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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 = | 5869x_1^4+31x_1^3x_2+1149x_1^2x_2^2+9456x_1x_2^3-10963x_2^4-8631x_1^3x
     ------------------------------------------------------------------------
     _3-9520x_1^2x_2x_3+6672x_1x_2^2x_3-3093x_2^3x_3+2422x_1^2x_3^2-13007x_1x
     ------------------------------------------------------------------------
     _2x_3^2-6925x_2^2x_3^2+2790x_1x_3^3-408x_2x_3^3+4346x_3^4 |

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

o3 = | x_2^2x_3-14438x_1x_3^2+13159x_2x_3^2+6787x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+9819x_1x_3^2-14482x_2x_3^2-8772x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+5490x_1x_3^2+6418x_2x_3^2+1540x_3^3
     ------------------------------------------------------------------------
     x_2^3-15543x_1x_3^2-7720x_2x_3^2-9310x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-3765x_1x_3^2+2358x_2x_3^2+14846x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+10763x_1x_3^2-12658x_2x_3^2-2617x_3^3
     ------------------------------------------------------------------------
     x_1^3+4894x_1x_3^2-15951x_2x_3^2+510x_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 :