{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:21:21Z","timestamp":1750306881929,"version":"3.41.0"},"publisher-location":"New York, NY, USA","reference-count":39,"publisher":"ACM","license":[{"start":{"date-parts":[[2013,6,26]],"date-time":"2013-06-26T00:00:00Z","timestamp":1372204800000},"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":[],"published-print":{"date-parts":[[2013,6,26]]},"DOI":"10.1145\/2465506.2465942","type":"proceedings-article","created":{"date-parts":[[2013,6,25]],"date-time":"2013-06-25T19:13:21Z","timestamp":1372187601000},"page":"45-52","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Integrability conditions for parameterized linear difference equations"],"prefix":"10.1145","author":[{"given":"Mariya","family":"Bessonov","sequence":"first","affiliation":[{"name":"Cornell University, Ithaca, NY, USA"}]},{"given":"Alexey","family":"Ovchinnikov","sequence":"additional","affiliation":[{"name":"CUNY Queens College, Queens, NY, USA"}]},{"given":"Maxwell","family":"Shapiro","sequence":"additional","affiliation":[{"name":"CUNY Graduate Center, New York, NY, USA"}]}],"member":"320","published-online":{"date-parts":[[2013,6,26]]},"reference":[{"key":"e_1_3_2_1_1_1","unstructured":"Arreche C.: Computing the differential Galois group of a one-parameter family of second order linear differential equations (2012). http:\/\/arxiv.org\/abs\/1208.2226  Arreche C.: Computing the differential Galois group of a one-parameter family of second order linear differential equations (2012). http:\/\/arxiv.org\/abs\/1208.2226"},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2442829.2442840"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"crossref","unstructured":"Cassidy P.: Differential algebraic groups. American Journal of Mathematicstextbf94 891--954 (1972). http:\/\/www.jstor.org\/stable\/2373764  Cassidy P.: Differential algebraic groups. American Journal of Mathematicstextbf94 891--954 (1972). http:\/\/www.jstor.org\/stable\/2373764","DOI":"10.2307\/2373764"},{"key":"e_1_3_2_1_4_1","doi-asserted-by":"crossref","unstructured":"Cassidy P.: The differential rational representation algebra on a linear differential algebraic group. Journal of Algebratextbf37(2) 223--238 (1975). http:\/\/dx.doi.org\/10.1016\/0021-8693(75)90075-7  Cassidy P.: The differential rational representation algebra on a linear differential algebraic group. Journal of Algebratextbf37(2) 223--238 (1975). http:\/\/dx.doi.org\/10.1016\/0021-8693(75)90075-7","DOI":"10.1016\/0021-8693(75)90075-7"},{"key":"e_1_3_2_1_5_1","doi-asserted-by":"crossref","unstructured":"Cassidy P. Singer M.: Galois theory of parametrized differential equations and linear differential algebraic group. IRMA Lectures in Mathematics and Theoretical Physicstextbf9 113--157 (2007). http:\/\/dx.doi.org\/10.4171\/020-1\/7  Cassidy P. Singer M.: Galois theory of parametrized differential equations and linear differential algebraic group. IRMA Lectures in Mathematics and Theoretical Physicstextbf9 113--157 (2007). http:\/\/dx.doi.org\/10.4171\/020-1\/7","DOI":"10.4171\/020-1\/7"},{"key":"e_1_3_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2010.08.019"},{"key":"e_1_3_2_1_7_1","unstructured":"Dreyfus T.: Computing the Galois group of some parameterized linear differential equation of order two (2012). http:\/\/arxiv.org\/abs\/1110.1053. To appear in the Proceedings of the AMS  Dreyfus T.: Computing the Galois group of some parameterized linear differential equation of order two (2012). http:\/\/arxiv.org\/abs\/1110.1053. To appear in the Proceedings of the AMS"},{"key":"e_1_3_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2008.02.010"},{"key":"e_1_3_2_1_9_1","first-page":"411","volume":"32","author":"Gillet H.","year":"2013","journal-title":"Mathematics"},{"key":"e_1_3_2_1_10_1","unstructured":"Gorchinskiy