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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 = | 14949x_1^4+10776x_1^3x_2-13665x_1^2x_2^2-9294x_1x_2^3-8425x_2^4+3945x_
     ------------------------------------------------------------------------
     1^3x_3-5848x_1^2x_2x_3-449x_1x_2^2x_3+2478x_2^3x_3+12855x_1^2x_3^2+
     ------------------------------------------------------------------------
     12661x_1x_2x_3^2-15133x_2^2x_3^2+8350x_1x_3^3+8861x_2x_3^3+13954x_3^4 |

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

o3 = | x_2^2x_3+9978x_1x_3^2-15027x_2x_3^2-10789x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-12986x_1x_3^2-554x_2x_3^2-5513x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+8512x_1x_3^2+5097x_2x_3^2-15184x_3^3
     ------------------------------------------------------------------------
     x_2^3+1039x_1x_3^2-11569x_2x_3^2+10823x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+14910x_1x_3^2-13847x_2x_3^2-7491x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-12457x_1x_3^2+10866x_2x_3^2+4958x_3^3
     ------------------------------------------------------------------------
     x_1^3-12352x_1x_3^2-11020x_2x_3^2+15882x_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 :