Barkatou, Moulay; Carnicero, Felix A.; Sanchez, Fernando Sanzs Turrittin’s normal forms for linear systems of meromorphic ODEs over the real field. (English) Zbl 1527.34067 Electron. J. Differ. Equ. 2023, Paper No. 79, 23 p. (2023). MSC: 34C20 34C08 34M03 34M25 PDFBibTeX XMLCite \textit{M. Barkatou} et al., Electron. J. Differ. Equ. 2023, Paper No. 79, 23 p. (2023; Zbl 1527.34067) Full Text: Link
Barkatou, Moulay; Carnicero-Martín, Félix Álvaro; Sánchez, Fernando Sanz Turrittin’s Theorem revisited. The real case. arXiv:2305.08211 Preprint, arXiv:2305.08211 [math.CA] (2023). MSC: 34C20 34C08 34M03 34M25 BibTeX Cite \textit{M. Barkatou} et al., ``Turrittin's Theorem revisited. The real case'', Preprint, arXiv:2305.08211 [math.CA] (2023) Full Text: arXiv OA License
Barkatou, Moulay A.; Saade, Joelle; Weil, Jacques-Arthur Formal reduction of singular linear differential systems using eigenrings: a refined approach. (English) Zbl 1457.12004 J. Symb. Comput. 102, 231-258 (2021). Reviewer: Mykola Grygorenko (Kyïv) MSC: 12H20 34A30 68W30 12H05 PDFBibTeX XMLCite \textit{M. A. Barkatou} et al., J. Symb. Comput. 102, 231--258 (2021; Zbl 1457.12004) Full Text: DOI
Barkatou, Moulay; Cluzeau, Thomas; Di Vizio, Lucia; Weil, Jacques-Arthur Reduced forms of linear differential systems and the intrinsic Galois-Lie algebra of Katz. (English) Zbl 1448.12002 SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 054, 13 p. (2020). Reviewer: Mykola Grygorenko (Kyïv) MSC: 12H05 12G05 34M03 34M15 34M35 PDFBibTeX XMLCite \textit{M. Barkatou} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 054, 13 p. (2020; Zbl 1448.12002) Full Text: DOI arXiv
Barkatou, Moulay; Cluzeau, Thomas; El Hajj, Ali Simple forms and rational solutions of pseudo-linear systems. (English) Zbl 1467.34012 Bradford, Russell (ed.), Proceedings of the 44th international symposium on symbolic and algebraic computation, ISSAC ’19, Beijing, China, July 15–18, 2019. New York, NY: Association for Computing Machinery (ACM). 26-33 (2019). MSC: 34A30 39A10 68W30 PDFBibTeX XMLCite \textit{M. Barkatou} et al., in: Proceedings of the 44th international symposium on symbolic and algebraic computation, ISSAC '19, Beijing, China, July 15--18, 2019. New York, NY: Association for Computing Machinery (ACM). 26--33 (2019; Zbl 1467.34012) Full Text: DOI
Barkatou, Moulay A.; Saade, Joelle; Weil, Jacques-Arthur A new approach for formal reduction of singular linear differential systems using eigenrings. (English) Zbl 1467.34010 Arreche, Carlos (ed.), Proceedings of the 43rd international symposium on symbolic and algebraic computation, ISSAC 2018, New York, NY, USA, July 16–19, 2018. New York, NY: Association for Computing Machinery (ACM). 47-54 (2018). MSC: 34A25 34A30 68W30 PDFBibTeX XMLCite \textit{M. A. Barkatou} et al., in: Proceedings of the 43rd international symposium on symbolic and algebraic computation, ISSAC 2018, New York, NY, USA, July 16--19, 2018. New York, NY: Association for Computing Machinery (ACM). 47--54 (2018; Zbl 1467.34010) Full Text: DOI
Barkatou, Moulay A.; Jaroschek, Maximilian; Maddah, Suzy S. Formal solutions of completely integrable Pfaffian systems with normal crossings. (English) Zbl 1377.35060 J. Symb. Comput. 81, 41-68 (2017). MSC: 35F05 35-04 68W30 68W40 35A30 35A08 PDFBibTeX XMLCite \textit{M. A. Barkatou} et al., J. Symb. Comput. 81, 41--68 (2017; Zbl 1377.35060) Full Text: DOI
