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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 = | -11560x_1^4+10268x_1^3x_2-11893x_1^2x_2^2+6705x_1x_2^3+1711x_2^4+
     ------------------------------------------------------------------------
     12260x_1^3x_3+10051x_1^2x_2x_3+9368x_1x_2^2x_3+1739x_2^3x_3-6383x_1^2x_3
     ------------------------------------------------------------------------
     ^2-12746x_1x_2x_3^2-8708x_2^2x_3^2+1292x_1x_3^3+7594x_2x_3^3+13474x_3^4
     ------------------------------------------------------------------------
     |

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

o3 = | x_2^2x_3-13198x_1x_3^2-4757x_2x_3^2+14683x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-5086x_1x_3^2+10729x_2x_3^2+5434x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-5418x_1x_3^2+9043x_2x_3^2-14550x_3^3
     ------------------------------------------------------------------------
     x_2^3+8571x_1x_3^2+2439x_2x_3^2+4822x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+8454x_1x_3^2-12206x_2x_3^2+9417x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-7907x_1x_3^2+10022x_2x_3^2-13843x_3^3
     ------------------------------------------------------------------------
     x_1^3-4443x_1x_3^2+3174x_2x_3^2-4822x_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 :