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 = | 6299x_1^4-170x_1^3x_2-12101x_1^2x_2^2+5874x_1x_2^3+7506x_2^4-10313x_1^
     ------------------------------------------------------------------------
     3x_3-7126x_1^2x_2x_3-323x_1x_2^2x_3-13331x_2^3x_3-6415x_1^2x_3^2-7409x_
     ------------------------------------------------------------------------
     1x_2x_3^2-10288x_2^2x_3^2+1333x_1x_3^3+15778x_2x_3^3+7090x_3^4 |

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

o3 = | x_2^2x_3+11697x_1x_3^2-7768x_2x_3^2+1832x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-11107x_1x_3^2-3794x_2x_3^2-1357x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-8712x_1x_3^2+8499x_2x_3^2-10021x_3^3
     ------------------------------------------------------------------------
     x_2^3+11272x_1x_3^2+3750x_2x_3^2-2270x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+15066x_1x_3^2-8927x_2x_3^2-6154x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+6777x_1x_3^2+2952x_2x_3^2-2620x_3^3
     ------------------------------------------------------------------------
     x_1^3+5570x_1x_3^2+15339x_2x_3^2+13311x_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 :