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

- 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

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/BoijSoederberg.m2:2098:0.