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 = | -8433x_1^4-5675x_1^3x_2-12017x_1^2x_2^2-15807x_1x_2^3-10927x_2^4+2741x
     ------------------------------------------------------------------------
     _1^3x_3+1762x_1^2x_2x_3+14858x_1x_2^2x_3+10605x_2^3x_3+6698x_1^2x_3^2+
     ------------------------------------------------------------------------
     7857x_1x_2x_3^2+15434x_2^2x_3^2-11440x_1x_3^3+13769x_2x_3^3-12015x_3^4 |

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

o3 = | x_2^2x_3-8744x_1x_3^2+3087x_2x_3^2+14584x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+6403x_1x_3^2+4390x_2x_3^2+15039x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+7011x_1x_3^2+15772x_2x_3^2+13312x_3^3
     ------------------------------------------------------------------------
     x_2^3-383x_1x_3^2+7659x_2x_3^2-5579x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-1547x_1x_3^2+8114x_2x_3^2-6482x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+10014x_1x_3^2-1889x_2x_3^2-15487x_3^3
     ------------------------------------------------------------------------
     x_1^3-12705x_1x_3^2-4903x_2x_3^2-15624x_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 :