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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 = | 3246x_1^4+2510x_1^3x_2-9686x_1^2x_2^2+1581x_1x_2^3-15624x_2^4+11625x_1
     ------------------------------------------------------------------------
     ^3x_3-6302x_1^2x_2x_3-483x_1x_2^2x_3-3213x_2^3x_3+12458x_1^2x_3^2+10797x
     ------------------------------------------------------------------------
     _1x_2x_3^2-6104x_2^2x_3^2-4846x_1x_3^3+5341x_2x_3^3+9391x_3^4 |

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

o3 = | x_2^2x_3+5335x_1x_3^2-11467x_2x_3^2-9311x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+738x_1x_3^2+11557x_2x_3^2-8974x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-14005x_1x_3^2+3186x_2x_3^2+6554x_3^3
     ------------------------------------------------------------------------
     x_2^3-11737x_1x_3^2+3227x_2x_3^2-6341x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+15981x_1x_3^2-1862x_2x_3^2-14631x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-430x_1x_3^2+11913x_2x_3^2+13689x_3^3
     ------------------------------------------------------------------------
     x_1^3-15194x_1x_3^2+5661x_2x_3^2-12387x_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 :