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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 = | 141x_1^4+8998x_1^3x_2+4869x_1^2x_2^2-1560x_1x_2^3+2250x_2^4+1077x_1^3x
     ------------------------------------------------------------------------
     _3+2749x_1^2x_2x_3+12955x_1x_2^2x_3-7948x_2^3x_3-497x_1^2x_3^2+12508x_1x
     ------------------------------------------------------------------------
     _2x_3^2-12049x_2^2x_3^2+8392x_1x_3^3+1417x_2x_3^3+8016x_3^4 |

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

o3 = | x_2^2x_3+15772x_1x_3^2-8049x_2x_3^2-643x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+4639x_1x_3^2-6777x_2x_3^2-14771x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+1291x_1x_3^2+7125x_2x_3^2-15722x_3^3
     ------------------------------------------------------------------------
     x_2^3+7825x_1x_3^2+9389x_2x_3^2+1819x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-13151x_1x_3^2+2689x_2x_3^2+13243x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-5387x_1x_3^2-283x_2x_3^2+4308x_3^3
     ------------------------------------------------------------------------
     x_1^3-10829x_1x_3^2+10095x_2x_3^2-4453x_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 :