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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 = | 12955x_1^4-562x_1^3x_2-8070x_1^2x_2^2+10122x_1x_2^3+5672x_2^4-14417x_1
     ------------------------------------------------------------------------
     ^3x_3+793x_1^2x_2x_3+3595x_1x_2^2x_3-11515x_2^3x_3+9418x_1^2x_3^2-5041x_
     ------------------------------------------------------------------------
     1x_2x_3^2+871x_2^2x_3^2-2953x_1x_3^3+11088x_2x_3^3-6731x_3^4 |

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

o3 = | x_2^2x_3+13562x_1x_3^2-8566x_2x_3^2-10908x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+13247x_1x_3^2+1471x_2x_3^2+5188x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+15365x_1x_3^2-14903x_2x_3^2-13084x_3^3
     ------------------------------------------------------------------------
     x_2^3+11041x_1x_3^2-2875x_2x_3^2-3258x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+9076x_1x_3^2-701x_2x_3^2+11272x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-14561x_1x_3^2-10579x_2x_3^2+729x_3^3
     ------------------------------------------------------------------------
     x_1^3+6088x_1x_3^2+8383x_2x_3^2-1663x_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 :