{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:16:49Z","timestamp":1750306609590,"version":"3.41.0"},"reference-count":4,"publisher":"Association for Computing Machinery (ACM)","issue":"3\/4","license":[{"start":{"date-parts":[[2015,2,5]],"date-time":"2015-02-05T00:00:00Z","timestamp":1423094400000},"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":[[2015,2,5]]},"abstract":"<jats:p>\n            The middle product computes the middle\n            <jats:italic>n<\/jats:italic>\n            terms of a (2\n            <jats:italic>n<\/jats:italic>\n            --1)xn polynomial product, with effectively the same cost as computing an\n            <jats:italic>n<\/jats:italic>\n            x\n            <jats:italic>n<\/jats:italic>\n            polynomial product. The middle product allows for faster power series operations and Newton iteration. Middle product variants of classical, Karatsuba, and FFT-based multiplication algorithms are known. We present a middle product algorithm based on the Truncated Fourier Transform.\n          <\/jats:p>","DOI":"10.1145\/2733693.2733698","type":"journal-article","created":{"date-parts":[[2015,2,10]],"date-time":"2015-02-10T13:19:47Z","timestamp":1423574387000},"page":"98-99","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["A Truncated Fourier Transform middle product"],"prefix":"10.1145","volume":"48","author":[{"given":"Andrew","family":"Arnold","sequence":"first","affiliation":[{"name":"University of Waterloo"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c9ric","family":"Schost","sequence":"additional","affiliation":[{"name":"Western University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,2,5]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2465506.2465957"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/860854.860870"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-003-0144-2"},{"key":"e_1_2_1_5_1","volume-title":"Notes on the truncated fourier transform. preprint","author":"van der Hoeven Joris","year":"2005","unstructured":"Joris van der Hoeven . Notes on the truncated fourier transform. preprint , 2005 . http:\/\/www.texmacs.org\/joris\/tft\/tft-abs.html. Joris van der Hoeven. Notes on the truncated fourier transform. preprint, 2005. http:\/\/www.texmacs.org\/joris\/tft\/tft-abs.html."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2733693.2733698","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2733693.2733698","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:17:02Z","timestamp":1750227422000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2733693.2733698"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,5]]},"references-count":4,"journal-issue":{"issue":"3\/4","published-print":{"date-parts":[[2015,2,5]]}},"alternative-id":["10.1145\/2733693.2733698"],"URL":"https:\/\/doi.org\/10.1145\/2733693.2733698","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2015,2,5]]},"assertion":[{"value":"2015-02-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}