{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T15:19:24Z","timestamp":1787498364814,"version":"3.56.0"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1979,2,1]],"date-time":"1979-02-01T00:00:00Z","timestamp":286675200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Computer and Information Sciences"],"published-print":{"date-parts":[[1979,2]]},"DOI":"10.1007\/bf00995426","type":"journal-article","created":{"date-parts":[[2005,1,18]],"date-time":"2005-01-18T12:55:18Z","timestamp":1106052918000},"page":"9-37","source":"Crossref","is-referenced-by-count":3,"title":["A structure theorem for the elementary functions and its application to the identity problem"],"prefix":"10.1007","volume":"8","author":[{"given":"H. I.","family":"Epstein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"B. F.","family":"Caviness","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"252","DOI":"10.2307\/1970774","volume":"93","author":"James Ax","year":"1971","unstructured":"James Ax, ?On Schanuel's conjectures,?Ann. Math. 93:252?568 (1971).","journal-title":"Ann. Math."},{"key":"CR2","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1080\/00029890.1969.12000326","volume":"76","author":"W. S. Brown","year":"1969","unstructured":"W. S. Brown, ?Rational exponential expressions and a conjecture concerning ? ande,?Am. Math. Mon. 76:28?34 (January 1969).","journal-title":"Am. Math. Mon."},{"key":"CR3","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1145\/321574.321591","volume":"17","author":"B. F. Caviness","year":"1970","unstructured":"B. F. Caviness, ?On canonical forms and simplification,?J. Ass. Comput. Mach. 17:385?396 (April 1970).","journal-title":"J. Ass. Comput. Mach."},{"key":"CR4","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1080\/00927877508822073","volume":"3","author":"B. F. Caviness","year":"1975","unstructured":"B. F. Caviness and Michael Rothstein, ?A Liouville theorem on integration in finite terms for line integrals,?Commun. Alg. 3:781?795 (1975).","journal-title":"Commun. Alg."},{"key":"CR5","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1145\/800204.806279","volume-title":"Proc. Second Symposium on Symbolic and Algebraic Manipulation","author":"G. E. Collins","year":"1971","unstructured":"G. E. Collins, ?The SAC-1 System: An Introduction and Survey,?Proc. Second Symposium on Symbolic and Algebraic Manipulation, S. R. Petrick, ed. (Association for Computing Machinery, New York, 1971), pp. 144?152."},{"key":"CR6","volume-title":"Ph.D. thesis","author":"H. I. Epstein","year":"1975","unstructured":"H. I. Epstein, ?Algorithms for Elementary Transcendental Function Arithmetic,? Ph.D. thesis, University of Wisconsin, Madison, Wisconsin (April 1975), 409 pp. (Available from University Microfilms International, Ann Arbor, Michigan)."},{"key":"CR7","volume-title":"Essays in Algebraic Simplification,? Project MAC TR-95","author":"R. J. Fateman","year":"1972","unstructured":"R. J. Fateman, ?Essays in Algebraic Simplification,? Project MAC TR-95, Massachusetts Institute of Technology, Cambridge, Mass. (April 1972)."},{"key":"CR8","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1093\/comjnl\/16.1.23","volume":"18","author":"J. P. Fitch","year":"1973","unstructured":"J. P. Fitch, ?On algebraic simplification,?Comput. J. 18:23?27 (February 1973).","journal-title":"Comput. J."},{"key":"CR9","doi-asserted-by":"crossref","unstructured":"J. H. Griesmer and R. D. Jenks, ?SCRATCHPAD\/1-An Interactive Facility for Symbolic Mathematics,?Proc. Second Symposium on Symbolic and Algebraic Manipulation, S. R. Petrick, ed. (Association for Computing Machinery, New York, 1971), pp. 42?58.","DOI":"10.1145\/800204.806266"},{"key":"CR10","volume-title":"Proc. Second Symposium on Symbolic and Algebraic Manipulation","author":"A. D. Hall Jr.","year":"1971","unstructured":"A. D. Hall Jr., ?The Altran System for Rational Function Manipulation-A Survey,Proc. Second Symposium on Symbolic and Algebraic Manipulation, S. R. Petrick, ed. (Association for Computing Machinery, New York, 1971)."},{"key":"CR11","volume-title":"The Integration of Functions of a Single Variable","author":"G. H. Hardy","year":"1928","unstructured":"G. H. Hardy,The Integration of Functions of a Single Variable, 2nd Ed. (Cambridge University Press, London, 1928).","edition":"2nd Ed."},{"key":"CR12","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1145\/800204.806277","volume-title":"Proc. Second Symposium on Symbolic and Algebraic Manipulation","author":"A. C. Hearn","year":"1971","unstructured":"A. C. Hearn, ?REDUCE-2: A System and Language for Algebraic Manipulation,?Proc. Second Symposium on Symbolic and Algebraic Manipulation, S. R. Petrick, ed. (Association for Computing Machinery, New York, 1971), pp. 128?133."