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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 = | -9952x_1^4+5620x_1^3x_2+14400x_1^2x_2^2-12569x_1x_2^3+5474x_2^4+15648x
     ------------------------------------------------------------------------
     _1^3x_3-15320x_1^2x_2x_3+13342x_1x_2^2x_3-11270x_2^3x_3-8699x_1^2x_3^2-
     ------------------------------------------------------------------------
     11624x_1x_2x_3^2-5424x_2^2x_3^2+11148x_1x_3^3+11261x_2x_3^3+5940x_3^4 |

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

o3 = | x_2^2x_3+15499x_1x_3^2-1673x_2x_3^2-6385x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-10509x_1x_3^2+15285x_2x_3^2+6065x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-7862x_1x_3^2-3782x_2x_3^2-7054x_3^3
     ------------------------------------------------------------------------
     x_2^3+7362x_1x_3^2-2653x_2x_3^2-7002x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+4482x_1x_3^2+8111x_2x_3^2+2302x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+405x_1x_3^2+655x_2x_3^2-13071x_3^3
     ------------------------------------------------------------------------
     x_1^3+4506x_1x_3^2+11526x_2x_3^2+9742x_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 :