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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 = | -14320x_1^4-10516x_1^3x_2+15025x_1^2x_2^2-959x_1x_2^3+5166x_2^4+10102x
     ------------------------------------------------------------------------
     _1^3x_3-15841x_1^2x_2x_3-868x_1x_2^2x_3-13835x_2^3x_3-13627x_1^2x_3^2+
     ------------------------------------------------------------------------
     4397x_1x_2x_3^2-2304x_2^2x_3^2-5220x_1x_3^3-4126x_2x_3^3+10076x_3^4 |

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

o3 = | x_2^2x_3-394x_1x_3^2-12056x_2x_3^2-9041x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-5370x_1x_3^2+10711x_2x_3^2+2242x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-3438x_1x_3^2+3090x_2x_3^2-7340x_3^3
     ------------------------------------------------------------------------
     x_2^3+12524x_1x_3^2-11250x_2x_3^2-242x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-14503x_1x_3^2-11362x_2x_3^2-11950x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+14531x_1x_3^2+14703x_2x_3^2-12345x_3^3
     ------------------------------------------------------------------------
     x_1^3+3931x_1x_3^2+2857x_2x_3^2-11316x_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 :