give1683Format -- Does the semigroup ideal of L has a resolution with total betti numbers 1,6,8,3?

• Usage:

  answer = give1683Format L

  answer = give1683Format(a,b,c,d)

  goodCases = give1683Format(r1,r2,r3,r4)

• Inputs:
  • L, a list, generators of a semigroup with 4 generators
  • a, an integer,
  • b, an integer,
  • c, an integer,
  • d, an integer, test the semigrups generated by {a,a+b,a+b+c,a+b+c+d}
  • r1, a list,
  • r2, a list,
  • r3, a list,
  • r4, a list, lists of integer a in r1,...,d in r4 to be tested
• Outputs:
  • answer, a Boolean value, the answer
  • goodCases, a list, list of semigroups which passed the test

i1 : L = {6,9,13,16}

o1 = {6, 9, 13, 16}

o1 : List

i2 : I = semigroupIdeal L

             3    2                2              2    2   2 3    3     4  
o2 = ideal (x  - x , x x  - x x , x x  - x x , x x  - x , x x  - x , x x  -
             0    3   3 1    0 4   0 1    3 4   0 1    4   0 3    1   0 3  
     ------------------------------------------------------------------------
      2
     x x )
      1 4

                ZZ
o2 : Ideal of -----[x , x , x , x ]
              10007  0   3   1   4

i3 : give1683Format L

o3 = true

i4 : give1683Format(6,3,4,3)

o4 = true

i5 : r1={6},r2={3,9},r3={2,4},r4={3}

o5 = ({6}, {3, 9}, {2, 4}, {3})

o5 : Sequence

i6 : give1683Format(r1,r2,r3,r4)

o6 = {{6, 9, 11, 14}, {6, 9, 13, 16}, {6, 15, 17, 20}, {6, 15, 19, 22}}

o6 : List