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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 = | 4421x_1^4+1931x_1^3x_2-13325x_1^2x_2^2-1388x_1x_2^3+9943x_2^4-15504x_1
     ------------------------------------------------------------------------
     ^3x_3-4457x_1^2x_2x_3-13650x_1x_2^2x_3+5177x_2^3x_3+4754x_1^2x_3^2+
     ------------------------------------------------------------------------
     12023x_1x_2x_3^2+6770x_2^2x_3^2-15591x_1x_3^3-9378x_2x_3^3+14886x_3^4 |

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

o3 = | x_2^2x_3-1899x_1x_3^2-6764x_2x_3^2-7590x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+3187x_1x_3^2+1586x_2x_3^2-2582x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+6693x_1x_3^2+11150x_2x_3^2+6890x_3^3
     ------------------------------------------------------------------------
     x_2^3-7508x_1x_3^2+10833x_2x_3^2+356x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+4006x_1x_3^2+14302x_2x_3^2+3571x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+9563x_1x_3^2+1921x_2x_3^2+6329x_3^3
     ------------------------------------------------------------------------
     x_1^3-10981x_1x_3^2-11062x_2x_3^2-9949x_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 :