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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 = | 7108x_1^4+12879x_1^3x_2-3125x_1^2x_2^2+1492x_1x_2^3-9587x_2^4+5598x_1^
     ------------------------------------------------------------------------
     3x_3+6143x_1^2x_2x_3+13606x_1x_2^2x_3-1064x_2^3x_3+15767x_1^2x_3^2+4344x
     ------------------------------------------------------------------------
     _1x_2x_3^2+3194x_2^2x_3^2+10949x_1x_3^3-6437x_2x_3^3-15482x_3^4 |

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

o3 = | x_2^2x_3-42x_1x_3^2+6104x_2x_3^2-6098x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-2667x_1x_3^2+5350x_2x_3^2-1793x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-7425x_1x_3^2+9792x_2x_3^2-1921x_3^3
     ------------------------------------------------------------------------
     x_2^3+12885x_1x_3^2+61x_2x_3^2-3725x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-8741x_1x_3^2+7215x_2x_3^2-3124x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+2232x_1x_3^2-15502x_2x_3^2+8018x_3^3
     ------------------------------------------------------------------------
     x_1^3+15168x_1x_3^2-13482x_2x_3^2-12028x_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 :