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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 = | 12003x_1^4+12972x_1^3x_2-10756x_1^2x_2^2+1712x_1x_2^3+6048x_2^4-1233x_
     ------------------------------------------------------------------------
     1^3x_3-11346x_1^2x_2x_3+8140x_1x_2^2x_3+12592x_2^3x_3+14335x_1^2x_3^2-
     ------------------------------------------------------------------------
     8098x_1x_2x_3^2-2430x_2^2x_3^2+8660x_1x_3^3+4625x_2x_3^3-2379x_3^4 |

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

o3 = | x_2^2x_3+14451x_1x_3^2+5786x_2x_3^2+8536x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+8661x_1x_3^2-5341x_2x_3^2+6572x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+14462x_1x_3^2+8398x_2x_3^2+12410x_3^3
     ------------------------------------------------------------------------
     x_2^3+13695x_1x_3^2+8258x_2x_3^2+13031x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+10494x_1x_3^2+864x_2x_3^2+1598x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+15166x_1x_3^2+7646x_2x_3^2-10203x_3^3
     ------------------------------------------------------------------------
     x_1^3-11257x_1x_3^2-7021x_2x_3^2-14607x_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 :