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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 = | -5061x_1^4+11346x_1^3x_2+5958x_1^2x_2^2-4942x_1x_2^3+1130x_2^4+8084x_1
     ------------------------------------------------------------------------
     ^3x_3+6735x_1^2x_2x_3+9950x_1x_2^2x_3-2398x_2^3x_3-12610x_1^2x_3^2-6872x
     ------------------------------------------------------------------------
     _1x_2x_3^2+15404x_2^2x_3^2+13199x_1x_3^3+11154x_2x_3^3-15588x_3^4 |

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

o3 = | x_2^2x_3+6570x_1x_3^2-10643x_2x_3^2+6908x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-4437x_1x_3^2-4436x_2x_3^2-13680x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3-7347x_1x_3^2+14019x_2x_3^2+13736x_3^3
     ------------------------------------------------------------------------
     x_2^3-10268x_1x_3^2+3058x_2x_3^2-7422x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+12624x_1x_3^2-239x_2x_3^2-8361x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-2332x_1x_3^2-14328x_2x_3^2+5674x_3^3
     ------------------------------------------------------------------------
     x_1^3+6756x_1x_3^2+15688x_2x_3^2-14153x_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 :