},{"key":"CR13","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1145\/321662.321669","volume":"18","author":"S. C. Johnson","year":"1971","unstructured":"S. C. Johnson, ?On the problem of recognizing zero,?J. Assoc. Comput. Mach. 18:559?565 (October 1971).","journal-title":"J. Assoc. Comput. Mach."},{"key":"CR14","volume-title":"An Introduction to Differential Algebra","author":"Irving Kaplansky","year":"1957","unstructured":"Irving Kaplansky,An Introduction to Differential Algebra (Hermann, Paris, 1957)."},{"key":"CR15","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.2307\/2373294","volume":"90","author":"E. R. Kolchin","year":"1968","unstructured":"E. R. Kolchin, ?Algebraic groups and algebraic dependence,?Am. J. Math. 90:1151?1164 (1968).","journal-title":"Am. J. Math."},{"key":"CR16","volume-title":"Differential Algebra and Algebraic Groups","author":"E. R. Kolchin","year":"1973","unstructured":"E. R. Kolchin,Differential Algebra and Algebraic Groups (Academic Press, New York, 1973)."},{"issue":"23","key":"CR17","first-page":"124","volume":"14","author":"Joseph Liouville","year":"1833","unstructured":"Joseph Liouville, ?Sur la d\u00e9termination des integrales dont la valeur est alg\u00e9brique,? J. \u00c9colePolytech. 14 (Sect. 23):124?193 (1833).","journal-title":"J. \u00c9cole Polytech."},{"issue":"24","key":"CR18","first-page":"57","volume":"14","author":"Joseph Liouville","year":"1833","unstructured":"Joseph Liouville, ?M\u00e9moire sur les transcendantes \u00e9lliptiques de premi\u00e8re et de seconde esp\u00e8ce, consid\u00e9r\u00e9es comme fonctions de leur amplitude,?J. \u00c9cole Polytech. 14 (Sect. 24):57?83 (1833).","journal-title":"J. \u00c9cole Polytech."},{"key":"CR19","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1515\/crll.1835.13.93","volume":"13","author":"Joseph Liouville","year":"1835","unstructured":"Joseph Liouville, ?M\u00e9moire sur l'int\u00e9gration d'une classe de fonctions transcendantes,?J. Reine Angew. Math. 13:93?118 (1835).","journal-title":"J. Reine Angew. Math."},{"key":"CR20","first-page":"56","volume":"2","author":"Joseph Liouville","year":"1837","unstructured":"Joseph Liouville, ?M\u00e9moire sur la classification des transcendantes et sur l'impossibilit\u00e9 d'exprimer les racines de certain \u00e9quations en fonction finie explicite des coefficients,?J. Math. Pures Appl. 2:56?104 (1837);3:523?546 (1838).","journal-title":"J. Math. Pures Appl."},{"key":"CR21","first-page":"423","volume":"4","author":"Joseph Liouville","year":"1839","unstructured":"Joseph Liouville, M\u00e9moire sur l'int\u00e9gration d'une classe d'\u00e9quations diff\u00e9rentielles du second ordre en quantit\u00e9s finies explicites,?J. Math. Pures Appl. 4:423?456 (1839).","journal-title":"J. Math. Pures Appl."},{"key":"CR22","first-page":"34","volume":"5","author":"Joseph Liouville","year":"1840","unstructured":"Joseph Liouville, ?M\u00e9moire sur les transcendantes \u00e9lliptiques de premi\u00e8re et de seconde esp\u00e8ce, consid\u00e9r\u00e9es comme fonction de leur module,?J. Math. Pures Appl. 5:34?36, 441?464 (1840).","journal-title":"J. Math. Pures Appl."},{"key":"CR23","first-page":"1","volume":"6","author":"Joseph Liouville","year":"1841","unstructured":"Joseph Liouville, ?Remarques nouvelles sur l'\u00e9quation de Riccati,?J. Math. Pures Appl. 6:1?13 (1841).","journal-title":"J. Math. Pures Appl."},{"key":"CR24","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1145\/800204.806267","volume-title":"Proc. Second Symposium on Symbolic and Algebraic Manipulation","author":"W. A. Martin","year":"1971","unstructured":"W. A. Martin and R. J. Fateman, ?The MACSYMA System,?Proc. Second Symposium on Symbolic and Algebraic Manipulation, S. R. Petrick, ed. (Association for Computing Machinery, New York, 1971), pp. 59?75."},{"key":"CR25","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1145\/362637.362648","volume":"14","author":"Joel Moses","year":"1971","unstructured":"Joel Moses, ?Algebraic simplification: a guide for the perplexed,?Commun. ACM 14:527?537 (August 1971).","journal-title":"Commun. ACM"},{"key":"CR26","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1145\/361454.361466","volume":"15","author":"Joel Moses","year":"1972","unstructured":"Joel Moses, ?Toward a general theory of special functions,?Commun. ACM 15:550?554 (July 1972).","journal-title":"Commun. ACM"},{"key":"CR27","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/BF02421605","volume":"78","author":"Alexandre Ostrowski","year":"1946","unstructured":"Alexandre Ostrowski, ?Sur les relations alg\u00e9briques entre les int\u00e9grales ind\u00e9fines,?Acta Math. 78:315?318 (1946).","journal-title":"Acta Math."