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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 = | -5774x_1^4+13584x_1^3x_2-13078x_1^2x_2^2-4592x_1x_2^3+13785x_2^4-6265x
     ------------------------------------------------------------------------
     _1^3x_3-233x_1^2x_2x_3+349x_1x_2^2x_3+14358x_2^3x_3-2774x_1^2x_3^2-6506x
     ------------------------------------------------------------------------
     _1x_2x_3^2+3721x_2^2x_3^2+12013x_1x_3^3-7745x_2x_3^3+5260x_3^4 |

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

o3 = | x_2^2x_3-9750x_1x_3^2-918x_2x_3^2-10802x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+5190x_1x_3^2+7959x_2x_3^2+10472x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+7875x_1x_3^2-3409x_2x_3^2-11067x_3^3
     ------------------------------------------------------------------------
     x_2^3+2655x_1x_3^2+7118x_2x_3^2-3854x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-8957x_1x_3^2+2497x_2x_3^2-1293x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+2794x_1x_3^2-1677x_2x_3^2+5618x_3^3
     ------------------------------------------------------------------------
     x_1^3+4036x_1x_3^2+12873x_2x_3^2+40x_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 :