S. Ovchinnikov A.: Isomonodromic differential equations and differential categories (2012). http:\/\/arxiv.org\/abs\/1202.0927  Gorchinskiy S. Ovchinnikov A.: Isomonodromic differential equations and differential categories (2012). http:\/\/arxiv.org\/abs\/1202.0927"},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"crossref","unstructured":"Granier A.: A Galois D-groupoid for q-difference equations. Annales de l'Institut Fourier(4) 1493--1516 (2011)  Granier A.: A Galois D-groupoid for q-difference equations. Annales de l'Institut Fourier(4) 1493--1516 (2011)","DOI":"10.5802\/aif.2648"},{"key":"e_1_3_2_1_12_1","doi-asserted-by":"crossref","unstructured":"Hardouin C.: Hypertranscendance des syst\u00e8mes aux diff\u00e9rences diagonaux. Compositio Mathematica(3) 565--581 (2008)  Hardouin C.: Hypertranscendance des syst\u00e8mes aux diff\u00e9rences diagonaux. Compositio Mathematica(3) 565--581 (2008)","DOI":"10.1112\/S0010437X07003430"},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"crossref","unstructured":"Hardouin C. Singer M.: Differential Galois theory of linear difference equations. Mathematische Annalen(2) 333--377 (2008). http:\/\/dx.doi.org\/10.1007\/s00208-008-0238-z  Hardouin C. Singer M.: Differential Galois theory of linear difference equations. Mathematische Annalen(2) 333--377 (2008). http:\/\/dx.doi.org\/10.1007\/s00208-008-0238-z","DOI":"10.1007\/s00208-008-0238-z"},{"key":"e_1_3_2_1_14_1","doi-asserted-by":"crossref","unstructured":"Hardouin C. di Vizio L.: Courbures groupes de Galois g\u00e9n\u00e9riques et D-groupo\u00efdes de Galois d'un syst\u00e8me aux D-diff\u00e9rences. C. R. Math. Acad. Sci. Paris (17-18) 951--954 (2010). http:\/\/dx.doi.org\/10.1016\/j.crma.2010.08.001  Hardouin C. di Vizio L.: Courbures groupes de Galois g\u00e9n\u00e9riques et D-groupo\u00efdes de Galois d'un syst\u00e8me aux D-diff\u00e9rences. C. R. Math. Acad. Sci. Paris (17-18) 951--954 (2010). http:\/\/dx.doi.org\/10.1016\/j.crma.2010.08.001","DOI":"10.1016\/j.crma.2010.08.001"},{"key":"e_1_3_2_1_15_1","unstructured":"Hardouin C. di Vizio L.: Galois theories for q-difference equations: comparison theorems (2011). http:\/\/arxiv.org\/abs\/1002.4839  Hardouin C. di Vizio L.: Galois theories for q-difference equations: comparison theorems (2011). http:\/\/arxiv.org\/abs\/1002.4839"},{"key":"e_1_3_2_1_16_1","unstructured":"Hardouin C. di Vizio L.: On the Grothendieck conjecture on p-curvatures for q-difference equations (2011). http:\/\/arxiv.org\/abs\/1002.4839  Hardouin C. di Vizio L.: On the Grothendieck conjecture on p -curvatures for q-difference equations (2011). http:\/\/arxiv.org\/abs\/1002.4839"},{"key":"e_1_3_2_1_17_1","unstructured":"Hardouin C. di Vizio L.: Parameterized generic Galois groups for q-difference equations followed by the appendix \"The Galois D-groupoid of a q-difference system\" by Anne Granier (2011). http:\/\/arxiv.org\/abs\/1002.4839  Hardouin C. di Vizio L.: Parameterized generic Galois groups for q-difference equations followed by the appendix \"The Galois D-groupoid of a q-difference system\" by Anne Granier (2011). http:\/\/arxiv.org\/abs\/1002.4839"},{"key":"e_1_3_2_1_18_1","doi-asserted-by":"crossref","unstructured":"Hardouin C. di Vizio L.: Descent for differential Galois theory of difference equations. Confluence and q-dependency. Pacific Journal of Mathematics(1) 79--104 (2012). http:\/\/dx.doi.org\/10.2140\/pjm.2012.256.79  Hardouin C. di Vizio L.: Descent for differential Galois theory of difference equations. Confluence and q-dependency. Pacific Journal of Mathematics(1) 79--104 (2012). http:\/\/dx.doi.org\/10.2140\/pjm.2012.256.79","DOI":"10.2140\/pjm.2012.256.79"},{"key":"e_1_3_2_1_19_1","first-page":"251","volume":"24","author":"H\u00f6lder O.","year":"1887","journal-title":"Mathematische