Barkatou, Moulay; Cluzeau, Thomas; Weil, Jacques-Arthur; Di Vizio, Lucia Computing the Lie algebra of the differential Galois group of a linear differential system. (English) Zbl 1364.12003 Rosenkranz, Markus (ed.), Proceedings of the 41st international symposium on symbolic and algebraic computation, ISSAC 2016, Waterloo, Canada, July 20–22, 2016. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-4380-0). 63-70 (2016). MSC: 12H05 17B45 68W30 34M15 PDFBibTeX XMLCite \textit{M. Barkatou} et al., in: Proceedings of the 41st international symposium on symbolic and algebraic computation, ISSAC 2016, Waterloo, Canada, July 20--22, 2016. New York, NY: Association for Computing Machinery (ACM). 63--70 (2016; Zbl 1364.12003) Full Text: DOI
Barkatou, Moulay A.; Maddah, Suzy S. Removing apparent singularities of systems of linear differential equations with rational function coefficients. (English) Zbl 1346.68268 Proceedings of the 40th international symposium on symbolic and algebraic computation, ISSAC 2015, Bath, UK, July 6–9, 2015. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-3435-8). 53-60 (2015). MSC: 68W30 34A30 PDFBibTeX XMLCite \textit{M. A. Barkatou} and \textit{S. S. Maddah}, in: Proceedings of the 40th international symposium on symbolic and algebraic computation, ISSAC 2015, Bath, UK, July 6--9, 2015. New York, NY: Association for Computing Machinery (ACM). 53--60 (2015; Zbl 1346.68268) Full Text: DOI
Barkatou, Moulay A.; Cluzeau, Thomas; Jalouli, Achref Formal solutions of linear differential systems with essential singularities in their coefficients. (English) Zbl 1345.68280 Proceedings of the 40th international symposium on symbolic and algebraic computation, ISSAC 2015, Bath, UK, July 6–9, 2015. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-3435-8). 45-52 (2015). MSC: 68W30 34M03 34M25 34M35 PDFBibTeX XMLCite \textit{M. A. Barkatou} et al., in: Proceedings of the 40th international symposium on symbolic and algebraic computation, ISSAC 2015, Bath, UK, July 6--9, 2015. New York, NY: Association for Computing Machinery (ACM). 45--52 (2015; Zbl 1345.68280) Full Text: DOI
Barkatou, Moulay; Cluzeau, Thomas; El Bacha, Carole A new approach for computing regular solutions of linear difference systems. (English) Zbl 1434.39001 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 17th international workshop, CASC 2015, Aachen, Germany, September 14–18, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9301, 72-86 (2015). MSC: 39A06 68W30 05A30 33E30 PDFBibTeX XMLCite \textit{M. Barkatou} et al., Lect. Notes Comput. Sci. 9301, 72--86 (2015; Zbl 1434.39001) Full Text: DOI
Maddah, Suzy S.; Barkatou, Moulay A.; Abbas, Hassan On the reduction of singularly-perturbed linear differential systems. (English) Zbl 1325.68294 Nabeshima, Katsusuke (ed.), Proceedings of the 39th international symposium on symbolic and algebraic computation, ISSAC 2014, Kobe, Japan, July 23–25, 2014. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-2501-1). 320-327 (2014). MSC: 68W30 34A30 34E20 PDFBibTeX XMLCite \textit{S. S. Maddah} et al., in: Proceedings of the 39th international symposium on symbolic and algebraic computation, ISSAC 2014, Kobe, Japan, July 23--25, 2014. New York, NY: Association for Computing Machinery (ACM). 320--327 (2014; Zbl 1325.68294) Full Text: DOI arXiv
