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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 = | -15870x_1^4-10462x_1^3x_2+4168x_1^2x_2^2+12857x_1x_2^3+8899x_2^4+6621x
     ------------------------------------------------------------------------
     _1^3x_3+10859x_1^2x_2x_3+9544x_1x_2^2x_3+15505x_2^3x_3-3604x_1^2x_3^2-
     ------------------------------------------------------------------------
     12949x_1x_2x_3^2-6703x_2^2x_3^2+13728x_1x_3^3+13489x_2x_3^3+3096x_3^4 |

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

o3 = | x_2^2x_3+12925x_1x_3^2+6009x_2x_3^2-13550x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-10340x_1x_3^2-14226x_2x_3^2-13283x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+2511x_1x_3^2-3679x_2x_3^2-9255x_3^3
     ------------------------------------------------------------------------
     x_2^3+10973x_1x_3^2+6947x_2x_3^2+5297x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-1785x_1x_3^2+13133x_2x_3^2-9955x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-3662x_1x_3^2-8500x_2x_3^2-6717x_3^3
     ------------------------------------------------------------------------
     x_1^3-8314x_1x_3^2-9653x_2x_3^2+3337x_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 :