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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 = | -15363x_1^4+5050x_1^3x_2-6070x_1^2x_2^2+7890x_1x_2^3-9511x_2^4-14695x_
     ------------------------------------------------------------------------
     1^3x_3-9649x_1^2x_2x_3+2389x_1x_2^2x_3+6247x_2^3x_3-12738x_1^2x_3^2-
     ------------------------------------------------------------------------
     4306x_1x_2x_3^2+5785x_2^2x_3^2+6828x_1x_3^3-11610x_2x_3^3+12253x_3^4 |

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

o3 = | x_2^2x_3+13207x_1x_3^2+3599x_2x_3^2+4724x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+11273x_1x_3^2+14943x_2x_3^2-15154x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-11350x_1x_3^2+5263x_2x_3^2+7818x_3^3
     ------------------------------------------------------------------------
     x_2^3-7559x_1x_3^2-2935x_2x_3^2+6947x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+1400x_1x_3^2-1626x_2x_3^2-4609x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-4928x_1x_3^2-14425x_2x_3^2-2524x_3^3
     ------------------------------------------------------------------------
     x_1^3-13038x_1x_3^2+11771x_2x_3^2-1182x_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 :