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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 = | -679x_1^4-14190x_1^3x_2+6453x_1^2x_2^2+11477x_1x_2^3+1654x_2^4+3383x_1
     ------------------------------------------------------------------------
     ^3x_3-11424x_1^2x_2x_3-5245x_1x_2^2x_3+15152x_2^3x_3+11969x_1^2x_3^2-
     ------------------------------------------------------------------------
     11469x_1x_2x_3^2-13517x_2^2x_3^2+332x_1x_3^3+6692x_2x_3^3-1319x_3^4 |

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

o3 = | x_2^2x_3-8936x_1x_3^2-10106x_2x_3^2+8047x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-3497x_1x_3^2+774x_2x_3^2-9967x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-3542x_1x_3^2+7427x_2x_3^2+15059x_3^3
     ------------------------------------------------------------------------
     x_2^3-8297x_1x_3^2+3370x_2x_3^2+5437x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+1295x_1x_3^2-7790x_2x_3^2-8314x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-5627x_1x_3^2-3472x_2x_3^2+4786x_3^3
     ------------------------------------------------------------------------
     x_1^3+9484x_1x_3^2-13288x_2x_3^2-14075x_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 :