Annalen"},{"key":"e_1_3_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.3792\/pjaa.56.143"},{"key":"e_1_3_2_1_21_1","doi-asserted-by":"crossref","unstructured":"Jimbo M. Miwa T. Ueno K.: Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I. General theory and \u03c4-function. Phyica D: Nonlinear Phenomena(2) 306--352 (1981). http:\/\/dx.doi.org\/10.1016\/0167-2789(81)90013-0  Jimbo M. Miwa T. Ueno K.: Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I. General theory and \u03c4-function. Phyica D: Nonlinear Phenomena(2) 306--352 (1981). http:\/\/dx.doi.org\/10.1016\/0167-2789(81)90013-0","DOI":"10.1016\/0167-2789(81)90013-0"},{"key":"e_1_3_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2011.0167"},{"key":"e_1_3_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2012.0224"},{"key":"e_1_3_2_1_24_1","first-page":"171","volume":"16","author":"Kamensky M.","year":"2012","journal-title":"International Mathematics Research Notices"},{"key":"e_1_3_2_1_25_1","unstructured":"Kolchin E.: Differential Algebra and Algebraic Groups. Academic Press New York (1973)  Kolchin E.: Differential Algebra and Algebraic Groups. Academic Press New York (1973)"},{"key":"e_1_3_2_1_26_1","doi-asserted-by":"crossref","unstructured":"Levin A.: Difference Algebra. Springer (2008). http:\/\/dx.doi.org\/10.1007\/978-1-4020-6947-5  Levin A.: Difference Algebra. Springer (2008). http:\/\/dx.doi.org\/10.1007\/978-1-4020-6947-5","DOI":"10.1007\/978-1-4020-6947-5"},{"key":"e_1_3_2_1_27_1","doi-asserted-by":"crossref","unstructured":"Minchenko A. Ovchinnikov A.: Zariski closures of reductive linear differential algebraic groups. Advances in Mathematics(3) 1195--1224 (2011). http:\/\/dx.doi.org\/10.1016\/j.aim.2011.03.002  Minchenko A. Ovchinnikov A.: Zariski closures of reductive linear differential algebraic groups. Advances in Mathematics(3) 1195--1224 (2011). http:\/\/dx.doi.org\/10.1016\/j.aim.2011.03.002","DOI":"10.1016\/j.aim.2011.03.002"},{"key":"e_1_3_2_1_28_1","doi-asserted-by":"crossref","unstructured":"Minchenko A. Ovchinnikov A.: Extensions of differential representations of SL2 and tori. Journal of the Institute of Mathematics of Jussieu(1) 199--224 (2013). http:\/\/dx.doi.org\/10.1017\/S1474748012000692  Minchenko A. Ovchinnikov A.: Extensions of differential representations of SL 2 and tori. Journal of the Institute of Mathematics of Jussieu(1) 199--224 (2013). http:\/\/dx.doi.org\/10.1017\/S1474748012000692","DOI":"10.1017\/S1474748012000692"},{"key":"e_1_3_2_1_29_1","unstructured":"Minchenko A. Ovchinnikov A. Singer M.F.: Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations (2013). http:\/\/arxiv.org\/abs\/1304.2693  Minchenko A. Ovchinnikov A. Singer M.F.: Reductive linear differential algebraic groups and the Galois groups of parameterized linear differential equations (2013). http:\/\/arxiv.org\/abs\/1304.2693"},{"key":"e_1_3_2_1_30_1","unstructured":"Minchenko A. Ovchinnikov A. Singer M.F.: Unipotent differential algebraic groups as parameterized differential Galois groups (2013). http:\/\/arxiv.org\/abs\/1301.0092  Minchenko A. Ovchinnikov A. Singer M.F.: Unipotent differential algebraic groups as parameterized differential Galois groups (2013). http:\/\/arxiv.org\/abs\/1301.0092"},{"key":"e_1_3_2_1_31_1","doi-asserted-by":"crossref","unstructured":"Morikawa S.: On a general difference Galois theory. I. Annales de l'Institut Fourier(7) 2709--2732 (2009)  Morikawa S.: On a general difference Galois theory. I. Annales de l'Institut Fourier(7) 2709--2732 (2009)","DOI":"10.5802\/aif.2505"},{"key":"e_1_3_2_1_32_1","doi-asserted-by":"crossref","unstructured":"Ovchinnikov A.: Tannakian approach to linear differential algebraic groups. Transformation Groups(2) 413--446 (2008). http:\/\/dx.doi.org\/10.1007\/s00031-008-9010-4  Ovchinnikov A.: Tannakian approach to linear differential algebraic groups. Transformation