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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 = | 10877x_1^4-4413x_1^3x_2-14793x_1^2x_2^2+14094x_1x_2^3-14694x_2^4+6473x
     ------------------------------------------------------------------------
     _1^3x_3+11032x_1^2x_2x_3-10971x_1x_2^2x_3+324x_2^3x_3-14027x_1^2x_3^2-
     ------------------------------------------------------------------------
     8679x_1x_2x_3^2+15569x_2^2x_3^2+4003x_1x_3^3-3311x_2x_3^3-14428x_3^4 |

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

o3 = | x_2^2x_3-7397x_1x_3^2-432x_2x_3^2+9906x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-15303x_1x_3^2+13939x_2x_3^2+11868x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-6507x_1x_3^2+2708x_2x_3^2-4220x_3^3
     ------------------------------------------------------------------------
     x_2^3+417x_1x_3^2+11516x_2x_3^2+15473x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+14671x_1x_3^2-7332x_2x_3^2-1084x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+11716x_1x_3^2+6497x_2x_3^2-9328x_3^3
     ------------------------------------------------------------------------
     x_1^3+6368x_1x_3^2+3719x_2x_3^2+13282x_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 :