A Note to Hermite and Smith Normal Form Computation
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چکیده
Hermite normal form and Smith normal form are canonic forms of integral matrices with respect to congruence produced by multiplication with right unimodular matrix resp. by multiplication with left and right unimodular matrix simultaneously. This lower-diagonal resp. diagonal form has many applications in various elds. Unfortunately, the computation of them is extremely resource consuming. The present note shows a construction of certain more complicated instances of integral matrices. The systematic construction of such matrices complements a research with respect to randomized versions of Hermite normal form and Smith normal form algorithms 11].
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