wrong caching in LLL when algorithm="NTL:LLL" #37236
Description
sage: m = matrix(ZZ, 2, 2, [-1,1,1,1])
sage: m.LLL(algorithm="NTL:LLL")
[-1 1]
[ 1 1]
sage: m.det()
2
sage: m = matrix(ZZ, 2, 2, [-1,1,1,1])
sage: m.det()
-2{{ message }}
sage: m = matrix(ZZ, 2, 2, [-1,1,1,1])
sage: m.LLL(algorithm="NTL:LLL")
[-1 1]
[ 1 1]
sage: m.det()
2
sage: m = matrix(ZZ, 2, 2, [-1,1,1,1])
sage: m.det()
-2