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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 = | -10741x_1^4-226x_1^3x_2+11103x_1^2x_2^2+6367x_1x_2^3-13686x_2^4+9517x_
     ------------------------------------------------------------------------
     1^3x_3-7659x_1^2x_2x_3+422x_1x_2^2x_3+5727x_2^3x_3+14097x_1^2x_3^2-2976x
     ------------------------------------------------------------------------
     _1x_2x_3^2+12443x_2^2x_3^2-4017x_1x_3^3-1610x_2x_3^3+14971x_3^4 |

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

o3 = | x_2^2x_3+5426x_1x_3^2+14602x_2x_3^2-5288x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+2413x_1x_3^2-49x_2x_3^2+14860x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+14433x_1x_3^2+11225x_2x_3^2-4453x_3^3
     ------------------------------------------------------------------------
     x_2^3-2512x_1x_3^2+13261x_2x_3^2+7278x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+14073x_1x_3^2+15620x_2x_3^2-6327x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+8398x_1x_3^2-11608x_2x_3^2-7372x_3^3
     ------------------------------------------------------------------------
     x_1^3-7276x_1x_3^2-14602x_2x_3^2-5740x_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 :