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 = {{| 3 |, {}}, {| 3 |, {}}, {| 4 |, {}}, {| 2 |, {}}} | 4 | | 9 | | 9 | | 4 | o2 : List |
Thus, when β=(4,9), (3,9), (2,4), or (3,4), the rank of the hypergeometric system Hβ(A) is higher than expected.