{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T08:04:44Z","timestamp":1742976284343,"version":"3.40.3"},"publisher-location":"Cham","reference-count":41,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030851644"},{"type":"electronic","value":"9783030851651"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-85165-1_4","type":"book-chapter","created":{"date-parts":[[2021,8,15]],"date-time":"2021-08-15T23:03:01Z","timestamp":1629068581000},"page":"42-61","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Rational Solutions of Pseudo-linear Systems"],"prefix":"10.1007","author":[{"given":"Moulay A.","family":"Barkatou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Cluzeau","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ali","family":"El Hajj","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,16]]},"reference":[{"issue":"4\u20135","key":"4_CR1","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1080\/10236199908808199","volume":"5","author":"S Abramov","year":"1999","unstructured":"Abramov, S.: EG-eliminations. J. Differ. Equations Appl. 5(4\u20135), 393\u2013433 (1999)","journal-title":"J. Differ. Equations Appl."},{"issue":"4","key":"4_CR2","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1016\/0041-5553(71)90028-0","volume":"11","author":"S Abramov","year":"1971","unstructured":"Abramov, S.: On the summation of rational functions. USSR Comput. Math. Math. Phys. 11(4), 324\u2013330 (1971)","journal-title":"USSR Comput. Math. Math. Phys."},{"issue":"6","key":"4_CR3","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1016\/S0041-5553(89)80002-3","volume":"29","author":"S Abramov","year":"1989","unstructured":"Abramov, S.: Rational solutions of linear differential and difference equations with polynomial coefficients. USSR Comput. Math. Math. Phys. 29(6), 7\u201312 (1989)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"4_CR4","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0012-365X(01)00248-5","volume":"246","author":"S Abramov","year":"2002","unstructured":"Abramov, S.: A direct algorithm to compute rational solutions of first order linear $$q$$-difference systems. Discret. Math. 246, 3\u201312 (2002)","journal-title":"Discret. Math."},{"doi-asserted-by":"crossref","unstructured":"Abramov, S., Barkatou, M.A.: Rational solutions of first order linear difference systems. In: Proceedings of ISSAC 1998, pp. 124\u2013131 (1998)","key":"4_CR5","DOI":"10.1145\/281508.281593"},{"key":"4_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1007\/978-3-642-15274-0_2","volume-title":"Computer Algebra in Scientific Computing","author":"SA Abramov","year":"2010","unstructured":"Abramov, S.A., Gheffar, A., Khmelnov, D.E.: Factorization of polynomials and GCD computations for finding universal denominators. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2010. LNCS, vol. 6244, pp. 4\u201318. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-15274-0_2"},{"key":"4_CR7","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0012-365X(97)00106-4","volume":"180","author":"S Abramov","year":"1998","unstructured":"Abramov, S., Paule, P., Petkovsek, M.: q-hypergeometric solutions of q-difference equations. Discret. Math. 180, 3\u201322 (1998)","journal-title":"Discret. Math."},{"key":"4_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-319-24021-3_1","volume-title":"Computer Algebra in Scientific Computing","author":"SA Abramov","year":"2015","unstructured":"Abramov, S.A., Petkov\u0161ek, M., Ryabenko, A.A.: Hypergeometric solutions of first-order linear difference systems with rational-function coefficients. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds.) CASC 2015. LNCS, vol. 9301, pp. 1\u201314. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-24021-3_1"},{"unstructured":"Barkatou, M.A.: Contribution \u00e0 l\u2019\u00e9tude des \u00e9quations diff\u00e9rentielles et aux diff\u00e9rences dans le champ complexe. Ph.D. Thesis, Institut Nat. Polytech. Grenoble (1989)","key":"4_CR9"},{"key":"4_CR10","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1006\/jsco.1999.0314","volume":"28","author":"MA Barkatou","year":"1999","unstructured":"Barkatou, M.A.: On rational solutions of systems of linear differential equations. J. Symb. Comput. 28, 547\u2013567 (1999)","journal-title":"J. Symb. Comput."},{"doi-asserted-by":"crossref","unstructured":"Barkatou, M.A.: Rational solutions of matrix difference equations: the problem of equivalence and factorization. In: Proceedings of ISSAC 1999, pp. 277\u2013282 (1999)","key":"4_CR11","DOI":"10.1145\/309831.309956"},{"doi-asserted-by":"crossref","unstructured":"Barkatou, M.A.: Factoring Systems of Linear Functional Systems Using Eigenrings. Computer algebra 2006, 22\u201342, World Sci. Publ., Hackensack, NJ (2007)","key":"4_CR12","DOI":"10.1142\/9789812778857_0003"},{"issue":"2\u20133","key":"4_CR13","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/s11786-010-0056-z","volume":"4","author":"MA Barkatou","year":"2010","unstructured":"Barkatou, M.A., Broughton, G., Pfl\u00fcgel, E.: A monomial-by-monomial method for computing regular solutions of systems of pseudo-linear equations. Math. Comp. Sci. 4(2\u20133), 267\u2013288 (2010)","journal-title":"Math. Comp. Sci."