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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 = | 5447x_1^4+7657x_1^3x_2-9240x_1^2x_2^2-12505x_1x_2^3+15649x_2^4-14125x_
     ------------------------------------------------------------------------
     1^3x_3+1456x_1^2x_2x_3+14365x_1x_2^2x_3-6533x_2^3x_3+15590x_1^2x_3^2-
     ------------------------------------------------------------------------
     6402x_1x_2x_3^2-12221x_2^2x_3^2+12694x_1x_3^3-607x_2x_3^3-5019x_3^4 |

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

o3 = | x_2^2x_3-8281x_1x_3^2-9853x_2x_3^2+4794x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+12052x_1x_3^2+12609x_2x_3^2+9412x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-29x_1x_3^2-10329x_2x_3^2-3259x_3^3
     ------------------------------------------------------------------------
     x_2^3+1753x_1x_3^2-9282x_2x_3^2-5202x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+3927x_1x_3^2-10549x_2x_3^2-2932x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-501x_1x_3^2+13742x_2x_3^2-7947x_3^3
     ------------------------------------------------------------------------
     x_1^3-11360x_1x_3^2+6170x_2x_3^2+11156x_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 :