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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 = | 1685x_1^4+7937x_1^3x_2+8386x_1^2x_2^2-3226x_1x_2^3-4557x_2^4+970x_1^3x
     ------------------------------------------------------------------------
     _3-10853x_1^2x_2x_3+1970x_1x_2^2x_3-13668x_2^3x_3+4125x_1^2x_3^2+325x_1x
     ------------------------------------------------------------------------
     _2x_3^2+6223x_2^2x_3^2+10445x_1x_3^3+11742x_2x_3^3-12793x_3^4 |

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

o3 = | x_2^2x_3+3802x_1x_3^2-1216x_2x_3^2-2812x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+14318x_1x_3^2+6105x_2x_3^2+9366x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-3933x_1x_3^2-15288x_2x_3^2+7498x_3^3
     ------------------------------------------------------------------------
     x_2^3+7060x_1x_3^2+7139x_2x_3^2-3537x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-12219x_1x_3^2+8373x_2x_3^2+9534x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+13845x_1x_3^2-8077x_2x_3^2+9931x_3^3
     ------------------------------------------------------------------------
     x_1^3-1956x_1x_3^2+8064x_2x_3^2+11138x_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 :