},{"key":"4_CR14","first-page":"2001","volume":"1\u201323","author":"MA Barkatou","year":"2001","unstructured":"Barkatou, M.A., Chen, G.: Some formal invariants of linear difference systems and their computations. Crelle\u2019s J. 1\u201323, 2001 (2001)","journal-title":"Crelle\u2019s J."},{"issue":"6","key":"4_CR15","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1016\/j.jsc.2011.01.001","volume":"46","author":"MA Barkatou","year":"2011","unstructured":"Barkatou, M.A., Cluzeau, T., El Bacha, C.: Simple forms of higher-order linear differential systems and their applications in computing regular solutions. J. Symb. Comput. 46(6), 633\u2013658 (2011)","journal-title":"J. Symb. Comput."},{"key":"4_CR16","series-title":"Springer Proceedings in Mathematics & Statistics","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/978-3-319-73232-9_2","volume-title":"Advances in Computer Algebra","author":"MA Barkatou","year":"2018","unstructured":"Barkatou, M.A., Cluzeau, T., El Bacha, C.: On the computation of simple forms and regular solutions of linear difference systems. In: Schneider, C., Zima, E. (eds.) WWCA 2016. SPMS, vol. 226, pp. 19\u201349. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-73232-9_2"},{"doi-asserted-by":"crossref","unstructured":"Barkatou, M.A., Cluzeau, T., El Bacha, C., Weil, J.A.: Computing closed form solutions of integrable connections. In: Proceedings of ISSAC 2012, pp. 43\u201350 (2012)","key":"4_CR17","DOI":"10.1145\/2442829.2442840"},{"doi-asserted-by":"crossref","unstructured":"Barkatou, M.A., Cluzeau, T., El Hajj, A.: Simple forms and rational solutions of pseudo-linear systems. In: Proceedings of ISSAC 2019, pp. 26\u201333 (2019)","key":"4_CR18","DOI":"10.1145\/3326229.3326246"},{"doi-asserted-by":"crossref","unstructured":"Barkatou, M.A., Cluzeau, T., El Hajj, A.: PseudoLinearSystems - a maple package for studying systems of pseudo-linear equations. Maple Math. Educ. Res. 327\u2013329. http:\/\/www.unilim.fr\/pages_perso\/ali.el-hajj\/PseudoLinearSystems.html","key":"4_CR19","DOI":"10.1007\/978-3-030-41258-6_24"},{"key":"4_CR20","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.jsc.2013.01.003","volume":"54","author":"MA Barkatou","year":"2013","unstructured":"Barkatou, M.A., El Bacha, C.: On $$k$$-simple forms of first-order linear differential systems and their computation. J. Symb. Comput. 54, 36\u201358 (2013)","journal-title":"J. Symb. Comput."},{"unstructured":"Barkatou, M.A., El Bacha, C., Pfl\u00fcgel, E.: An algorithm computing the regular formal solutions of a system of linear differential equations. In: Proceedings of ISSAC 2010, pp. 45\u201352 (2010)","key":"4_CR21"},{"issue":"4\u20135","key":"4_CR22","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1006\/jsco.1999.0315","volume":"28","author":"MA Barkatou","year":"1999","unstructured":"Barkatou, M.A., Pfl\u00fcgel, E.: Simultaneously row- and column-reduced higher-order linear differential systems. J. Symb. Comput. 28(4\u20135), 569\u2013587 (1999)","journal-title":"J. Symb. Comput."},{"issue":"8","key":"4_CR23","doi-asserted-by":"publisher","first-page":"1017","DOI":"10.1016\/j.jsc.2009.01.002","volume":"44","author":"MA Barkatou","year":"2009","unstructured":"Barkatou, M.A., Pfl\u00fcgel, E.: On the Moser- and super-reduction algorithms of systems of linear differential equations and their complexity. J. Symb. Comput. 44(8), 1017\u20131036 (2009)","journal-title":"J. Symb. Comput."},{"doi-asserted-by":"crossref","unstructured":"Bronstein, M., Li, Z., Wu, M.: Picard-Vessiot extensions for linear functional systems. In: Proceedings of ISSAC 2005, pp. 68\u201375 (2005)","key":"4_CR24","DOI":"10.1145\/1073884.1073896"},{"key":"4_CR25","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/0304-3975(95)00173-5","volume":"157","author":"M Bronstein","year":"1996","unstructured":"Bronstein, M., Petkovsek, M.: An introduction to pseudo-linear algebra. Theor. Comput. Sci. 157, 3\u201333 (1996)","journal-title":"Theor. Comput. Sci."},{"unstructured":"Broughton, G.: Symbolic algorithms for the local analysis of systems of pseudo-linear equations. Ph.D. Thesis, Kingston University (2013)","key":"4_CR26"},{"key":"4_CR27","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s00200-005-0192-x","volume":"17","author":"T Cluzeau","year":"2006","unstructured":"Cluzeau, T., van Hoeij, M.: Computing hypergeometric solutions of linear difference equations. Appl. Algebra Eng. Commun. Comput. 17, 83\u2013115 (2006). https:\/\/doi.org\/10.1007\/s00200-005-0192-x","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"3","key":"4_CR28","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1016\/j.jsc.2009.09.002","volume":"45","author":"R Feng","year":"2010","unstructured":"Feng, R., Singer, M.F., Wu, M.: An algorithm to compute Liouvillian solutions of prime order linear difference-differential equations. J. Symb. Comput. 45(3), 306\u2013323 (2010)","journal-title":"J. Symb. Comput."