///
TEST /// -- singularLocus
+-* no-check-flag *-
X10 = coincidentRootLocus(toList(10:1),ZZ/101,Variable=>x)
A10 = {{},{{10}},{{10}},{{9,1}},{{10}},{{7,3},{8,2},{9,1}},{{8,1,1}},{{10}},{{6,4},{7,3},{9,1}},{{8,2}},{{6,2,2},{6,3,1},{7,2,1},{8,1,1}},{{7,1,1,1}},{},{{5,5},{6,4},{9,1}},{{5,5},{7,3},{8,2}},{{5,4,1},{6,3,1},{8,1,1}},{{5,3,2},{6,2,2},{7,2,1}},{{5,2,2,1},{5,3,1,1},{6,2,1,1},{7,1,1,1}},{{5,5},{6,1,1,1,1}},{{6,4}},{{5,4,1}},{{7,3}},{{4,3,3},{4,4,2},{5,3,2},{5,4,1},{6,3,1},{7,2,1}},{{4,3,3},{4,4,1,1},{5,3,1,1},{7,1,1,1}},{{4,4,2},{6,2,2}},{{4,2,2,2},{4,3,2,1},{4,4,1,1},{5,2,2,1},{6,2,1,1}},{{4,2,2,1,1},{4,3,1,1,1},{4,4,2},{5,2,1,1,1},{6,1,1,1,1}},{{4,4,1,1},{5,1,1,1,1,1}},{{4,3,3}},{{5,3,2}},{{3,3,2,2},{3,3,3,1},{4,3,2,1},{5,3,1,1}},{{3,3,3,1},{4,3,1,1,1}},{{3,3,2,2},{4,2,2,2},{5,2,2,1}},{{3,2,2,2,1},{3,3,2,1,1},{3,3,2,2},{4,2,2,1,1},{5,2,1,1,1}},{{3,2,2,1,1,1},{3,3,1,1,1,1},{3,3,2,1,1},{4,2,1,1,1,1},{5,1,1,1,1,1}},{{3,3,1,1,1,1},{4,1,1,1,1,1,1}},{},{{2,2,2,2,2},{3,2,2,2,1}},{{2,2,2,2,1,1},{3,2,2,1,1,1},{4,4,2}},{{2,2,2,1,1,1,1},{3,2,1,1,1,1,1},{4,4,1,1}},{{2,2,1,1,1,1,1,1},{3,1,1,1,1,1,1,1}},{}}
assert(sort apply(apply(subsets X10,singularLocus),L -> sort apply(L,partition)) === sort apply(A10,sort))