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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 = | -13760x_1^4-12372x_1^3x_2+10273x_1^2x_2^2+14679x_1x_2^3-2058x_2^4-
     ------------------------------------------------------------------------
     6359x_1^3x_3+9330x_1^2x_2x_3+2905x_1x_2^2x_3+2031x_2^3x_3-12846x_1^2x_3^
     ------------------------------------------------------------------------
     2-1094x_1x_2x_3^2-8399x_2^2x_3^2-496x_1x_3^3-12606x_2x_3^3+3913x_3^4 |

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

o3 = | x_2^2x_3+11082x_1x_3^2+11133x_2x_3^2+11240x_3^3
     ------------------------------------------------------------------------
     x_1x_2x_3+8075x_1x_3^2+1732x_2x_3^2+12116x_3^3
     ------------------------------------------------------------------------
     x_1^2x_3+11624x_1x_3^2+6929x_2x_3^2+10844x_3^3
     ------------------------------------------------------------------------
     x_2^3+6893x_1x_3^2+7078x_2x_3^2-6152x_3^3
     ------------------------------------------------------------------------
     x_1x_2^2+5339x_1x_3^2-12700x_2x_3^2-14557x_3^3
     ------------------------------------------------------------------------
     x_1^2x_2+14340x_1x_3^2+6938x_2x_3^2+12283x_3^3
     ------------------------------------------------------------------------
     x_1^3-9027x_1x_3^2+4749x_2x_3^2+3140x_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 :