Maddah, Suzy S.; Barkatou, Moulay A.; Abbas, Hassan Formal solutions of a class of Pfaffian systems in two variables. (English) Zbl 1325.68293 Nabeshima, Katsusuke (ed.), Proceedings of the 39th international symposium on symbolic and algebraic computation, ISSAC 2014, Kobe, Japan, July 23–25, 2014. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-2501-1). 312-319 (2014). MSC: 68W30 34A30 35F35 PDFBibTeX XMLCite \textit{S. S. Maddah} et al., in: Proceedings of the 39th international symposium on symbolic and algebraic computation, ISSAC 2014, Kobe, Japan, July 23--25, 2014. New York, NY: Association for Computing Machinery (ACM). 312--319 (2014; Zbl 1325.68293) Full Text: DOI arXiv
Abramov, Sergei A.; Barkatou, Moulay A. On solution spaces of products of linear differential or difference operators. (English) Zbl 1322.68269 ACM Commun. Comput. Algebra 48, No. 4, 155-165 (2014). MSC: 68W30 34A30 39A06 PDFBibTeX XMLCite \textit{S. A. Abramov} and \textit{M. A. Barkatou}, ACM Commun. Comput. Algebra 48, No. 4, 155--165 (2014; Zbl 1322.68269) Full Text: DOI
Abramov, Sergei A.; Barkatou, Moulay A. Computable infinite power series in the role of coefficients of linear differential systems. (English) Zbl 1416.68211 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 16th international workshop, CASC 2014, Warsaw, Poland, September 8–12, 2014. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8660, 1-12 (2014). MSC: 68W30 12H20 PDFBibTeX XMLCite \textit{S. A. Abramov} and \textit{M. A. Barkatou}, Lect. Notes Comput. Sci. 8660, 1--12 (2014; Zbl 1416.68211) Full Text: DOI
Abramov, S. A.; Barkatou, M. A. On the dimension of solution spaces of full rank linear differential systems. (English) Zbl 1412.34055 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 15th international workshop, CASC 2013, Berlin, Germany, September 9–13, 2013. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8136, 1-9 (2013). MSC: 34A30 34C20 68W30 PDFBibTeX XMLCite \textit{S. A. Abramov} and \textit{M. A. Barkatou}, Lect. Notes Comput. Sci. 8136, 1--9 (2013; Zbl 1412.34055) Full Text: DOI
Barkatou, Moulay A.; El Bacha, Carole; Labahn, George; Pflügel, Eckhard On simultaneous row and column reduction of higher-order linear differential systems. (English) Zbl 1258.34028 J. Symb. Comput. 49, 45-64 (2013). MSC: 34A30 34-04 34C20 68W30 PDFBibTeX XMLCite \textit{M. A. Barkatou} et al., J. Symb. Comput. 49, 45--64 (2013; Zbl 1258.34028) Full Text: DOI
Barkatou, Moulay A.; Raab, Clemens G. Solving linear ordinary differential systems in hyperexponential extensions. (English) Zbl 1323.68581 van der Hoeven, Joris (ed.) et al., Proceedings of the 37th international symposium on symbolic and algebraic computation, ISSAC 2012, Grenoble, France, July 22–25, 2012. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-1269-1). 51-58 (2012). MSC: 68W30 34A30 PDFBibTeX XMLCite \textit{M. A. Barkatou} and \textit{C. G. Raab}, in: Proceedings of the 37th international symposium on symbolic and algebraic computation, ISSAC 2012, Grenoble, France, July 22--25, 2012. New York, NY: Association for Computing Machinery (ACM). 51--58 (2012; Zbl 1323.68581) Full Text: DOI
Barkatou, M. A.; Cluzeau, T.; El Bacha, C.; Weil, J.-A. Computing closed form solutions of integrable connections. (English) Zbl 1323.68580 van der Hoeven, Joris (ed.) et al., Proceedings of the 37th international symposium on symbolic and algebraic computation, ISSAC 2012, Grenoble, France, July 22–25, 2012. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-1269-1). 43-50 (2012). MSC: 68W30 35A24 35F35 68Q25 PDFBibTeX XMLCite \textit{M. A. Barkatou} et al., in: Proceedings of the 37th international symposium on symbolic and algebraic computation, ISSAC 2012, Grenoble, France, July 22--25, 2012. New York, NY: Association for Computing Machinery (ACM). 43--50 (2012; Zbl 1323.68580) Full Text: DOI
