Complexity of the Havas, Majewski, Matthews LLL Hermite Normal Form algorithm
Wilberd van der Kallen, Wilberd Van, Der Kallen · 2000
this paper a pivot is an entry of A that is the first nonzero entry in its row and also in its column.) Put m iso = m \\Gamma rank and let b i denote the i-th Gram-Schmidt vector with respect to ( ; ) mix . We may characterize the b i as follows. Firstly, b i lies in (b i + P i\\Gamma1 j=1 Rb i ). Secondly, if 1 j ! i m and j m iso then (b i ; b j ) = 0, but if 1 j ! i m and j ? m iso then hb i ; b j i = 0