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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 = | -10367x_1^4-11577x_1^3x_2+10826x_1^2x_2^2-5904x_1x_2^3+15506x_2^4+162x
     ------------------------------------------------------------------------
     _1^3x_3-7364x_1^2x_2x_3-7760x_1x_2^2x_3+10081x_2^3x_3+8570x_1^2x_3^2+
     ------------------------------------------------------------------------
     8161x_1x_2x_3^2-13625x_2^2x_3^2+7458x_1x_3^3+9784x_2x_3^3-4629x_3^4 |

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

o3 = | x_2^2x_3+15275x_1x_3^2-8823x_2x_3^2+1299x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-14557x_1x_3^2+531x_2x_3^2-14358x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+15251x_1x_3^2-8289x_2x_3^2-11703x_3^3
     ------------------------------------------------------------------------
     x_2^3+7049x_1x_3^2-10100x_2x_3^2+15972x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-6735x_1x_3^2+9152x_2x_3^2-6774x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-1413x_1x_3^2-7552x_2x_3^2+5259x_3^3
     ------------------------------------------------------------------------
     x_1^3-11639x_1x_3^2-10102x_2x_3^2-9062x_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 :