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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 = | 11200x_1^4+12039x_1^3x_2+7829x_1^2x_2^2+9006x_1x_2^3+4867x_2^4-12902x_
     ------------------------------------------------------------------------
     1^3x_3+15030x_1^2x_2x_3+4702x_1x_2^2x_3-278x_2^3x_3+6817x_1^2x_3^2-7154x
     ------------------------------------------------------------------------
     _1x_2x_3^2+5293x_2^2x_3^2+12025x_1x_3^3-9956x_2x_3^3-7876x_3^4 |

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

o3 = | x_2^2x_3-12355x_1x_3^2+6934x_2x_3^2+8739x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+1235x_1x_3^2-6478x_2x_3^2-9069x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-9518x_1x_3^2-1516x_2x_3^2-13464x_3^3
     ------------------------------------------------------------------------
     x_2^3-12650x_1x_3^2+9513x_2x_3^2-1693x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+2975x_1x_3^2+1053x_2x_3^2-14663x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+9718x_1x_3^2+1703x_2x_3^2-9857x_3^3
     ------------------------------------------------------------------------
     x_1^3-13349x_1x_3^2+2226x_2x_3^2+15068x_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 :