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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 = | 10797x_1^4+880x_1^3x_2+9357x_1^2x_2^2-2747x_1x_2^3-1725x_2^4-2778x_1^
     ------------------------------------------------------------------------
     3x_3-1067x_1^2x_2x_3-14458x_1x_2^2x_3+15339x_2^3x_3+6277x_1^2x_3^2+
     ------------------------------------------------------------------------
     11675x_1x_2x_3^2-12871x_2^2x_3^2-4842x_1x_3^3+9766x_2x_3^3+9931x_3^4 |

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

o3 = | x_2^2x_3-10938x_1x_3^2+3736x_2x_3^2-5029x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+554x_1x_3^2-7574x_2x_3^2+9019x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+8910x_1x_3^2-8490x_2x_3^2-14235x_3^3
     ------------------------------------------------------------------------
     x_2^3-8502x_1x_3^2-14301x_2x_3^2-4037x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+2322x_1x_3^2+1086x_2x_3^2-9776x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2-4680x_1x_3^2-10086x_2x_3^2+14968x_3^3
     ------------------------------------------------------------------------
     x_1^3+11460x_1x_3^2+14932x_2x_3^2+3823x_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 :