{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:42:02Z","timestamp":1750308122957,"version":"3.41.0"},"reference-count":0,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[1981,2,1]],"date-time":"1981-02-01T00:00:00Z","timestamp":349833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[1981,2]]},"abstract":"<jats:p>\n            To illustrate the difference between numeric and symbolic processing, consider a computer program (in FORTRAN, say) which given the quantities\n            <jats:italic>a<\/jats:italic>\n            ,\n            <jats:italic>b<\/jats:italic>\n            , and\n            <jats:italic>c<\/jats:italic>\n            , can apply the quadratic formula to approximate the roots of the quadratic about 40 equation\n            <jats:italic>\n              ax\n              <jats:sup>2<\/jats:sup>\n              +bx+c=0.\n            <\/jats:italic>\n            The names\n            <jats:italic>a, b<\/jats:italic>\n            , and\n            <jats:italic>c<\/jats:italic>\n            must of course correspond to numerical values at run-time because the program has been written to provide numerical processing. If\n            <jats:italic>a<\/jats:italic>\n            had as its run-time value the expression\n            <jats:italic>q<\/jats:italic>\n            , b had value -\n            <jats:italic>pq<\/jats:italic>\n            - 1 and\n            <jats:italic>c<\/jats:italic>\n            had value\n            <jats:italic>p<\/jats:italic>\n            , the FORTRAN program would not be applicable. Nevertheless, by applying the quadratic formula symbolically, the two roots[EQUATION]can be represented. By further efforts, this expression can be reduced to the set of values\n            <jats:italic>p<\/jats:italic>\n            , 1\/\n            <jats:italic>q<\/jats:italic>\n            . This substitution (in this case, into the quadratic formula) and subsequent simplification are but two of the necessary operations in an algebra system. Some of the more elaborate facilities that can be built up (and have been, in some systems), bring us to the edge of research areas in several fields of mathematics, and present us with problems in representation and communication of \"knowledge\" which border on the hardest problems in computer \"artificial intelligence\" -- natural language processing, representation of complex data, heuristic programming.\n          <\/jats:p>","DOI":"10.1145\/1089242.1089245","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"21-32","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Symbolic and algebraic computer programming systems"],"prefix":"10.1145","volume":"15","author":[{"given":"Richard J.","family":"Fateman","sequence":"first","affiliation":[{"name":"University of California, Berkeley, CA"}]}],"member":"320","published-online":{"date-parts":[[1981,2]]},"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089242.1089245","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1089242.1089245","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:08:22Z","timestamp":1750262902000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089242.1089245"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1981,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1981,2]]}},"alternative-id":["10.1145\/1089242.1089245"],"URL":"https:\/\/doi.org\/10.1145\/1089242.1089245","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1981,2]]},"assertion":[{"value":"1981-02-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}