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Referencias:

• Atiyah, M., MacDonald, I., (1969) Introduction to Commutative Algebra, , Addison-Wesley Reading 0175.03601
• Brenan, K., Campbell, S., Petzold, L., (1996) Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, , SIAM's Classics in Applied Mathematics Philadelphia 0844.65058
• Campbell, S.L., Gear, C.W., The index of general nonlinear DAEs (1995) Numerische Mathematik, 72 (2), pp. 173-196. , DOI 10.1007/s002110050165
• Carrà Ferro, G., Some upper bounds for the multiplicity of an autoreduced subset of N m and its applications (1986) Algebraic Algorithms and Error Correcting Codes, 229, pp. 306-315. , In: Calmet, J. (ed.) AAECC-3, Grenoble, July 1985, Lectecture Notes in Computer Science
• Cartan, E., (1946) Les Systèmes Différentiels Extérieurs et Leurs Applications Geométriqués, , Hermann Paris
• Cohn, R., The Greenspan bound for the order of differential systems (1980) Proc. Am. Math. Soc., 79 (4), pp. 523-526. , 0436.12018 10.2307/2042489
• D'Alfonso, L., Jeronimo, G., Solerno, P., On the complexity of the resolvent representation of some prime differential ideals (2006) Journal of Complexity, 22 (3), pp. 396-430. , DOI 10.1016/j.jco.2005.10.002, PII S0885064X05001093
• Fliess, M., Implicit differential equations and lie-Bäcklund mappings (1995) Proceedings of the 34th Conference on Decision and Control, pp. 2704-2709. , New Orleans
• Greenspan, B., A bound for the orders of components of a system of algebraic difference equations (1959) Pacific J. Math., 9, pp. 473-486. , 0215.36203 109153
• Heintz, J., Definability and fast quantifier elimination in algebraically closed fields (1983) Theoret. Comput. Sci., 24 (3), pp. 239-277. , 0546.03017 10.1016/0304-3975(83)90002-6 716823
• Heintz, J., Krick, T., Puddu, S., Sabia, J., Waissbein, A., Deformation techniques for efficient polynomial equation solving (2000) J. Complexity, 16 (1), pp. 70-109. , 1041.65044 10.1006/jcom.1999.0529 1762400
• Jacobi, C., (1890) De Investigando Ordine Systematis Aequationum Differentialum Vulgarium Cujuscunque, pp. 193-216. , http://www.lix.polytechnique.fr/~ollivier/JACOBI/jacobiEngl.htm, C. G. J. Jacobi's gesammelte Werke, fünfter Band, herausgegeben von K. Weierstrass, Berlin, Bruck und Verlag von Georg Reimer Translated from latin by F. Ollivier (Ecole Polytechnique, Palaiseau)
• Jacobi, C., (1890) De Aequationum Differentialum Systemate Non Normali Ad Formam Normalem Revocando, pp. 485-513. , http://www.lix.polytechnique.fr/~ollivier/JACOBI/jacobiEngl.htm, published by A. Clebsch, C.G.J. Jacobi's gesammelte Werke, fünfter Band, herausgegeben von K. Weierstrass, Berlin, Bruck und Verlag von Georg Reimer Translated from latin by F. Ollivier (Ecole Polytechnique, Palaiseau)
• Kolchin, E.R., (1973) Differential Algebra and Algebraic Groups, , Academic Press New York 0264.12102
• Kondratieva, M., Mihalev, A., Pankratiev, E., (1982) Jacobi's Bound for Systems of Ordinary Differential Polynomials (In Russian), pp. 79-85. , http://shade.msu.ru/~kondra_m/scan.pdf, Algebra, M.: MGU
• Kunkel, P., Mehrmann, V., (2006) Differential-Algebraic Equations. Analysis and Numerical Solutions, , EMS Publishing House Zurich
• Kunz, E., (1985) Introduction to Commutative Algebra and Algebraic Geometry, , Birkhäuser Basel 0563.13001
