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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 = | -13229x_1^4+5837x_1^3x_2-8355x_1^2x_2^2-6915x_1x_2^3-14855x_2^4+4400x_
     ------------------------------------------------------------------------
     1^3x_3+1852x_1^2x_2x_3-13277x_1x_2^2x_3+3694x_2^3x_3+1557x_1^2x_3^2+
     ------------------------------------------------------------------------
     6811x_1x_2x_3^2-597x_2^2x_3^2-8568x_1x_3^3+14940x_2x_3^3-9451x_3^4 |

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

o3 = | x_2^2x_3+7707x_1x_3^2-7451x_2x_3^2-2085x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+14671x_1x_3^2-6923x_2x_3^2+801x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-14392x_1x_3^2+8553x_2x_3^2-481x_3^3
     ------------------------------------------------------------------------
     x_2^3-7086x_1x_3^2+838x_2x_3^2+8301x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+4473x_1x_3^2-1520x_2x_3^2+4661x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-12499x_1x_3^2-7490x_2x_3^2-7149x_3^3
     ------------------------------------------------------------------------
     x_1^3+10288x_1x_3^2-3769x_2x_3^2+9181x_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 :