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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 = | -14389x_1^4+4628x_1^3x_2+5341x_1^2x_2^2+13483x_1x_2^3-10599x_2^4+3602x
     ------------------------------------------------------------------------
     _1^3x_3+5836x_1^2x_2x_3+833x_1x_2^2x_3-10158x_2^3x_3-8966x_1^2x_3^2-
     ------------------------------------------------------------------------
     8641x_1x_2x_3^2-7176x_2^2x_3^2+13583x_1x_3^3+3223x_2x_3^3-7203x_3^4 |

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

o3 = | x_2^2x_3+11502x_1x_3^2-1204x_2x_3^2-6832x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-5352x_1x_3^2+9171x_2x_3^2-2529x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-15947x_1x_3^2-2852x_2x_3^2+45x_3^3
     ------------------------------------------------------------------------
     x_2^3+9266x_1x_3^2-15195x_2x_3^2-15301x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+15016x_1x_3^2-8190x_2x_3^2-7680x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+9006x_1x_3^2+8311x_2x_3^2-1588x_3^3
     ------------------------------------------------------------------------
     x_1^3+6273x_1x_3^2-6873x_2x_3^2-13003x_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 :