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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 = | 15536x_1^4-11977x_1^3x_2-15352x_1^2x_2^2-337x_1x_2^3-2489x_2^4-2668x_1
     ------------------------------------------------------------------------
     ^3x_3+360x_1^2x_2x_3-5879x_1x_2^2x_3-15875x_2^3x_3-4454x_1^2x_3^2+10175x
     ------------------------------------------------------------------------
     _1x_2x_3^2+70x_2^2x_3^2-8410x_1x_3^3+14818x_2x_3^3-11472x_3^4 |

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

o3 = | x_2^2x_3-15929x_1x_3^2-5875x_2x_3^2+3291x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-14231x_1x_3^2+12475x_2x_3^2+12953x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+6641x_1x_3^2+6122x_2x_3^2+9879x_3^3
     ------------------------------------------------------------------------
     x_2^3-13394x_1x_3^2+9467x_2x_3^2-12002x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-13167x_1x_3^2+15613x_2x_3^2-7995x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+4736x_1x_3^2-13469x_2x_3^2+5214x_3^3
     ------------------------------------------------------------------------
     x_1^3-7093x_1x_3^2-11243x_2x_3^2+15762x_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 :