},{"key":"4_CR29","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1007\/BF01396663","volume":"50","author":"A Hilali","year":"1987","unstructured":"Hilali, A., Wazner, A.: Formes super-irr\u00e9ductibles des syst\u00e8mes diff\u00e9rentiels lin\u00e9aires. Numer. Math. 50, 429\u2013449 (1987)","journal-title":"Numer. Math."},{"issue":"2","key":"4_CR30","doi-asserted-by":"publisher","first-page":"484","DOI":"10.2307\/1968565","volume":"38","author":"N Jacobson","year":"1937","unstructured":"Jacobson, N.: Pseudo-linear transformations. Annals Math. 38(2), 484\u2013507 (1937). Second series","journal-title":"Annals Math."},{"doi-asserted-by":"crossref","unstructured":"Khmelnov, D.E.: Improved algorithms for solving difference and $$q$$-difference equations. Program. Comput. Softw. 26(2), 107\u2013115 (2000). (translated from Programmirovanie No. 2)","key":"4_CR31","DOI":"10.1007\/BF02759198"},{"doi-asserted-by":"crossref","unstructured":"Kauers, M., Schneider, C.: Partial denominator bounds for partial linear difference equations. In: Proceedings of ISSAC 2010, pp. 211\u2013218 (2010)","key":"4_CR32","DOI":"10.1145\/1837934.1837976"},{"doi-asserted-by":"crossref","unstructured":"Kauers, M., Schneider, C.: A refined denominator bounding algorithm for multivariate linear difference equations. In: Proceedings of ISSAC 2011, pp. 201\u2013208 (2011)","key":"4_CR33","DOI":"10.1145\/1993886.1993919"},{"doi-asserted-by":"crossref","unstructured":"Li, Z., Singer, M.F., Wu, M., Zheng, D.: A recursive method for determining the one-dimensional submodules of Laurent-Ore modules. In: Proceedings of ISSAC 2006, pp. 200\u2013208 (2006)","key":"4_CR34","DOI":"10.1145\/1145768.1145806"},{"doi-asserted-by":"crossref","unstructured":"Li, Z., Wu, M.: On solutions of linear systems and factorization of Laurent-Ore modules. Computer algebra 2006, 109\u2013136, World Sci. Publ., Hackensack, NJ (2007)","key":"4_CR35","DOI":"10.1142\/9789812778857_0007"},{"doi-asserted-by":"crossref","unstructured":"Man, Y.K., Write, F.J: Fast polynomial dispersion computation and its application to indefnite summation. In: Proceedings of ISSAC 1994, pp. 175\u2013180 (1994)","key":"4_CR36","DOI":"10.1145\/190347.190413"},{"key":"4_CR37","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1134\/S0361768813020060","volume":"39","author":"SV Paramonov","year":"2013","unstructured":"Paramonov, S.V.: On rational solutions of linear partial differential or difference equations. Program Comput. Soft 39, 57\u201360 (2013)","journal-title":"Program Comput. Soft"},{"key":"4_CR38","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1134\/S0361768814020078","volume":"40","author":"SV Paramonov","year":"2014","unstructured":"Paramonov, S.V.: Checking existence of solutions of partial differential equations in the fields of Laurent series. Program Comput. Soft. 40, 58\u201362 (2014)","journal-title":"Program Comput. Soft."},{"doi-asserted-by":"crossref","unstructured":"Pfl\u00fcgel, E.: An algorithm for computing exponential solutions of first order linear differential systems. In: Proceedings of ISSAC 1997, pp. 146\u2013171 (1997)","key":"4_CR39","DOI":"10.1145\/258726.258773"},{"key":"4_CR40","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1007\/978-1-4613-9647-5_23","volume-title":"Computers and Mathematics","author":"MF Singer","year":"1989","unstructured":"Singer, M.F.: Liouvillian solutions of linear differential equations with Liouvillian coefficients. In: Kaltofen, E., Watt, S.M. (eds.) Computers and Mathematics, pp. 182\u2013191. Springer, New York (1989)"},{"unstructured":"Wu, M.: On solutions of linear functional systems and factorization of modules over Laurent-Ore algebras. Ph.D. Thesis, Univ. of Nice-Sophia Antipolis (2005)","key":"4_CR41"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-85165-1_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T14:57:54Z","timestamp":1725634674000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-85165-1_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030851644","9783030851651"],"references-count":41,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-85165-1_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"16 August 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CASC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Computer Algebra in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Sochi","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Russia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13 September 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 September 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/casc-conference.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Easychair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"40","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"24","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"1","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"60% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.41","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"5","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}