Abstract
Let S,T be n×n integral matrices and one of them positive definite. We develop a method to decide whether a solution X∈ℤn×n of XtrSX=T exists and, if the answer is affirmative, an algorithm for the computation of X. Some applications in algebraic number theory and lattice construction are presented.
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References
G. Havas and L. Sterling, "Integer matrices and Abelian groups", Symbolic and Algebraic Computation (E. W. Ng, ed.), Lecture Notes in Computer Science 72, Springer Verlag (1979), 431–451.
W. Plesken and M. Pohst, "Constructing integral lattices with prescribed minimum I", to appear.
M. Pohst, "On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications", ACM SIGSAM Bulletin vol. 15, no. 1 (1981), 37–44.
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© 1983 Springer-Verlag
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Pohst, M. (1983). Computation of integral solutions of a special type of systems of quadratic equations. In: van Hulzen, J.A. (eds) Computer Algebra. EUROCAL 1983. Lecture Notes in Computer Science, vol 162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12868-9_104
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DOI: https://doi.org/10.1007/3-540-12868-9_104
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