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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 = | 2239x_1^4-6867x_1^3x_2-5559x_1^2x_2^2-7130x_1x_2^3+4461x_2^4-3405x_1^
     ------------------------------------------------------------------------
     3x_3+6794x_1^2x_2x_3+445x_1x_2^2x_3+10385x_2^3x_3+9170x_1^2x_3^2-10877x_
     ------------------------------------------------------------------------
     1x_2x_3^2+10563x_2^2x_3^2+13092x_1x_3^3+6669x_2x_3^3-11217x_3^4 |

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

o3 = | x_2^2x_3+11699x_1x_3^2+10545x_2x_3^2-1961x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+11945x_1x_3^2-14334x_2x_3^2+11507x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+13343x_1x_3^2-15657x_2x_3^2+12177x_3^3
     ------------------------------------------------------------------------
     x_2^3+8114x_1x_3^2+10662x_2x_3^2-13799x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+13830x_1x_3^2+4880x_2x_3^2-4295x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-4535x_1x_3^2+8484x_2x_3^2+7940x_3^3
     ------------------------------------------------------------------------
     x_1^3-10856x_1x_3^2-11173x_2x_3^2-12552x_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 :