466x_2x_3^2-7676x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+221x_1x_3^2+4015x_2x_3^2-4424x_3^3
     ------------------------------------------------------------------------
     x_2^3+10805x_1x_3^2-8110x_2x_3^2+5281x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-14488x_1x_3^2+1252x_2x_3^2+14237x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+9631x_1x_3^2+5397x_2x_3^2-8927x_3^3
     ------------------------------------------------------------------------
     x_1^3-12642x_1x_3^2-12965x_2x_3^2-15200x_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 :