Groups(2) 413--446 (2008). http:\/\/dx.doi.org\/10.1007\/s00031-008-9010-4","DOI":"10.1007\/s00031-008-9010-4"},{"key":"e_1_3_2_1_33_1","doi-asserted-by":"crossref","unstructured":"Sabbah C.: The work of Andrey Bolibrukh on isomonodromic deformations. IRMA Lectures in Mathematics and Theoretical Physics 9--25 (2007). http:\/\/dx.doi.org\/10.4171\/020-1\/2  Sabbah C.: The work of Andrey Bolibrukh on isomonodromic deformations. IRMA Lectures in Mathematics and Theoretical Physics 9--25 (2007). http:\/\/dx.doi.org\/10.4171\/020-1\/2","DOI":"10.4171\/020-1\/2"},{"key":"e_1_3_2_1_34_1","unstructured":"Sibuya Y.: Linear differential equations in the complex domain: problems of analytic continuation vol. 82. American Mathematical Society Providence RI (1990)  Sibuya Y.: Linear differential equations in the complex domain: problems of analytic continuation vol. 82. American Mathematical Society Providence RI (1990)"},{"key":"e_1_3_2_1_35_1","doi-asserted-by":"crossref","unstructured":"Singer M.: Linear algebraic groups as parameterized Picard-Vessiot Galois groups. Journal of Algebra(1) 153--161 (2013). http:\/\/dx.doi.org\/10.1016\/j.jalgebra.2012.09.037  Singer M.: Linear algebraic groups as parameterized Picard-Vessiot Galois groups. Journal of Algebra(1) 153--161 (2013). http:\/\/dx.doi.org\/10.1016\/j.jalgebra.2012.09.037","DOI":"10.1016\/j.jalgebra.2012.09.037"},{"key":"e_1_3_2_1_36_1","unstructured":"Takano K.: On the hypertranscendency of solutions of a difference equation of Kimura. Funkcialaj Ekvacioj. Serio Internaciatextbf16 241--254 (1973). http:\/\/fe.math.kobe-u.ac.jp\/FE\/FE_pdf_with_bookmark\/FE11-20-e_KML\/fe16-241-254\/fe16-241-254.pdf  Takano K.: On the hypertranscendency of solutions of a difference equation of Kimura. Funkcialaj Ekvacioj. Serio Internaciatextbf16 241--254 (1973). http:\/\/fe.math.kobe-u.ac.jp\/FE\/FE_pdf_with_bookmark\/FE11-20-e_KML\/fe16-241-254\/fe16-241-254.pdf"},{"key":"e_1_3_2_1_37_1","doi-asserted-by":"crossref","unstructured":"Trushin D.: Splitting fields and general differential Galois theory. Sbornik: Mathematics(9) 1323--1353 (2010). http:\/\/dx.doi.org\/10.1070\/SM2010v201n09ABEH004114  Trushin D.: Splitting fields and general differential Galois theory. Sbornik: Mathematics(9) 1323--1353 (2010). http:\/\/dx.doi.org\/10.1070\/SM2010v201n09ABEH004114","DOI":"10.1070\/SM2010v201n09ABEH004114"},{"key":"e_1_3_2_1_38_1","unstructured":"di Vizio L.: Approche galoisienne de la transcendance diff\u00e9rentielle (2012). Journ\u00e9e annuelle 2012 de la SMF http:\/\/divizio.perso.math.cnrs.fr\/PREPRINTS\/16-JourneeAnnuelleSMF\/difftransc.pdf.  di Vizio L.: Approche galoisienne de la transcendance diff\u00e9rentielle (2012). Journ\u00e9e annuelle 2012 de la SMF http:\/\/divizio.perso.math.cnrs.fr\/PREPRINTS\/16-JourneeAnnuelleSMF\/difftransc.pdf."},{"key":"e_1_3_2_1_39_1","first-page":"171","volume":"16","author":"Wibmer M.","year":"2012","journal-title":"Algebra"}],"event":{"name":"ISSAC'13: International Symposium on Symbolic and Algebraic Computation","sponsor":["SIGSAM ACM Special Interest Group on Symbolic and Algebraic Manipulation"],"location":"Boston Maine USA","acronym":"ISSAC'13"},"container-title":["Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2465506.2465942","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2465506.2465942","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T08:18:36Z","timestamp":1750234716000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2465506.2465942"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6,26]]},"references-count":39,"alternative-id":["10.1145\/2465506.2465942","10.1145\/2465506"],"URL":"https:\/\/doi.org\/10.1145\/2465506.2465942","relation":{},"subject":[],"published":{"date-parts":[[2013,6,26]]},"assertion":[{"value":"2013-06-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}