Aparicio-Monforte, Ainhoa; Barkatou, Moulay A.; Simon, Sergi; Weil, Jacques-Arthur Formal first integrals along solutions of differential systems. I. (English) Zbl 1323.34097 Leykin, Anton (ed.), Proceedings of the 36th international symposium on symbolic and algebraic computation, ISSAC 2011, San Jose, CA, USA, June 7–11, 2011. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0675-1). 19-26 (2011). MSC: 34M25 47J30 68W30 PDFBibTeX XMLCite \textit{A. Aparicio-Monforte} et al., in: Proceedings of the 36th international symposium on symbolic and algebraic computation, ISSAC 2011, San Jose, CA, USA, June 7--11, 2011. New York, NY: Association for Computing Machinery (ACM). 19--26 (2011; Zbl 1323.34097) Full Text: DOI
Abramov, S. A.; Barkatou, M. A.; Pflügel, E. Higher-order linear differential systems with truncated coefficients. (English) Zbl 1344.68290 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 13th international workshop, CASC 2011, Kassel, Germany, September 5–9, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-23567-2/pbk). Lecture Notes in Computer Science 6885, 10-24 (2011). MSC: 68W30 34A25 34A30 PDFBibTeX XMLCite \textit{S. A. Abramov} et al., Lect. Notes Comput. Sci. 6885, 10--24 (2011; Zbl 1344.68290) Full Text: DOI
Barkatou, Moulay A.; Cluzeau, Thomas; El Bacha, Carole Simple forms of higher-order linear differential systems and their applications in computing regular solutions. (English) Zbl 1216.34096 J. Symb. Comput. 46, No. 6, 633-658 (2011). MSC: 34M25 34M03 68W30 PDFBibTeX XMLCite \textit{M. A. Barkatou} et al., J. Symb. Comput. 46, No. 6, 633--658 (2011; Zbl 1216.34096) Full Text: DOI
Barkatou, Moulay A.; El Bacha, Carole; Pflügel, Eckhard Simultaneously row- and column-reduced higher-order linear differential systems. (English) Zbl 1321.68521 Watt, Stephen M. (ed.), Proceedings of the 35th international symposium on symbolic and algebraic computation, ISSAC 2010, Munich, Germany, July 25–28, 2010. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0150-3). 45-52 (2010). MSC: 68W30 34A09 34A30 34C20 PDFBibTeX XMLCite \textit{M. A. Barkatou} et al., in: Proceedings of the 35th international symposium on symbolic and algebraic computation, ISSAC 2010, Munich, Germany, July 25--28, 2010. New York, NY: Association for Computing Machinery (ACM). 45--52 (2010; Zbl 1321.68521) Full Text: DOI
Barkatou, Moulay A.; Broughton, Gary; Pflügel, Eckhard A monomial-by-monomial method for computing regular solutions of systems of pseudo-linear equations. (English) Zbl 1218.68201 Math. Comput. Sci. 4, No. 2-3, 267-288 (2010). MSC: 68W30 39A06 PDFBibTeX XMLCite \textit{M. A. Barkatou} et al., Math. Comput. Sci. 4, No. 2--3, 267--288 (2010; Zbl 1218.68201) Full Text: DOI
Barkatou, Moulay A.; Cluzeau, Thomas; El Bacha, Carole Algorithms for regular solutions of higher-order linear differential systems. (English) Zbl 1237.68249 May, John P. (ed.), ISSAC 2009. Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation, Seoul, July 28–31, 2009. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-60558-609-0). 7-14 (2009). MSC: 68W30 34A25 34A30 PDFBibTeX XMLCite \textit{M. A. Barkatou} et al., in: Proceedings of the 2009 international symposium on symbolic and algebraic computation, ISSAC 2009, Seoul, July 28--31, 2009. New York, NY: Association for Computing Machinery (ACM). 7--14 (2009; Zbl 1237.68249) Full Text: DOI
