Differential algebra (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Differential algebra" in English language version.

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31doi.org

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3inria.fr

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ams.org

bookstore.ams.org

Ritt 1950 Ritt, Joseph Fels (1950). Differential Algebra. Vol. 33. Providence, Rhode Island: American Mathematical Society Colloquium Publications. ISBN 978-0-8218-3205-9.

community.ams.org

Ritt 1930 Ritt, Joseph Fels (1930). "Manifolds of functions defined by systems of algebraic differential equations" (PDF). Transactions of the American Mathematical Society. 32 (4): 569–598. doi:10.1090/S0002-9947-1930-1501554-4. S2CID 54064812.

ams.org

Lando 1970 Lando, Barbara A. (1970). "Jacobi's bound for the order of systems of first order differential equations". Transactions of the American Mathematical Society. 152 (1): 119–135. doi:10.1090/S0002-9947-1970-0279079-1. ISSN 0002-9947.

archive.org

Ritt 1932, pp. iii–iv Ritt, Joseph (1932). differential equations from the algebraic standpoint. Vol. 14. American Mathematical Society.
Ritt 1932 Ritt, Joseph (1932). differential equations from the algebraic standpoint. Vol. 14. American Mathematical Society.
Dummit & Foote 2004, p. 343 Dummit, David Steven; Foote, Richard Martin (2004). Abstract algebra (Third ed.). Hoboken, NJ: John Wiley & Sons. ISBN 0-471-43334-9.
Dummit & Foote 2004, p. 337 Dummit, David Steven; Foote, Richard Martin (2004). Abstract algebra (Third ed.). Hoboken, NJ: John Wiley & Sons. ISBN 0-471-43334-9.
Taylor 1991 Taylor, Michael E. (1991). Pseudodifferential operators and nonlinear PDE. Boston: Birkhäuser. ISBN 978-0-8176-3595-4.

arxiv.org

Clarkson & Mansfield 1994 Clarkson, Peter A.; Mansfield, Elizabeth L. (January 1994). "Symmetry reductions and exact solutions of a class of nonlinear heat equations". Physica D: Nonlinear Phenomena. 70 (3): 250–288. arXiv:solv-int/9306002. Bibcode:1994PhyD...70..250C. doi:10.1016/0167-2789(94)90017-5. S2CID 16858637.
Parshin 1999, p. 268 Parshin, Aleksei Nikolaevich (1999). "On a ring of formal pseudo-differential operators". Proc. Steklov Math. Institute. 224: 266–280. arXiv:math/9911098. Bibcode:1999math.....11098P.
Golubitsky, Kondratieva & Ovchinnikov 2009 Golubitsky, O. D.; Kondratieva, M. V.; Ovchinnikov, A. I. (2009). "On the generalized Ritt problem as a computational problem". Journal of Mathematical Sciences. 163 (5): 515–522. arXiv:0809.1128. doi:10.1007/s10958-009-9689-3. S2CID 17503904.
Freitag, Sánchez & Simmons 2016 Freitag, James; Sánchez, Omar León; Simmons, William (2 June 2016). "On Linear Dependence Over Complete Differential Algebraic Varieties". Communications in Algebra. 44 (6): 2645–2669. arXiv:1401.6211. doi:10.1080/00927872.2015.1057828. S2CID 56218725.

books.google.com

Kolchin 1973 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Kolchin 1973, pp. 58–59 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Kolchin 1973, pp. 58–60 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Kolchin 1973, pp. 61–62 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Buium 1994, p. 21 Buium, Alexandru (1994). Differential algebra and diophantine geometry. Hermann. ISBN 978-2-7056-6226-4.
Kolchin 1973, pp. 126–129 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Kolchin 1973, pp. 75–76 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Kolchin 1973, p. 75 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Kolchin 1973, p. 81 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Kolchin 1973, p. 82 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Kolchin 1973, p. 136 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Kolchin 1973, p. 60 Kolchin, Ellis (1973). Differential Algebra And Algebraic Groups. Academic Press. ISBN 978-0-08-087369-5.
Buium 1994 Buium, Alexandru (1994). Differential algebra and diophantine geometry. Hermann. ISBN 978-2-7056-6226-4.

core.ac.uk

Diop 1992 Diop, Sette (May 1992). "Differential-algebraic decision methods and some applications to system theory" (PDF). Theoretical Computer Science. 98 (1): 137–161. doi:10.1016/0304-3975(92)90384-R.

