next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
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 = | 862x_1^4-11719x_1^3x_2-2486x_1^2x_2^2-1686x_1x_2^3-576x_2^4+1851x_1^3x
     ------------------------------------------------------------------------
     _3-3138x_1^2x_2x_3+8983x_1x_2^2x_3+5501x_2^3x_3-2514x_1^2x_3^2-3278x_1x_
     ------------------------------------------------------------------------
     2x_3^2-469x_2^2x_3^2-8578x_1x_3^3-6455x_2x_3^3+633x_3^4 |

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

o3 = | x_2^2x_3-5382x_1x_3^2-9909x_2x_3^2-3145x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-6487x_1x_3^2-10956x_2x_3^2-15596x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-14776x_1x_3^2+14679x_2x_3^2-5849x_3^3
     ------------------------------------------------------------------------
     x_2^3+3484x_1x_3^2-5670x_2x_3^2-9756x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-12969x_1x_3^2+9165x_2x_3^2-3634x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+15619x_1x_3^2-1577x_2x_3^2+12361x_3^3
     ------------------------------------------------------------------------
     x_1^3-4738x_1x_3^2+230x_2x_3^2+4569x_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 :