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Quasidegrees :: exceptionalSet

exceptionalSet -- returns the exceptional set of a matrix

Synopsis

Description

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.

Ways to use exceptionalSet :