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 = | -14831x_1^4-11326x_1^3x_2-2950x_1^2x_2^2+10279x_1x_2^3-6359x_2^4+8547x
     ------------------------------------------------------------------------
     _1^3x_3+8156x_1^2x_2x_3-10861x_1x_2^2x_3+15753x_2^3x_3-7991x_1^2x_3^2-
     ------------------------------------------------------------------------
     13769x_1x_2x_3^2-13133x_2^2x_3^2+4344x_1x_3^3-3758x_2x_3^3+3843x_3^4 |

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

o3 = | x_2^2x_3-13188x_1x_3^2+5407x_2x_3^2-5351x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-8328x_1x_3^2+8905x_2x_3^2+3069x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-325x_1x_3^2+9272x_2x_3^2-6028x_3^3
     ------------------------------------------------------------------------
     x_2^3+14697x_1x_3^2-15454x_2x_3^2+4704x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-6701x_1x_3^2+14485x_2x_3^2+2880x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-4341x_1x_3^2-14005x_2x_3^2+11912x_3^3
     ------------------------------------------------------------------------
     x_1^3+13485x_1x_3^2+4675x_2x_3^2+9754x_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 :