randomModule(List,ZZ) -- module with random relations in prescribed degrees

Synopsis

• Function: randomModule

• Usage:

  randomModule(L,m)

• Inputs:
  • L, a list, a strictly increasing degree sequence of integers
  • m, an integer
• Optional inputs:
  • CoefficientRing (missing documentation) => ..., default value ZZ/101, The base field for the resulting module
• Outputs:
  • a module, randomly generated having m b_0 generators in degree L_0 and m b_1 relations in degree L_1, where b = pureBetti L

Description

i1 : L={0,4,9,10}

o1 = {0, 4, 9, 10}

o1 : List

i2 : B = pureBetti L

o2 = {1, 3, 8, 6}

o2 : List

i3 : betti res randomModule(L,1)

            0 1 2 3
o3 = total: 1 3 3 1
         0: 1 . . .
         1: . . . .
         2: . . . .
         3: . 3 . .
         4: . . . .
         5: . . . .
         6: . . 3 .
         7: . . . .
         8: . . . .
         9: . . . 1

o3 : BettiTally

i4 : betti res randomModule(L,2)

            0 1  2  3
o4 = total: 2 6 16 12
         0: 2 .  .  .
         1: . .  .  .
         2: . .  .  .
         3: . 6  .  .
         4: . .  .  .
         5: . .  .  .
         6: . .  .  .
         7: . . 16 12

o4 : BettiTally

i5 : betti res randomModule(L,2, CoefficientRing=>ZZ/5)

            0 1  2  3
o5 = total: 2 6 16 12
         0: 2 .  .  .
         1: . .  .  .
         2: . .  .  .
         3: . 6  .  .
         4: . .  .  .
         5: . .  .  .
         6: . .  .  .
         7: . . 16 12

o5 : BettiTally

See also

• randomSocleModule -- random finite length module with prescribed number of socle elements in single degree
• pureBetti -- list of smallest integral Betti numbers corresponding to a degree sequence