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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 = | -7442x_1^4-13790x_1^3x_2-1750x_1^2x_2^2-11743x_1x_2^3-12133x_2^4+7541x
     ------------------------------------------------------------------------
     _1^3x_3-4759x_1^2x_2x_3-10310x_1x_2^2x_3-7x_2^3x_3+11280x_1^2x_3^2+3139x
     ------------------------------------------------------------------------
     _1x_2x_3^2+6389x_2^2x_3^2-11148x_1x_3^3-5691x_2x_3^3+8175x_3^4 |

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

o3 = | x_2^2x_3+563x_1x_3^2+12400x_2x_3^2+15193x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+3285x_1x_3^2+5513x_2x_3^2+14843x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+10145x_1x_3^2-13187x_2x_3^2-14220x_3^3
     ------------------------------------------------------------------------
     x_2^3-3625x_1x_3^2-11727x_2x_3^2+5488x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+3304x_1x_3^2+13517x_2x_3^2+3707x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-4335x_1x_3^2-1373x_2x_3^2-4467x_3^3
     ------------------------------------------------------------------------
     x_1^3+14199x_1x_3^2+15460x_2x_3^2-11693x_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 :