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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 = | 3982x_1^4+11660x_1^3x_2+11822x_1^2x_2^2+13760x_1x_2^3-8451x_2^4+4334x_
     ------------------------------------------------------------------------
     1^3x_3-11099x_1^2x_2x_3+9670x_1x_2^2x_3+240x_2^3x_3-2405x_1^2x_3^2+1365x
     ------------------------------------------------------------------------
     _1x_2x_3^2-2498x_2^2x_3^2+903x_1x_3^3-11890x_2x_3^3-2480x_3^4 |

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

o3 = | x_2^2x_3-13376x_1x_3^2-2365x_2x_3^2-11186x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+11958x_1x_3^2+15251x_2x_3^2-14088x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-13352x_1x_3^2+680x_2x_3^2+4872x_3^3
     ------------------------------------------------------------------------
     x_2^3-14821x_1x_3^2+12635x_2x_3^2+13144x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-12540x_1x_3^2-10589x_2x_3^2+1556x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+5846x_1x_3^2-4732x_2x_3^2+12255x_3^3
     ------------------------------------------------------------------------
     x_1^3-13032x_1x_3^2-10x_2x_3^2+12261x_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 :