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pureAll -- Vector of first Betti number of our three specific exact complexes

Synopsis

Description

pureAll returns all three numbers at one time.
i1 : L = {0,2,3,9}

o1 = {0, 2, 3, 9}

o1 : List
i2 : B = pureBettiDiagram L

            0  1  2 3
o2 = total: 7 27 21 1
         0: 7  .  . .
         1: . 27 21 .
         2: .  .  . .
         3: .  .  . .
         4: .  .  . .
         5: .  .  . .
         6: .  .  . 1

o2 : BettiTally
i3 : pureCharFree L

o3 = 56
i4 : pureTwoInvariant L 

o4 = 196
i5 : pureWeyman L

o5 = 21
i6 : pureAll L

o6 = (56, 196, 21)

o6 : Sequence
i7 : gcd pureAll L

o7 = 7
Thus, for large enough multiples m, m*B occurs as the Betti diagram of a module.

However, B itself occurs:
i8 : betti res randomSocleModule(L,1)

            0  1  2 3
o8 = total: 7 27 21 1
         0: 7  .  . .
         1: . 27 21 .
         2: .  .  . .
         3: .  .  . .
         4: .  .  . .
         5: .  .  . .
         6: .  .  . 1

o8 : BettiTally
i9 : betti res randomModule(L,1)

            0  1  2  3
o9 = total: 7 27 35 15
         0: 7  .  .  .
         1: . 27 11  .
         2: .  . 24 15

o9 : BettiTally
i10 : betti res randomModule({0,6,7,9},1)

             0  1  2 3
o10 = total: 1 21 27 7
          0: 1  .  . .
          1: .  .  . .
          2: .  .  . .
          3: .  .  . .
          4: .  .  . .
          5: . 21 27 .
          6: .  .  . 7

o10 : BettiTally

See also

Ways to use pureAll :

For the programmer

The object pureAll is a method function.