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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 = | -2147x_1^4+11145x_1^3x_2-4451x_1^2x_2^2+51x_1x_2^3-15184x_2^4+7259x_1^
     ------------------------------------------------------------------------
     3x_3+14663x_1^2x_2x_3+14145x_1x_2^2x_3-3981x_2^3x_3+5653x_1^2x_3^2-9714x
     ------------------------------------------------------------------------
     _1x_2x_3^2+59x_2^2x_3^2+14408x_1x_3^3-7840x_2x_3^3+744x_3^4 |

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

o3 = | x_2^2x_3+12437x_1x_3^2-2458x_2x_3^2-705x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-4165x_1x_3^2-5565x_2x_3^2+13856x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+8857x_1x_3^2-12825x_2x_3^2+9872x_3^3
     ------------------------------------------------------------------------
     x_2^3+9856x_1x_3^2-10433x_2x_3^2+10669x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-5290x_1x_3^2-14950x_2x_3^2-3710x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-15431x_1x_3^2+15397x_2x_3^2+13920x_3^3
     ------------------------------------------------------------------------
     x_1^3+3871x_1x_3^2-4936x_2x_3^2+3132x_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 :