• Kuranishi, M., On E. Cartan's prolongation theorem of exterior differential systems (1957) Am. J. Math., 79, pp. 1-47. , 0077.29701 10.2307/2372381 81957
• Lamour, R., Index determination and calculation of consistent initial values for DAEs (2005) Computers and Mathematics with Applications, 50 (7), pp. 1125-1140. , DOI 10.1016/j.camwa.2005.08.014, PII S089812210500341X, Numerical Methods and Computational Mechanics
• Lando, B., Jacobi's bound for the order of systems of first order differential equations (1970) Trans. Am. Math. Soc., 152, pp. 119-135. , 0215.07502 10.2307/1995642 279079
• Le Vey, G., Differential Algebraic Equations: A new look at the index Rapp. Rech., 2239. , INRIA 1994
• Matera, G., Sedoglavic, A., Fast computation of discrete invariants associated to a differential rational mapping (2003) Journal of Symbolic Computation, 36 (3-4), pp. 473-499. , DOI 10.1016/S0747-7171(03)00091-9
• Ollivier, F., Jacobi's bound and normal form computations (2007) An Historical Survey
• Ollivier, F., Sadik, B., La borne de Jacobi pour une diffiété définie par un système quasi régulier (2007) C. R. Acad. Sci.Paris Sér. i, 345, pp. 139-144. , 1120.35005 2344812
• Pantelides, C., The consistent inicialization of differential-algebraic equations (1988) SIAM J. Sci. Stat. Comput., 9 (2), pp. 213-231. , 0643.65039 10.1137/0909014 930042
• Poulsen, M., (2001) Structural Analysis of DAEs, , PhD Thesis, Technical University of Denmark
• Pritchard, F.L., Sit, W.Y., On initial value problems for ordinary differential-algebraic equations (2007) Radon Ser. Comp. Appl. Math, 1, pp. 1-57
• Rabier, P., Rheinboldt, W., A geometric treatment of implicit differential-algebraic equations (1994) J. Diff. Equ., 109, pp. 110-146. , 0804.34004 10.1006/jdeq.1994.1046 1272402
• Reid, G.J., Lin, P., Wittkopf, A.D., Differential elimination - Completion algorithms for DAE and PDAE (2001) Studies in Applied Mathematics, 106 (1), pp. 1-45
• Ritt, J.F., (1950) Differential Algebra, Vol. 33, , American Mathematical Society Colloquium Publications New York
• Ritt, J.F., Jacobi's problem on the order of a system of differential equations (1935) Ann. Math., 36, pp. 303-312. , 10.2307/1968572 1503224
• Sadik, B., Bound for the order of characteristic set elements of an ordinary prime differential ideal and some applications (2000) Applicable Algebra in Engineering, Communications and Computing, 10 (3), pp. 251-268. , DOI 10.1007/s002000050128
• Sadik, B., (1995) Contributions À l'Étude de la Complexité du Calcul d'Un Ensemble Caractéristique en Algèbre Différentielle, , PhD Thesis
• Schost, E., Computing parametric geometric resolutions (2003) Appl. Algebra Eng. Comm. Comput., 13 (5), pp. 349-393. , 10.1007/s00200-002-0109-x 1959170
• Seiler, W., Indices and Solvability of General Systems of Differential equations (1999) Comput. Algebra in Scientific Computing, CASC 99, pp. 365-385. , V. Ghanza E. Mayr E. Vorozhtsov (eds). Springer Heidelberg
• Sedoglavic, A., (2000) A Mixed Symbolic-numeric Method to Study Prime Ordinary Differential Ideals
• Thomas, G., Symbolic computation of the index of quasilinear differential-algebraic equations (1996) Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, Zurich, Switzerland, pp. 196-203. , Y. Lakshman (eds). ACM Press New York. 10.1145/236869.237074

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