This method takes a d×n integer matrix A and computes the exceptional parameters of A. The exceptional parameters of A are the β∈Cd such that the rank of the hypergeometric system Hβ(A) does not take the expected value. The exceptional parameters of A are indexed by a list of pairs (v,F) where v is a vector and F is a list of vectors. The pair (v,F) represents the plane v+spanC F. The set of exceptional parameters of A is the union of all such planes given by the pairs (v,F).
i1 : A=matrix{{1,1,1,1},{0,1,5,11}}
o1 = | 1 1 1 1 |
| 0 1 5 11 |
2 4
o1 : Matrix ZZ <--- ZZ
|
i2 : exceptionalSet A
o2 = {{| 2 |, {}}, {| 3 |, {}}, {| 3 |, {}}, {| 4 |, {}}}
| 4 | | 4 | | 9 | | 9 |
o2 : List
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Thus, when β=(4,9), (3,9), (2,4), or (3,4), the rank of the hypergeometric system Hβ(A) is higher than expected.