Barkatou, Moulay A.; Pflügel, Eckhard On the Moser- and super-reduction algorithms of systems of linear differential equations and their complexity. (English) Zbl 1183.34134 J. Symb. Comput. 44, No. 8, 1017-1036 (2009). MSC: 68W30 34C20 34-04 65L99 PDFBibTeX XMLCite \textit{M. A. Barkatou} and \textit{E. Pflügel}, J. Symb. Comput. 44, No. 8, 1017--1036 (2009; Zbl 1183.34134) Full Text: DOI
Barkatou, Moulay A.; Pflügel, Eckhard Computing super-irreducible forms of systems of linear differential equations via Moser-reduction: a new approach. (English) Zbl 1189.68178 Brown, C. W. (ed.), ISSAC 2007. Proceedings of the 32nd international symposium on symbolic and algebraic computation (ISSAC 2007), Waterloo, ON, Canada, July 29–August 1, 2007. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-59593-743-8). 1-8 (2007). MSC: 68W30 34-04 34C20 65L99 PDFBibTeX XMLCite \textit{M. A. Barkatou} and \textit{E. Pflügel}, in: Proceedings of the 2007 international symposium on symbolic and algebraic computation, ISSAC 2007, Waterloo, ON, Canada, July 29--August 1, 2007. New York, NY: Association for Computing Machinery (ACM). 1--8 (2007; Zbl 1189.68178)
Barkatou, Moulay; Chyzak, Frédéric; Loday-Richaud, Michèle Algorithmic methods involving the rank of a differential operator. (Remarques algorithmiques liées au rang d’un opérateur différentiel linéaire.) (French) Zbl 1070.34117 Fauvet, F. (ed.) et al., From combinatorics to dynamical systems. Journées de calcul formel en l’honneur de Jean Thomann, Marseille, France, March 22–23, 2002. Berlin: de Gruyter (ISBN 3-11-017875-3/pbk). IRMA Lect. Math. Theor. Phys. 3, 87-129 (2003). Reviewer: Jacques Sauloy (Toulouse) MSC: 34M25 12H05 12H10 68W30 39A12 PDFBibTeX XMLCite \textit{M. Barkatou} et al., IRMA Lect. Math. Theor. Phys. 3, 87--129 (2003; Zbl 1070.34117)
Barkatou, M. A.; Pflügel, E. On the equivalence problem of linear differential systems and its application for factoring completely reducible systems. (English) Zbl 0928.65082 Gloor, Oliver (ed.), Proceedings of the 1998 international symposium on symbolic and algebraic computation, ISSAC ’98, Rostock, Germany, August 13–15, 1998. New York, NY: ACM Press. 268-275 (1998). Reviewer: H.Ade (Mainz) MSC: 65L05 34A30 34C20 PDFBibTeX XMLCite \textit{M. A. Barkatou} and \textit{E. Pflügel}, in: Proceedings of the 1998 international symposium on symbolic and algebraic computation, ISSAC '98, Rostock, Germany, August 13--15, 1998. New York, NY: ACM Press. 268--275 (1998; Zbl 0928.65082)
Barkatou, M. A. An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system. (English) Zbl 0867.65034 Appl. Algebra Eng. Commun. Comput. 8, No. 1, 1-23 (1997). Reviewer: M.Calvo (Zaragoza) MSC: 65L05 68W30 34A30 PDFBibTeX XMLCite \textit{M. A. Barkatou}, Appl. Algebra Eng. Commun. Comput. 8, No. 1, 1--23 (1997; Zbl 0867.65034) Full Text: DOI
Barkatou, M. A.; Richard-Jung, F. Formal solutions of linear differential and difference equations. (English. Russian original) Zbl 0973.68668 Program. Comput. Softw. 23, No. 1, 17-30 (1997); translation from Programmirovanie 1997, No. 1, 24-42 (1997). MSC: 68W30 68M99 65M99 PDFBibTeX XMLCite \textit{M. A. Barkatou} and \textit{F. Richard-Jung}, Program. Comput. Softw. 23, No. 1, 17--30 (1997; Zbl 0973.68668); translation from Programmirovanie 1997, No. 1, 24--42 (1997)