
- 1.BAREISS, E. Computational sohltions of' matrix problems over an integral domain. J. Inst. Maths Applies 10 (1972), 68--104.]]Google Scholar
Cross Ref
- 2.BREIMAN, L. Probability. Addison--\Vesley, 1968.]] Google Scholar
Digital Library
- 3.BRONNIMANN. H., EMIR1S, I., PAN, V., AND PIO..X', S. Computing exact geometric predicat, es using modular arithmetic with single precision. In Symposium on Computational Geometry '97 (1997), pp. 174--182.]] Google Scholar
Digital Library
- 4.C, APANI. A.. NIESI, G., AND ~,OBBIANO, L. CoCoA" Computations in commutative algebra, http'//cocoa. dima. unige, it/.]]Google Scholar
- 5.C, LARKSO.\', K. Safe and effe(:tive determinant evaluation. In Proc. 33rd Ann. IEEE Syrup. Foundations of Comp. Science (1992), pp. 387-395.]]Google Scholar
- 6.DixoN, J. Exact solution of linear equations using padic expansions. Numer. Math. 40 (1982), 137-141.]]Google Scholar
Cross Ref
- 7.DOMI(::H, P., KANNAN, R., AND TROTTER, L. Hermite norlual fornl coinputa.tion using modulo deternlinant arithmetic. Math. Oper. Re.s. 12 (1987), 50 59.]] Google Scholar
Digital Library
- 8.FItUMKIN, M. Polynomial time algorithms in tile theory of linear diophantine equations. LNCS 56 (1977), 386- 392.]]Google Scholar
- 9.HAFNEII, J., AND MCC, URLEY, K. Asymptotically fast triangularization of matrices over rings. SIAM J. Comput. 20 (1991), 1068-1083.]] Google Scholar
Digital Library
- 10.HOKN, R.. AND JOItNSON, C. Matrix Analysis. Cambridge University Press, 1985.]]Google Scholar
- 11.HOWELL, J. Spans in the inodule (Z,~)~. Linear and Mv ltilinear Algebra 19 (1986), 67-77.]]Google Scholar
- 12.MULDERS, T., AND STORJOIIANN, A. Diot)hantine lin- (tar syst, eln solving. In these proceedings (1999).]] Google Scholar
Digital Library
- 13.N I~WMAN, M. Integral Matrices. Academic Press, 1972.]]Google Scholar
- 14.PAN, V. CoIuputing the determinant and the charactersitic i)olynomial of a matrix via solving linear systems of equations. Inf. Proc. Letters 28 (1988), 71-75.]] Google Scholar
Digital Library
- 15.SHouP, V. NTL' A library ibr doing number theory. http"//www, cs. wisc. edu/~shoup/ntl.]]Google Scholar
- 16.S'I'OI?~JOHANN, A., AND .~"}~ULDERS, T. F~k~t, &lgorit.llms for linear algebra modulo N. In Proc. 6th Ann. European Syrup. on Algorithms (1998), LNCS 1461, pp. 139- 150.]] Google Scholar
Digital Library
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Fast deterministic computation of determinants of dense matrices
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