doi.org

Ritt 1930 Ritt, Joseph Fels (1930). "Manifolds of functions defined by systems of algebraic differential equations" (PDF). Transactions of the American Mathematical Society. 32 (4): 569–598. doi:10.1090/S0002-9947-1930-1501554-4. S2CID 54064812.
Bronstein 2005, p. 76 Bronstein, Manuel (2005). Symbolic integration I : transcendental functions. Algorithms and Computation in Mathematics. Vol. 1 (2nd ed.). Berlin: Springer. doi:10.1007/b138171. ISBN 3-540-21493-3.
Sit 2002, pp. 3–4 Sit, William Y. (2002). "The Ritt-Kolchin theory for differential polynomials". In Guo, Li; Cassidy, Phyllis J; Keigher, William F; Sit, William Y (eds.). Differential algebra and related topics: proceedings of the International Workshop, Newark Campus of Rutgers, the State University of New Jersey, 2-3 November 2000. River Edge, NJ: World Scientific. doi:10.1142/4768. ISBN 981-02-4703-6.
Li & Yuan 2019 Li, Wei; Yuan, Chun-Ming (February 2019). "Elimination Theory in Differential and Difference Algebra". Journal of Systems Science and Complexity. 32 (1): 287–316. doi:10.1007/s11424-019-8367-x. S2CID 255158214.
Ferro 2005 Ferro, Giuseppa Carrá (2005). "Generalized Differential Resultant Systems of Algebraic ODEs and Differential Elimination Theory". Differential equations with symbolic computation. Trends in Mathematics. Birkhäuser. pp. 343–350. doi:10.1007/3-7643-7429-2_18. ISBN 978-3-7643-7429-7.
Chardin 1991 Chardin, Marc (1991). "Differential resultants and subresultants". In Budach, L. (ed.). Fundamentals of Computation Theory. FCT 1991. Lecture Notes in Computer Science. Vol. 529. Berlin, Heidelberg: Springer. pp. 180–189. doi:10.1007/3-540-54458-5_62. ISBN 978-3-540-38391-8.
Wu 2005b Wu, Wen-tsün (2005b). "On the Construction of Groebner Basis of a Polynomial Ideal Based on Riquier–Janet Theory". Differential equations with symbolic computation. Trends in Mathematics. Birkhäuser. pp. 351–368. doi:10.1007/3-7643-7429-2_20. ISBN 978-3-7643-7429-7.
Gao et al. 2009, p. 1141 Gao, X. S.; Van der Hoeven, J.; Yuan, C. M.; Zhang, G. L. (1 September 2009). "Characteristic set method for differential–difference polynomial systems". Journal of Symbolic Computation. 44 (9): 1137–1163. doi:10.1016/j.jsc.2008.02.010.
Ferro & Gerdt 2003, p. 83 Ferro, Giuseppa Carrá; Gerdt, V. P. (2003). "Improved Kolchin–Ritt Algorithm". Programming and Computer Software. 29 (2): 83–87. doi:10.1023/A:1022996615890. S2CID 26280002.
Wu 2005a, p. 4 Wu, Wen-tsün (2005a). "On "Good" Bases of Algebraic-Differential Ideals". Differential equations with symbolic computation. Birkhäuser. pp. 343–350. doi:10.1007/3-7643-7429-2_19. ISBN 978-3-7643-7429-7.
Ferro & Gerdt 2003, p. 84 Ferro, Giuseppa Carrá; Gerdt, V. P. (2003). "Improved Kolchin–Ritt Algorithm". Programming and Computer Software. 29 (2): 83–87. doi:10.1023/A:1022996615890. S2CID 26280002.
Sit 2002, p. 6 Sit, William Y. (2002). "The Ritt-Kolchin theory for differential polynomials". In Guo, Li; Cassidy, Phyllis J; Keigher, William F; Sit, William Y (eds.). Differential algebra and related topics: proceedings of the International Workshop, Newark Campus of Rutgers, the State University of New Jersey, 2-3 November 2000. River Edge, NJ: World Scientific. doi:10.1142/4768. ISBN 981-02-4703-6.
Li & Yuan 2019, p. 294 Li, Wei; Yuan, Chun-Ming (February 2019). "Elimination Theory in Differential and Difference Algebra". Journal of Systems Science and Complexity. 32 (1): 287–316. doi:10.1007/s11424-019-8367-x. S2CID 255158214.
Morrison 1999 Morrison, Sally (1 October 1999). "The Differential Ideal [ P ] : M∞" (PDF). Journal of Symbolic Computation. 28 (4): 631–656. doi:10.1006/jsco.1999.0318. ISSN 0747-7171.
Boulier et al. 2009b Boulier, François; Lazard, Daniel; Ollivier, François; Petitot, Michel (April 2009b). "Computing representations for radicals of finitely generated differential ideals". Applicable Algebra in Engineering, Communication and Computing. 20 (1): 73–121. doi:10.1007/s00200-009-0091-7. S2CID 5482290.
