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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 = | 4816x_1^4+3777x_1^3x_2+3711x_1^2x_2^2+6295x_1x_2^3+15024x_2^4+11156x_1
     ------------------------------------------------------------------------
     ^3x_3+9677x_1^2x_2x_3-11667x_1x_2^2x_3+513x_2^3x_3-14649x_1^2x_3^2-
     ------------------------------------------------------------------------
     10246x_1x_2x_3^2-15307x_2^2x_3^2+1349x_1x_3^3-11410x_2x_3^3+9008x_3^4 |

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

o3 = | x_2^2x_3+14659x_1x_3^2-1458x_2x_3^2+6561x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+11699x_1x_3^2+4464x_2x_3^2+15965x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-8417x_1x_3^2+6639x_2x_3^2+2097x_3^3
     ------------------------------------------------------------------------
     x_2^3-9613x_1x_3^2+1254x_2x_3^2+x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+13974x_1x_3^2+6951x_2x_3^2-3636x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-10045x_1x_3^2-2689x_2x_3^2+2396x_3^3
     ------------------------------------------------------------------------
     x_1^3-11647x_1x_3^2-485x_2x_3^2+7385x_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 :