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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 = | 6978x_1^4-12248x_1^3x_2+6818x_1^2x_2^2+10939x_1x_2^3-8601x_2^4-601x_1^
     ------------------------------------------------------------------------
     3x_3+4019x_1^2x_2x_3-12500x_1x_2^2x_3+12826x_2^3x_3+13852x_1^2x_3^2+
     ------------------------------------------------------------------------
     14311x_1x_2x_3^2-2165x_2^2x_3^2-11791x_1x_3^3-10893x_2x_3^3-859x_3^4 |

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

o3 = | x_2^2x_3-1054x_1x_3^2+2325x_2x_3^2-1308x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+5620x_1x_3^2-3615x_2x_3^2+421x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+10713x_1x_3^2+10725x_2x_3^2+12998x_3^3
     ------------------------------------------------------------------------
     x_2^3+10424x_1x_3^2-85x_2x_3^2+7033x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-1428x_1x_3^2+1977x_2x_3^2+2750x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-8119x_1x_3^2+7138x_2x_3^2-14908x_3^3
     ------------------------------------------------------------------------
     x_1^3+8273x_1x_3^2+11070x_2x_3^2-4844x_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 :