Rota, Kahaner & Odlyzko 1973, p. 694 Rota, Gian-Carlo; Kahaner, David; Odlyzko, Andrew (1973). "On the foundations of combinatorial theory. VIII. Finite operator calculus". Journal of Mathematical Analysis and Applications. 42 (3): 684–760. doi:10.1016/0022-247X(73)90172-8.
Sit 2002, p. 4 Sit, William Y. (2002). "The Ritt-Kolchin theory for differential polynomials". In Guo, Li; Cassidy, Phyllis J; Keigher, William F; Sit, William Y (eds.). Differential algebra and related topics: proceedings of the International Workshop, Newark Campus of Rutgers, the State University of New Jersey, 2-3 November 2000. River Edge, NJ: World Scientific. doi:10.1142/4768. ISBN 981-02-4703-6.
Bronstein 2005, pp. 41, 51, 53, 102, 299, 309 Bronstein, Manuel (2005). Symbolic integration I : transcendental functions. Algorithms and Computation in Mathematics. Vol. 1 (2nd ed.). Berlin: Springer. doi:10.1007/b138171. ISBN 3-540-21493-3.
Harrington & VanGorder 2017 Harrington, Heather A.; VanGorder, Robert A. (2017). "Reduction of dimension for nonlinear dynamical systems". Nonlinear Dynamics. 88 (1): 715–734. doi:10.1007/s11071-016-3272-5. PMC 7089670. PMID 32226227. S2CID 254893812.
Boulier 2007 Boulier, François (31 December 2007). "Differential Elimination and Biological Modelling". Gröbner Bases in Symbolic Analysis. 2: 109–138. doi:10.1515/9783110922752.109. ISBN 978-3-11-019323-7. S2CID 61916692.
Boulier & Lemaire 2009a Boulier, François; Lemaire, François (2009a). "Differential algebra and QSSA methods in biochemistry". IFAC Proceedings Volumes. 42 (10): 33–38. doi:10.3182/20090706-3-FR-2004.00004.
Clarkson & Mansfield 1994 Clarkson, Peter A.; Mansfield, Elizabeth L. (January 1994). "Symmetry reductions and exact solutions of a class of nonlinear heat equations". Physica D: Nonlinear Phenomena. 70 (3): 250–288. arXiv:solv-int/9306002. Bibcode:1994PhyD...70..250C. doi:10.1016/0167-2789(94)90017-5. S2CID 16858637.
Diop 1992 Diop, Sette (May 1992). "Differential-algebraic decision methods and some applications to system theory" (PDF). Theoretical Computer Science. 98 (1): 137–161. doi:10.1016/0304-3975(92)90384-R.
Gao et al. 2009 Gao, X. S.; Van der Hoeven, J.; Yuan, C. M.; Zhang, G. L. (1 September 2009). "Characteristic set method for differential–difference polynomial systems". Journal of Symbolic Computation. 44 (9): 1137–1163. doi:10.1016/j.jsc.2008.02.010.
Keller 2019, p. 48 Keller, Corina (2019). Chern-Simons theory and equivariant factorization algebras. BestMasters. Wiesbaden, Germany. doi:10.1007/978-3-658-25338-7. ISBN 978-3-658-25337-0. S2CID 128325519.{{cite book}}: CS1 maint: location missing publisher (link)
Keller 2019, pp. 50–51 Keller, Corina (2019). Chern-Simons theory and equivariant factorization algebras. BestMasters. Wiesbaden, Germany. doi:10.1007/978-3-658-25338-7. ISBN 978-3-658-25337-0. S2CID 128325519.{{cite book}}: CS1 maint: location missing publisher (link)
Keller 2019, pp. 58–59 Keller, Corina (2019). Chern-Simons theory and equivariant factorization algebras. BestMasters. Wiesbaden, Germany. doi:10.1007/978-3-658-25338-7. ISBN 978-3-658-25337-0. S2CID 128325519.{{cite book}}: CS1 maint: location missing publisher (link)
Lam 1991, pp. 7–8 Lam, T. Y. (1991). A first course in noncommutative rings. Graduate Texts in Mathematics. Vol. 131. New York: Springer-Verlag. doi:10.1007/978-1-4419-8616-0. ISBN 0-387-97523-3.
Golubitsky, Kondratieva & Ovchinnikov 2009 Golubitsky, O. D.; Kondratieva, M. V.; Ovchinnikov, A. I. (2009). "On the generalized Ritt problem as a computational problem". Journal of Mathematical Sciences. 163 (5): 515–522. arXiv:0809.1128. doi:10.1007/s10958-009-9689-3. S2CID 17503904.
Freitag, Sánchez & Simmons 2016 Freitag, James; Sánchez, Omar León; Simmons, William (2 June 2016). "On Linear Dependence Over Complete Differential Algebraic Varieties". Communications in Algebra. 44 (6): 2645–2669. arXiv:1401.6211. doi:10.1080/00927872.2015.1057828. S2CID 56218725.
Lando 1970 Lando, Barbara A. (1970). "Jacobi's bound for the order of systems of first order differential equations". Transactions of the American Mathematical Society. 152 (1): 119–135. doi:10.1090/S0002-9947-1970-0279079-1. ISSN 0002-9947.

