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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 = | 12464x_1^4-3x_1^3x_2+2750x_1^2x_2^2-295x_1x_2^3-5655x_2^4+6303x_1^3x_3
     ------------------------------------------------------------------------
     -3345x_1^2x_2x_3-8646x_1x_2^2x_3-6594x_2^3x_3+12894x_1^2x_3^2-6011x_1x_
     ------------------------------------------------------------------------
     2x_3^2-7778x_2^2x_3^2-12073x_1x_3^3+13644x_2x_3^3-13132x_3^4 |

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

o3 = | x_2^2x_3-2174x_1x_3^2-7138x_2x_3^2+5022x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+5531x_1x_3^2+7118x_2x_3^2+11137x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-1165x_1x_3^2+4550x_2x_3^2+650x_3^3
     ------------------------------------------------------------------------
     x_2^3-5551x_1x_3^2-7245x_2x_3^2-12336x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+12814x_1x_3^2-10428x_2x_3^2-7906x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+7681x_1x_3^2+13358x_2x_3^2-9321x_3^3
     ------------------------------------------------------------------------
     x_1^3-15836x_1x_3^2+15617x_2x_3^2+10926x_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 :