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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 = | -11962x_1^4-12363x_1^3x_2-8778x_1^2x_2^2+9048x_1x_2^3+13331x_2^4+9030x
     ------------------------------------------------------------------------
     _1^3x_3-3059x_1^2x_2x_3-7342x_1x_2^2x_3-7482x_2^3x_3-14050x_1^2x_3^2+
     ------------------------------------------------------------------------
     6314x_1x_2x_3^2+1187x_2^2x_3^2+12033x_1x_3^3+7888x_2x_3^3-3298x_3^4 |

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

o3 = | x_2^2x_3-12588x_1x_3^2+8871x_2x_3^2-12416x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-7824x_1x_3^2+3268x_2x_3^2-2951x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-9698x_1x_3^2-15686x_2x_3^2+1348x_3^3
     ------------------------------------------------------------------------
     x_2^3+11073x_1x_3^2-3358x_2x_3^2+5536x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-4973x_1x_3^2-15823x_2x_3^2+6957x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-11456x_1x_3^2-7802x_2x_3^2-7409x_3^3
     ------------------------------------------------------------------------
     x_1^3-12835x_1x_3^2+629x_2x_3^2-11233x_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 :