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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 = | 107x_1^4+4376x_1^3x_2+3187x_1^2x_2^2+8570x_1x_2^3+10359x_2^4-5570x_1^
     ------------------------------------------------------------------------
     3x_3+3783x_1^2x_2x_3-15344x_1x_2^2x_3-7464x_2^3x_3-5307x_1^2x_3^2+8444x_
     ------------------------------------------------------------------------
     1x_2x_3^2-8251x_2^2x_3^2-10480x_1x_3^3+2653x_2x_3^3+5071x_3^4 |

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

o3 = | x_2^2x_3-1990x_1x_3^2+422x_2x_3^2-602x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-6143x_1x_3^2+11220x_2x_3^2+3149x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-9615x_1x_3^2+1977x_2x_3^2-1176x_3^3
     ------------------------------------------------------------------------
     x_2^3-7928x_1x_3^2+5677x_2x_3^2+7191x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+10146x_1x_3^2-6442x_2x_3^2+6898x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-6929x_1x_3^2-14079x_2x_3^2+896x_3^3
     ------------------------------------------------------------------------
     x_1^3-2708x_1x_3^2-1803x_2x_3^2+9150x_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 :