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 = | 8587x_1^4+14190x_1^3x_2+3394x_1^2x_2^2-14074x_1x_2^3+4813x_2^4-5335x_1
     ------------------------------------------------------------------------
     ^3x_3+735x_1^2x_2x_3+15156x_1x_2^2x_3-2753x_2^3x_3+8561x_1^2x_3^2-9118x_
     ------------------------------------------------------------------------
     1x_2x_3^2-11309x_2^2x_3^2+11355x_1x_3^3-14556x_2x_3^3+43x_3^4 |

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

o3 = | x_2^2x_3+527x_1x_3^2-13762x_2x_3^2+8161x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-6095x_1x_3^2-9623x_2x_3^2-742x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+8774x_1x_3^2+5444x_2x_3^2-3176x_3^3
     ------------------------------------------------------------------------
     x_2^3-6464x_1x_3^2+15657x_2x_3^2-9012x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+5650x_1x_3^2-11291x_2x_3^2-9426x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-2743x_1x_3^2+6811x_2x_3^2-7379x_3^3
     ------------------------------------------------------------------------
     x_1^3-1748x_1x_3^2+12521x_2x_3^2+12899x_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 :