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Macaulay2Doc :: fromDual

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 = | -5640x_1^4+5920x_1^3x_2+14248x_1^2x_2^2+8697x_1x_2^3+5538x_2^4+13486x_
     ------------------------------------------------------------------------
     1^3x_3-3997x_1^2x_2x_3-8402x_1x_2^2x_3-13634x_2^3x_3+6475x_1^2x_3^2+
     ------------------------------------------------------------------------
     14252x_1x_2x_3^2-4279x_2^2x_3^2-14716x_1x_3^3-5849x_2x_3^3+11851x_3^4 |

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

o3 = | x_2^2x_3+15682x_1x_3^2-5983x_2x_3^2-11456x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+10642x_1x_3^2-11739x_2x_3^2-8259x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-13285x_1x_3^2-9774x_2x_3^2-9693x_3^3
     ------------------------------------------------------------------------
     x_2^3+11842x_1x_3^2+12164x_2x_3^2-4375x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-80x_1x_3^2-11042x_2x_3^2-1603x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+1610x_1x_3^2+15194x_2x_3^2-14522x_3^3
     ------------------------------------------------------------------------
     x_1^3-2138x_1x_3^2-6273x_2x_3^2-14145x_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 :