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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 = | 251x_1^4-6135x_1^3x_2-15846x_1^2x_2^2+11255x_1x_2^3+1409x_2^4+9246x_1^
     ------------------------------------------------------------------------
     3x_3-12362x_1^2x_2x_3-1789x_1x_2^2x_3-13068x_2^3x_3+11704x_1^2x_3^2+
     ------------------------------------------------------------------------
     11586x_1x_2x_3^2-10231x_2^2x_3^2-13763x_1x_3^3+11306x_2x_3^3-7118x_3^4 |

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

o3 = | x_2^2x_3+393x_1x_3^2-4320x_2x_3^2+1441x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3-12113x_1x_3^2+14704x_2x_3^2+8557x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+7746x_1x_3^2-1690x_2x_3^2-476x_3^3
     ------------------------------------------------------------------------
     x_2^3+704x_1x_3^2-7805x_2x_3^2+798x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2-1020x_1x_3^2+11847x_2x_3^2+4626x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+14648x_1x_3^2-11098x_2x_3^2+5411x_3^3
     ------------------------------------------------------------------------
     x_1^3+15x_1x_3^2-4005x_2x_3^2+12337x_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 :