{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T14:14:07Z","timestamp":1725459247236},"publisher-location":"Berlin\/Heidelberg","reference-count":34,"publisher":"Springer-Verlag","isbn-type":[{"type":"print","value":"354019200X"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/bfb0039181","type":"book-chapter","created":{"date-parts":[[2006,1,25]],"date-time":"2006-01-25T14:19:45Z","timestamp":1138198785000},"page":"77-87","source":"Crossref","is-referenced-by-count":0,"title":["On the integration of numeric and algebraic computations"],"prefix":"10.1007","author":[{"given":"Gianfranco","family":"Mascari","sequence":"first","affiliation":[]},{"given":"Alfonso","family":"Miola","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"9_CR1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/978-3-7091-8577-3_2","volume":"2","author":"R. Albrecht","year":"1980","unstructured":"R. ALBRECHT: Roundings and Approximations in Ordered Sets, Computing Suppl. 2, 17\u201331 (1980).","journal-title":"Computing Suppl."},{"key":"9_CR2","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1145\/321992.321997","volume":"24","author":"ADJ","year":"1977","unstructured":"ADJ: Initial algebra semantics and continuous algebras, JACM 24 68\u201395 (1977).","journal-title":"JACM"},{"key":"9_CR3","unstructured":"G. AUSIELLO, G.F. MASCARI: On the Design of Algebraic Data Structures with the Approach of Abstract Data Types, Proc. Of EUROSAM 79, Springer Verlag (1979)."},{"key":"9_CR4","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/0304-3975(80)90045-6","volume":"11","author":"A. Arnold","year":"1980","unstructured":"A. ARNOLD, M. NIVAT: Metric interpretations of infinite trees and semantics of non deterministic programs, Theoretical Computer Science 11 181\u2013205 (1980).","journal-title":"Theoretical Computer Science"},{"key":"9_CR5","doi-asserted-by":"crossref","unstructured":"H.J. BOEHM, R. CARTWRIGHT, M. RIGGLE, O'DONNELL: Exact Real Arithmetic: A Case Study in Higher Order Programming. Proc. Lisp Conference (1986).","DOI":"10.1145\/319838.319860"},{"key":"9_CR6","unstructured":"S.R. BALZAC, and others: The SCRATCHPAD II, IBM Research Report (1984)."},{"key":"9_CR7","doi-asserted-by":"crossref","unstructured":"M. BERGMAN: Algebraic specifications: a constructive methodology in logic programming, in Proc. EUROCAM '82, L.N.C.S. vol. 144, Springer Verlag (1982).","DOI":"10.1007\/3-540-11607-9_11"},{"key":"9_CR8","doi-asserted-by":"crossref","unstructured":"R.P. BRENT, F.G. GUSTAVSON, D.Y.Y. YUN: Fast solution of Toeplitz systems of equations and computation of Pade approximants, J. of Algorithms, 1, (1980).","DOI":"10.1016\/0196-6774(80)90013-9"},{"key":"9_CR9","doi-asserted-by":"crossref","unstructured":"W.S. BROWN: A simple but Realistic Model of Floating-Point Computation, ACM Transactions of Mathematical Software, Vol. 7, n. 4 (1981).","DOI":"10.1145\/355972.355975"},{"key":"9_CR10","doi-asserted-by":"crossref","unstructured":"W.S. BROWN, A.C. HEARN: Applications of Symbolic Algebraic Computation. Comp. Comm. 17 (1979).","DOI":"10.1016\/0010-4655(79)90082-1"},{"key":"9_CR11","doi-asserted-by":"crossref","unstructured":"B. COURCELLE, F. LAVANDIER: A class of program schemes based on tree rewriting systems, Proc. of CAAP \u2014 83, LNCS n., L'Aquila (1983).","DOI":"10.1007\/3-540-12727-5_11"},{"key":"9_CR12","doi-asserted-by":"crossref","unstructured":"B. COURCELLE, M. NIVAT: Algebraic families of interpretations, 17th FOCS 137\u2013146 (1976).","DOI":"10.1109\/SFCS.1976.3"},{"issue":"4","key":"9_CR13","first-page":"1","volume":"85","author":"M.M. Cerimele","year":"1985","unstructured":"M.M. CERIMELE, M. VENTURINI ZILLI: Effective Numerical Approximations by Intervals, Freiburger Interwall-Berichte 85\/4, 1\u201324 (1985).","journal-title":"Freiburger Interwall-Berichte"},{"key":"9_CR14","unstructured":"E. ENGELER, R. M\u00c4DER: Scientific Computation: The Integration of Symbolic, Numeric and Graphic Computation, L.N.C.S. 203 (1985)."