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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 = | -8782x_1^4+12103x_1^3x_2+13533x_1^2x_2^2+2739x_1x_2^3-13356x_2^4+9533x
     ------------------------------------------------------------------------
     _1^3x_3+7271x_1^2x_2x_3+10462x_1x_2^2x_3-11440x_2^3x_3+3691x_1^2x_3^2+
     ------------------------------------------------------------------------
     14132x_1x_2x_3^2+8965x_2^2x_3^2-2918x_1x_3^3-2289x_2x_3^3+3725x_3^4 |

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

o3 = | x_2^2x_3-676x_1x_3^2+7126x_2x_3^2-5406x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-8587x_1x_3^2-14819x_2x_3^2+13271x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-6481x_1x_3^2+10604x_2x_3^2-13760x_3^3
     ------------------------------------------------------------------------
     x_2^3-9853x_1x_3^2-13580x_2x_3^2-13457x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+7687x_1x_3^2+3571x_2x_3^2-7174x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+6678x_1x_3^2+8434x_2x_3^2-1427x_3^3
     ------------------------------------------------------------------------
     x_1^3-5575x_1x_3^2-4282x_2x_3^2-7843x_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 :