{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T14:02:06Z","timestamp":1725804126316},"publisher-location":"Cham","reference-count":23,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319105147"},{"type":"electronic","value":"9783319105154"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-319-10515-4_1","type":"book-chapter","created":{"date-parts":[[2014,9,1]],"date-time":"2014-09-01T01:23:50Z","timestamp":1409534630000},"page":"1-12","source":"Crossref","is-referenced-by-count":5,"title":["Computable Infinite Power Series in the Role of Coefficients of Linear Differential Systems"],"prefix":"10.1007","author":[{"given":"Sergei A.","family":"Abramov","sequence":"first","affiliation":[]},{"given":"Moulay A.","family":"Barkatou","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"1_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-319-02297-0_1","volume-title":"Computer Algebra in Scientific Computing","author":"S.A. Abramov","year":"2013","unstructured":"Abramov, S.A., Barkatou, M.A.: On the dimension of solution spaces of full rank linear differential systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2013. LNCS, vol.\u00a08136, pp. 1\u20139. Springer, Heidelberg (2013)"},{"key":"1_CR2","unstructured":"Abramov, S.A., Barkatou, M.A.: On solution spaces of products of linear differential or difference operators. ACM Communications in Computer Algebra (accepted)"},{"key":"1_CR3","unstructured":"Abramov, S.A., Barkatou, M.A., Khmelnov, D.E.: On full-rank differential systems with power series coefficients. J. Symbolic Comput. (accepted)"},{"key":"1_CR4","unstructured":"Abramov, S.A., Khmelnov, D.E.: Desingularization of leading matrices of systems of linear ordinary differential equations with polynomial coefficients. In: International Conference \u201cDifferential Equations and Related Topics\u201d Dedicated to I.G.Petrovskii, Moscow, MSU, May 30-June 4, p. 5. Book of Abstracts (2011)"},{"issue":"3","key":"1_CR5","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/s10958-012-0919-8","volume":"185","author":"S.A. Abramov","year":"2012","unstructured":"Abramov, S.A., Khmelnov, D.E.: On singular points of solutions of linear differential systems with polynomial coefficients. J. Math. Sciences\u00a0185(3), 347\u2013359 (2012)","journal-title":"J. Math. Sciences"},{"issue":"2","key":"1_CR6","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1134\/S0361768814020029","volume":"40","author":"S.A. Abramov","year":"2014","unstructured":"Abramov, S.A., Khmelnov, D.E.: Regular solutions of linear differential systems with power series coefficients. Programming and Computer Software\u00a040(2), 98\u2013106 (2014)","journal-title":"Programming and Computer Software"},{"key":"1_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s002000050048","volume":"8","author":"M.A. Barkatou","year":"1997","unstructured":"Barkatou, M.A.: An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system. Applicable Algebra in Engineering, Communication and Computing\u00a08, 1\u201323 (1997)","journal-title":"Applicable Algebra in Engineering, Communication and Computing"},{"issue":"1","key":"1_CR8","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.jsc.2011.12.016","volume":"49","author":"M.A. Barkatou","year":"2013","unstructured":"Barkatou, M.A., El Bacha, C., Labahn, G., Pfl\u00fcgel, E.: On simultaneous row and column reduction of higher-order linear differential systems. J. Symbolic Comput.\u00a049(1), 45\u201364 (2013)","journal-title":"J. Symbolic Comput."},{"issue":"5","key":"1_CR9","doi-asserted-by":"publisher","first-page":"513","DOI":"10.1016\/j.jsc.2005.10.002","volume":"41","author":"B. Beckermann","year":"2006","unstructured":"Beckermann, B., Cheng, H., Labahn, G.: Fraction-free row reduction of matrices of Ore polynomials. J. Symbolic Comput.\u00a041(5), 513\u2013543 (2006)","journal-title":"J. Symbolic Comput."},{"key":"1_CR10","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/BF01579200","volume":"267","author":"J. Denef","year":"1984","unstructured":"Denef, J., Lipshitz, L.: Power series solutions of algebraic differential equations. Math. Ann.\u00a0267, 213\u2013238 (1984)","journal-title":"Math. Ann."},{"issue":"950","key":"1_CR11","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1098\/rsta.1956.0003","volume":"248","author":"A. Fr\u00f6lich","year":"1956","unstructured":"Fr\u00f6lich, A., Shepherdson, J.C.: Effective procedures in field theory. Phil. Trans. R. Soc. Lond.