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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 = | 15445x_1^4-4076x_1^3x_2-7685x_1^2x_2^2-14055x_1x_2^3-7929x_2^4+2218x_1
     ------------------------------------------------------------------------
     ^3x_3-13161x_1^2x_2x_3-7853x_1x_2^2x_3+12741x_2^3x_3-3499x_1^2x_3^2+
     ------------------------------------------------------------------------
     14002x_1x_2x_3^2+8757x_2^2x_3^2+11926x_1x_3^3+15970x_2x_3^3-12599x_3^4 |

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

o3 = | x_2^2x_3+107x_1x_3^2+896x_2x_3^2+3440x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+12700x_1x_3^2+324x_2x_3^2-9719x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+9392x_1x_3^2-6361x_2x_3^2-2818x_3^3
     ------------------------------------------------------------------------
     x_2^3-6824x_1x_3^2+5382x_2x_3^2+2830x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-524x_1x_3^2-10079x_2x_3^2-6221x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-5376x_1x_3^2-237x_2x_3^2-11893x_3^3
     ------------------------------------------------------------------------
     x_1^3+11543x_1x_3^2-4190x_2x_3^2-11510x_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 :