hal.science

Boulier 2007 Boulier, François (31 December 2007). "Differential Elimination and Biological Modelling". Gröbner Bases in Symbolic Analysis. 2: 109–138. doi:10.1515/9783110922752.109. ISBN 978-3-11-019323-7. S2CID 61916692.

harvard.edu

ui.adsabs.harvard.edu

Clarkson & Mansfield 1994 Clarkson, Peter A.; Mansfield, Elizabeth L. (January 1994). "Symmetry reductions and exact solutions of a class of nonlinear heat equations". Physica D: Nonlinear Phenomena. 70 (3): 250–288. arXiv:solv-int/9306002. Bibcode:1994PhyD...70..250C. doi:10.1016/0167-2789(94)90017-5. S2CID 16858637.
Parshin 1999, p. 268 Parshin, Aleksei Nikolaevich (1999). "On a ring of formal pseudo-differential operators". Proc. Steklov Math. Institute. 224: 266–280. arXiv:math/9911098. Bibcode:1999math.....11098P.

inria.fr

www-sop.inria.fr

Hubert 2002, p. 8 Hubert, Evelyne (2002). "Notes on Triangular Sets and Triangulation-Decomposition Algorithms II: Differential Systems". In Winkler, Franz; Langer, Ulrich (eds.). Symbolic and Numerical Scientific Computing. Second International Conference, SNSC 2001 Hagenberg, Austria, September 12-14, 2001 Revised Papers (PDF). Berlin: Springer-Verlag. pp. 40–87. ISBN 3-540-40554-2.
Hubert 2002, p. 10 Hubert, Evelyne (2002). "Notes on Triangular Sets and Triangulation-Decomposition Algorithms II: Differential Systems". In Winkler, Franz; Langer, Ulrich (eds.). Symbolic and Numerical Scientific Computing. Second International Conference, SNSC 2001 Hagenberg, Austria, September 12-14, 2001 Revised Papers (PDF). Berlin: Springer-Verlag. pp. 40–87. ISBN 3-540-40554-2.
Hubert 2002, pp. 41–47 Hubert, Evelyne (2002). "Notes on Triangular Sets and Triangulation-Decomposition Algorithms II: Differential Systems". In Winkler, Franz; Langer, Ulrich (eds.). Symbolic and Numerical Scientific Computing. Second International Conference, SNSC 2001 Hagenberg, Austria, September 12-14, 2001 Revised Papers (PDF). Berlin: Springer-Verlag. pp. 40–87. ISBN 3-540-40554-2.

iss.ac.cn

mmrc.iss.ac.cn

Morrison 1999 Morrison, Sally (1 October 1999). "The Differential Ideal [ P ] : M∞" (PDF). Journal of Symbolic Computation. 28 (4): 631–656. doi:10.1006/jsco.1999.0318. ISSN 0747-7171.

kent.ac.uk

Mansfield 1991 Mansfield, Elizabeth (1991). Differential Bases (PhD). University of Sydney.