\u00a0248(950), 407\u2013432 (1956)","journal-title":"Phil. Trans. R. Soc. Lond."},{"issue":"1","key":"1_CR12","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/0304-3975(95)00176-X","volume":"157","author":"D. Grigoriev","year":"1996","unstructured":"Grigoriev, D.: NC solving of a system of linear differential equations in several unknowns. Theor. Comput. Sci.\u00a0157(1), 79\u201390 (1996)","journal-title":"Theor. Comput. Sci."},{"issue":"4","key":"1_CR13","doi-asserted-by":"publisher","first-page":"1004","DOI":"10.1016\/j.jsc.2006.06.001","volume":"41","author":"J. Hoeven van der","year":"2006","unstructured":"van der Hoeven, J., Shackell, J.R.: Complexity bounds for zero-test algorithms. J. Symbolic Comput.\u00a041(4), 1004\u20131020 (2006)","journal-title":"J. Symbolic Comput."},{"key":"1_CR14","unstructured":"Kushner, B.A.: Lectures on Constructive Mathematical Analysis (Translations of Mathematical Monographs) Amer. Math. Soc. (1984)"},{"key":"1_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0024-3795(85)90140-5","volume":"72","author":"D.A. Lutz","year":"1985","unstructured":"Lutz, D.A., Sch\u00e4fke, R.: On the identification and stability of formal invariants for singular differential equations. Linear Algebra and Its Applications\u00a072, 1\u201346 (1985)","journal-title":"Linear Algebra and Its Applications"},{"volume-title":"Notes on Constructive Mathematics","year":"1970","author":"P. Martin-L\u00f6f","key":"1_CR16","unstructured":"Martin-L\u00f6f, P.: Notes on Constructive Mathematics. Almquist & Wiskell, Stokholm (1970)"},{"issue":"2","key":"1_CR17","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/s002000050002","volume":"10","author":"E. Pfl\u00fcgel","year":"2000","unstructured":"Pfl\u00fcgel, E.: Effective formal reduction of linear differential systems. Applicable Algebra in Engineering, Communication and Computation\u00a010(2), 153\u2013187 (2000)","journal-title":"Applicable Algebra in Engineering, Communication and Computation"},{"key":"1_CR18","series-title":"Grundlehren der mathematischen Wissenschaften","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-55750-7","volume-title":"Galois Theory of Linear Differential Equations","author":"M. Put van der","year":"2003","unstructured":"van der Put, M., Singer, M.F.: Galois Theory of Linear Differential Equations. Grundlehren der mathematischen Wissenschaften, vol.\u00a0328. Springer, Heidelberg (2003)"},{"key":"1_CR19","unstructured":"Ryabenko, A.: On exponential-logarithmic solutions of linear differential systems with power series coefficients (In preparation)"},{"volume-title":"Handbuch der Theorie der linearen Differentialgleichungen","year":"1895","author":"L. Schlesinger","key":"1_CR20","unstructured":"Schlesinger, L.: Handbuch der Theorie der linearen Differentialgleichungen, vol.\u00a01. Teubner, Leipzig (1895)"},{"key":"1_CR21","first-page":"362","volume":"67","author":"G.S. Tseitin","year":"1962","unstructured":"Tseitin, G.S.: Mean-value Theorems in Constructive Analysis. Problems of the Constructive Direction in Mathematics. Part\u00a02. Constructive Mathematical Analysis. Collection of Articles: Trudy Mat. Inst. Steklov, Acad. Sci. USSR\u00a067, 362\u2013384 (1962)","journal-title":"Problems of the Constructive Direction in Mathematics. Part\u00a02. Constructive Mathematical Analysis. Collection of Articles: Trudy Mat. Inst. Steklov, Acad. Sci. USSR"},{"key":"1_CR22","first-page":"230","volume":"42","author":"A. Turing","year":"1936","unstructured":"Turing, A.: On computable numbers, with an application to the Entscheidungsproblem. Proc. London Math. Soc., Series 2\u00a042, 230\u2013265 (1936)","journal-title":"Proc. London Math. Soc., Series 2"},{"key":"1_CR23","unstructured":"Maple online help, \n \n http:\/\/www.maplesoft.com\/support\/help\/"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-10515-4_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T14:35:38Z","timestamp":1558967738000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-10515-4_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783319105147","9783319105154"],"references-count":23,"URL":"http:\/\/dx.doi.org\/10.1007\/978-3-319-10515-4_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]}}}