},{"key":"CR28","doi-asserted-by":"crossref","first-page":"514","DOI":"10.2307\/2271358","volume":"33","author":"Daniel Richardson","year":"1968","unstructured":"Daniel Richardson. ?Some unsolvable problems involving elementary functions of a real variable,?J. Symb. Logic 33:514?520 (1968).","journal-title":"J. Symb. Logic"},{"key":"CR29","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1002\/malq.19690152003","volume":"15","author":"Daniel Richardson","year":"1969","unstructured":"Daniel Richardson, ?A solution of the identity problem for integral exponential functions,?Z. Math. Logik Grundlagen Math. 15:333?340 (1969).","journal-title":"Z. Math. Logik Grundlagen Math."},{"key":"CR30","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1002\/malq.19710170118","volume":"17","author":"Daniel Richardson","year":"1971","unstructured":"Daniel Richardson, ?The simple exponential constant problem,?Z. Math. Logik Grundlagen Math. 17:133?136 (1971).","journal-title":"Z. Math. Logik Grundlagen Math."},{"key":"CR31","series-title":"IBM Technical Report RC","volume-title":"Further Results on Elementary Functions","author":"R. H. Risch","year":"1969","unstructured":"R. H. Risch, ?Further Results on Elementary Functions,? IBM Technical Report RC 2402, Yorktown Heights, New York (March 1969)."},{"key":"CR32","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1090\/S0002-9947-1969-0237477-8","volume":"139","author":"R. H. Risch","year":"1969","unstructured":"R. H. Risch, ?The problem of integration in finite terms,?Trans. Am. Math. Soc. 139:167?189 (May 1969).","journal-title":"Trans. Am. Math. Soc."},{"key":"CR33","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1090\/S0002-9904-1970-12454-5","volume":"76","author":"R. H. Risch","year":"1970","unstructured":"R. H. Risch, ?The solution of the problem of integration in finite terms,?Bull. Am. Math. Soc. 76:605?608 (May 1970).","journal-title":"Bull. Am. Math. Soc."},{"key":"CR34","series-title":"IBM Technical Report RC","volume-title":"Algebraic Properties of the Elementary Functions of Analysis","author":"R. H. Risch","year":"1975","unstructured":"R. H. Risch, ?Algebraic Properties of the Elementary Functions of Analysis,? IBM Technical Report RC 5565, Yorktown Heights, New York (August 1975)."},{"key":"CR35","doi-asserted-by":"crossref","DOI":"10.7312\/ritt91596","volume-title":"Integration in Finite Terms: Liouville's Theory of Elementary Methods","author":"J. F. Ritt","year":"1948","unstructured":"J. F. Ritt,Integration in Finite Terms: Liouville's Theory of Elementary Methods (Columbia University Press, New York, 1948)."},{"key":"CR36","doi-asserted-by":"crossref","DOI":"10.1090\/coll\/033","volume-title":"Differential Algebra","author":"J. F. Ritt","year":"1950","unstructured":"J. F. Ritt,Differential Algebra (American Mathematical Society, Providence, Rhode Island, 1950); republished by Dover Publications, Inc., New York, 1966."},{"key":"CR37","doi-asserted-by":"crossref","first-page":"153","DOI":"10.2140\/pjm.1968.24.153","volume":"24","author":"Maxwell Rosenlicht","year":"1968","unstructured":"Maxwell Rosenlicht, ?Liouville's theorem on functions with elementary integrals,?Pacific J. Math. 24:153?161 (1968).","journal-title":"Pacific J. Math."},{"key":"CR38","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1080\/00029890.1972.11993166","volume":"79","author":"Maxwell Rosenlicht","year":"1972","unstructured":"Maxwell Rosenlicht, ?Integration in finite terms,?Am. Math. Mon. 79:963?972 (November 1972).","journal-title":"Am. Math. Mon."},{"key":"CR39","unstructured":"Maxwell Rosenlicht, ?On theory of elementary functions? (preprint)."}],"container-title":["International Journal of Computer &amp; Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00995426.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF00995426\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF00995426","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,5]],"date-time":"2020-04-05T06:31:27Z","timestamp":1586068287000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF00995426"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,2]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1979,2]]}},"alternative-id":["BF00995426"],"URL":"https:\/\/doi.org\/10.1007\/bf00995426","relation":{},"ISSN":["0091-7036","1573-7640"],"issn-type":[{"value":"0091-7036","type":"print"},{"value":"1573-7640","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,2]]}}}