{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:27:48Z","timestamp":1750220868062,"version":"3.41.0"},"reference-count":13,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2019,12,17]],"date-time":"2019-12-17T00:00:00Z","timestamp":1576540800000},"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":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2019,12,17]]},"abstract":"\n Let\n K<\/jats:italic>\n be a tower of logarithmic extensions over\n C<\/jats:italic>\n (\n x<\/jats:italic>\n ). There exists a well-generated tower\n E<\/jats:italic>\n of logarithmic extensions containing\n K.<\/jats:italic>\n We outline an additive decomposition in\n E.<\/jats:italic>\n More precisely, for an element\n f<\/jats:italic>\n of\n E<\/jats:italic>\n , the additive decomposition computes\n g<\/jats:italic>\n ,\n r<\/jats:italic>\n \u2208\n E<\/jats:italic>\n such that\n f<\/jats:italic>\n =\n g'<\/jats:italic>\n +\n r<\/jats:italic>\n with the following two properties: (i)\n r<\/jats:italic>\n is minimal in some sense; (ii)\n f<\/jats:italic>\n has an integral in\n E<\/jats:italic>\n if and only if\n r<\/jats:italic>\n = 0. Furthermore,\n f<\/jats:italic>\n \u2208\n K<\/jats:italic>\n has an elementary integral over\n K<\/jats:italic>\n if and only if\n r<\/jats:italic>\n is a\n C<\/jats:italic>\n -linear combination of some logarithmic derivatives in\n E.<\/jats:italic>\n Consequently, we can determine elementary integrability in logarithmic extensions without solving any Risch's equation. This is a generalization of the results in the paper\n Additive Decompositions in Primitive Extensions<\/jats:italic>\n by S. Chen, H. Du and Z. Li in Proc. of ISSAC 2018.\n <\/jats:p>","DOI":"10.1145\/3377006.3377013","type":"journal-article","created":{"date-parts":[[2019,12,18]],"date-time":"2019-12-18T13:21:11Z","timestamp":1576675271000},"page":"110-113","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["An additive decomposition in multiple logarithmic extensions"],"prefix":"10.1145","volume":"53","author":[{"given":"Hao","family":"Du","sequence":"first","affiliation":[{"name":"University of Chinese Academy of Sciences"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Guo","sequence":"additional","affiliation":[{"name":"University of Chinese Academy of Sciences"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziming","family":"Li","sequence":"additional","affiliation":[{"name":"University of Chinese Academy of Sciences"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,12,17]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/220346.220386"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1837934.1837975"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2465506.2465946"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/3208976.3208992"},{"volume-title":"Symbolic Integration I: transcendental functions","year":"2005","author":"Bronstein M.","key":"e_1_2_1_5_1"},{"volume-title":"Proceedings of the 2018 International Symposium on Symbolic and Algebraic Computation","author":"Chen S.","key":"e_1_2_1_6_1"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2017.07.005"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/2755996.2756648"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2930889.2930901"},{"volume-title":"A q-analogue of the modified Abramov-Petkov\u0161ek reduction. Advances in Computer Algebra","year":"2018","author":"Du H.","key":"e_1_2_1_10_1"},{"issue":"1","key":"e_1_2_1_11_1","first-page":"215","article-title":"des fractions rationnelles. Ann. Sci. \u00c9cole Norm","volume":"1872","author":"Hermite C.","journal-title":"Sup.(2)"},{"key":"e_1_2_1_12_1","first-page":"145","article-title":"des fractions rationnelles. Bull. de la classe physico-math\u00e9matique de l'Acad","volume":"4","author":"Ostrogradsky M. V.","year":"1845","journal-title":"Imp\u00e9riale des Sciences de Saint-P\u00e9tersbourg"},{"volume-title":"Constructing reductions for creative telescoping","year":"2017","author":"van der Hoeven J.","key":"e_1_2_1_13_1"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3377006.3377013","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3377006.3377013","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T23:23:49Z","timestamp":1750202629000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3377006.3377013"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,17]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,12,17]]}},"alternative-id":["10.1145\/3377006.3377013"],"URL":"https:\/\/doi.org\/10.1145\/3377006.3377013","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2019,12,17]]},"assertion":[{"value":"2019-12-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}