},{"key":"9_CR15","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/0304-3975(82)90111-6","volume":"18","author":"A.P. Ershov","year":"1982","unstructured":"A.P. ERSHOV: Mixed computation: Potential applications and problems for study, Theoretical Computer Sciernce 18, 41\u201367 (1982).","journal-title":"Theoretical Computer Sciernce"},{"key":"9_CR16","doi-asserted-by":"crossref","unstructured":"R.T. GREGORY, E.V. KRISHNAMURTHY: Methods and Applications of Error-Free Computation, Springer Verlag (1984).","DOI":"10.1007\/978-1-4612-5242-9"},{"key":"9_CR17","unstructured":"F.G. GUSTAVSON, D.Y.Y. YUN: Fast algorithms for rational Hermite approximation and solution of Toeplitz systems, IEEE Trans. Circuits and Systems, CAS 26, n. 9 (1979)."},{"key":"9_CR18","volume-title":"Theorie der Algebraischen Zahlen","author":"K. Hensel","year":"1908","unstructured":"K. HENSEL: Theorie der Algebraischen Zahlen, Teubner, Leipzig-Stuttgart (1908)."},{"key":"9_CR19","unstructured":"R. JENKS: MODLISP: An Introduction, Proc. of EUROSAM '79 Conference, Marseille, June 1979, Ed. by Ed, Ng, LNCS, n. 72, 1979."},{"key":"9_CR20","unstructured":"P. KEMP: Symbolic-numeric interface (abstract), SIGSAM Bulletin 15, 2, 6, ACM (1981)."},{"key":"9_CR21","unstructured":"N. KOBLITZ: p-adic Numbers, p-adic Analysis and Zeta Functions, Springer Verlag (1977)."},{"key":"9_CR22","first-page":"9","volume":"23","author":"P. Kornerup","year":"1983","unstructured":"P. KORNERUP, R.T. GREGORY: Mapping integers and Hensel-codes onto Farey fractions, DAIMI PB 149, Comp. Sc. Dept. of Aarhus University, Denmark (1982). BIT 23, 9\u201320 (1983).","journal-title":"Comp. Sc. Dept. of Aarhus University, Denmark (1982)"},{"key":"9_CR23","doi-asserted-by":"crossref","unstructured":"U. KULISCH, W,L, MIRANKER: Computer arithmetic in theory and practice, Academic Press (1980).","DOI":"10.1016\/B978-0-12-428650-4.50009-9"},{"key":"9_CR24","doi-asserted-by":"crossref","unstructured":"J.D. LIPSON: Newton's Method: A Great Algebraic Algorithm, Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation (1976).","DOI":"10.1145\/800205.806344"},{"key":"9_CR25","doi-asserted-by":"crossref","unstructured":"R. LOOS: Toward a Formal Implementation of Computer Algebra, Proc. of EUROSAM '74, ACM SIGSAM Bulletin, Vol., 8, n. 3 (1974).","DOI":"10.1145\/1086837.1086839"},{"key":"9_CR26","first-page":"4","volume":"34","author":"R,J","year":"1978","unstructured":"R,J, McELIECE, J.B. SKEARER: A property of Euclid's algorithm and an application to Pade approximation, SIAM J. Appl. Math. 34, n. 4 (1978).","journal-title":"SIAM J. Appl. Math."},{"key":"9_CR27","doi-asserted-by":"crossref","unstructured":"A. MIOLA: A unified view of approximate rational arithmetics and rational interpolation, Proc. of IEEE ARITH-6 Conference, Aarhus (1983).","DOI":"10.1109\/ARITH.1983.6158089"},{"key":"9_CR28","doi-asserted-by":"crossref","unstructured":"A. MIOLA: Algebraic Approach to p-adic conversion of Rational Numbers, IPL 18 (1984).","DOI":"10.1016\/0020-0190(84)90022-X"},{"key":"9_CR29","doi-asserted-by":"crossref","unstructured":"W.L. MIRANKER, R. A. TOUPIN (Eds.): Accurate Scientific Computations. L.N.C.S. 235 (1985).","DOI":"10.1007\/3-540-16798-6"},{"key":"9_CR30","unstructured":"A. MIOLA, D.Y.Y. YUN: Computational aspects of univariate polynomial GCD, Proc. ACM EUROSAM '74, SIGSAM Bulletin (8), (1974)."},{"key":"9_CR31","doi-asserted-by":"crossref","unstructured":"E.W. NG: Symbolic-Numeric Interface: a Review, Proc. of EUROSAM '79, Springer Verlag (1979).","DOI":"10.1007\/3-540-09519-5_85"},{"key":"9_CR32","unstructured":"M. SMYTH, S. VICKERS: The Domain of p-adic Integers. Report of the 2nd British Theoretical Computer Science Colloquium, Bulletin of the EATCS Number 30, (1986)."},{"key":"9_CR33","unstructured":"D.Y.Y. YUN: Hensel meets Newton-Algebraic constructions in an analytic setting, IBM Tech. Report RC 5538 (1975)."},{"key":"9_CR34","doi-asserted-by":"crossref","unstructured":"D.Y.Y. YUN: Algebraic Algorithms using p-adic Constructions, Proc. 1976 ACM, Symposium on Symbolic and Algebraic Computation (1976).","DOI":"10.1145\/800205.806343"}],"container-title":["Lecture Notes in Computer Science","Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0039181.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,9]],"date-time":"2020-12-09T22:24:54Z","timestamp":1607552694000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0039181"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["354019200X"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/bfb0039181","relation":{},"subject":[]}}