- 1 BAREISS, E. H. Sylvester's identity and multistep integer-preserving Gaussian ehmination. Math Compt. 22, 103 (july 1968), 565-578.Google Scholar
- 2 BAR~ISS, E. H Computational solutions of matrix problems over an integral domain. J. Inst. Math. and Appls. 10 (1972), 68-104.Google Scholar
- 3 BAREISS, E. H., AND MAZUKELLI, D Multmtep elimination over commutative rings. Argonne National Lab Rep. ANL-7898, April 1972.Google Scholar
- 4 CABAY, S. Exact solution of linear equations. Proc. Second Sympomum on Symbolic and Algebram Manipulation, ACM, Los Angeles, Cahf, March 1971, pp. 392-398 Google Scholar
- 5 COLLINS, G. The SAC-1 system An introduction and survey. Proc. of the Second Symposium on Symbohc and Algebraic Manipulation, ACM, Los Angeles, Calif., March 1971, pp 144-152. Google Scholar
- 6 DORR, F W. An example of ill-conditioning in the numemcal solution of singular perturbation problems Math. Comput. 25,114 (April 1971), 271-284.Google Scholar
- 7 GENTLEMAN, W. M., AND JOHNSON, S.C. Analysis of algorithms, a case study" Determinants of polynomials Proc of the Fifth Annual ACM Symposmm on Theory of Computing, Austin, Texas, April 30, 1973, pp 135-142. Google Scholar
- 8 HonowiTz, E. The efficient calculation of powers of a polynomial. J. Comput. ,Syst. Sc~. 7, 5 (Oct. 1973), 469-481.Google Scholar
- 9 HOROWITZ, E., AND SAnNI, S. On computing the determinant of matrices with polynomial entries. Comput Scl Tit 73-180, Cornell U, Ithaca, N Y, June 1973.Google Scholar
- 10 HOWELL, J., AND GREGORY, R. T Solving systems of linear algebraic equations using residue arithmetic I, II, and III. BIT 9 (1969), 200-224, 324-337, and BIT 10 (1970), 23-27.Google Scholar
- 11 ISAACSON, E , ANn KELLER, H. B Analys~s of Numemcal Methods Wiley, New York, 1966.Google Scholar
- 12 KNtTTtt, D. E The Art of Computer Programming, Vol. 2: Semznumerwal Algorithms. Addison- Wesley, Reading, Mass., 1969.Google Scholar
- 13 LIPsoN, J. D Symbolic methods for the computer solution of linear equations with apphcations to flow graphs Proc of the 1968 Summer Institute on Symbolic Mathematmal Computatmn, IBM, Boston, June 1969, pp 233-303.Google Scholar
- 14 McCLELLAN, M.T. The exact solution of systems of linear equations with polynomial coefficients. J. ACM 20, 4 (Oct. 1973), 563-588. Google Scholar
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On Computing the Exact Determinant of Matrices with Polynomial Entries
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