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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 = | -12880x_1^4-5403x_1^3x_2-1672x_1^2x_2^2+4636x_1x_2^3-923x_2^4-4063x_1^
     ------------------------------------------------------------------------
     3x_3-4350x_1^2x_2x_3-3943x_1x_2^2x_3+1331x_2^3x_3+9861x_1^2x_3^2+15373x_
     ------------------------------------------------------------------------
     1x_2x_3^2+9072x_2^2x_3^2+5658x_1x_3^3+13110x_2x_3^3+3441x_3^4 |

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

o3 = | x_2^2x_3+6365x_1x_3^2-7815x_2x_3^2+11131x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-13039x_1x_3^2-5448x_2x_3^2+12635x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+5703x_1x_3^2+7661x_2x_3^2-14266x_3^3
     ------------------------------------------------------------------------
     x_2^3+8569x_1x_3^2-2834x_2x_3^2-2614x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+2777x_1x_3^2-12115x_2x_3^2+8371x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-1333x_1x_3^2-13152x_2x_3^2-15834x_3^3
     ------------------------------------------------------------------------
     x_1^3-14217x_1x_3^2-11370x_2x_3^2-2015x_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 :