msri.org

library.msri.org

Marker 2000 Marker, David (2000). "Model theory of differential fields". In Haskell, Deirdre; Pillay, Anand; Steinhorn, Charles (eds.). Model theory, algebra, and geometry (PDF). Vol. 39. Cambridge: Cambridge University Press. pp. 53–64. ISBN 0-521-78068-3.

nih.gov

ncbi.nlm.nih.gov

Harrington & VanGorder 2017 Harrington, Heather A.; VanGorder, Robert A. (2017). "Reduction of dimension for nonlinear dynamical systems". Nonlinear Dynamics. 88 (1): 715–734. doi:10.1007/s11071-016-3272-5. PMC 7089670. PMID 32226227. S2CID 254893812.

pubmed.ncbi.nlm.nih.gov

Harrington & VanGorder 2017 Harrington, Heather A.; VanGorder, Robert A. (2017). "Reduction of dimension for nonlinear dynamical systems". Nonlinear Dynamics. 88 (1): 715–734. doi:10.1007/s11071-016-3272-5. PMC 7089670. PMID 32226227. S2CID 254893812.

sciencedirect.com

Boulier & Lemaire 2009a Boulier, François; Lemaire, François (2009a). "Differential algebra and QSSA methods in biochemistry". IFAC Proceedings Volumes. 42 (10): 33–38. doi:10.3182/20090706-3-FR-2004.00004.

semanticscholar.org

api.semanticscholar.org

Ritt 1930 Ritt, Joseph Fels (1930). "Manifolds of functions defined by systems of algebraic differential equations" (PDF). Transactions of the American Mathematical Society. 32 (4): 569–598. doi:10.1090/S0002-9947-1930-1501554-4. S2CID 54064812.
Li & Yuan 2019 Li, Wei; Yuan, Chun-Ming (February 2019). "Elimination Theory in Differential and Difference Algebra". Journal of Systems Science and Complexity. 32 (1): 287–316. doi:10.1007/s11424-019-8367-x. S2CID 255158214.
Ferro & Gerdt 2003, p. 83 Ferro, Giuseppa Carrá; Gerdt, V. P. (2003). "Improved Kolchin–Ritt Algorithm". Programming and Computer Software. 29 (2): 83–87. doi:10.1023/A:1022996615890. S2CID 26280002.
Ferro & Gerdt 2003, p. 84 Ferro, Giuseppa Carrá; Gerdt, V. P. (2003). "Improved Kolchin–Ritt Algorithm". Programming and Computer Software. 29 (2): 83–87. doi:10.1023/A:1022996615890. S2CID 26280002.
Li & Yuan 2019, p. 294 Li, Wei; Yuan, Chun-Ming (February 2019). "Elimination Theory in Differential and Difference Algebra". Journal of Systems Science and Complexity. 32 (1): 287–316. doi:10.1007/s11424-019-8367-x. S2CID 255158214.
Boulier et al. 2009b Boulier, François; Lazard, Daniel; Ollivier, François; Petitot, Michel (April 2009b). "Computing representations for radicals of finitely generated differential ideals". Applicable Algebra in Engineering, Communication and Computing. 20 (1): 73–121. doi:10.1007/s00200-009-0091-7. S2CID 5482290.
Harrington & VanGorder 2017 Harrington, Heather A.; VanGorder, Robert A. (2017). "Reduction of dimension for nonlinear dynamical systems". Nonlinear Dynamics. 88 (1): 715–734. doi:10.1007/s11071-016-3272-5. PMC 7089670. PMID 32226227. S2CID 254893812.
Boulier 2007 Boulier, François (31 December 2007). "Differential Elimination and Biological Modelling". Gröbner Bases in Symbolic Analysis. 2: 109–138. doi:10.1515/9783110922752.109. ISBN 978-3-11-019323-7. S2CID 61916692.
Clarkson & Mansfield 1994 Clarkson, Peter A.; Mansfield, Elizabeth L. (January 1994). "Symmetry reductions and exact solutions of a class of nonlinear heat equations". Physica D: Nonlinear Phenomena. 70 (3): 250–288. arXiv:solv-int/9306002. Bibcode:1994PhyD...70..250C. doi:10.1016/0167-2789(94)90017-5. S2CID 16858637.
Keller 2019, p. 48 Keller, Corina (2019). Chern-Simons theory and equivariant factorization algebras. BestMasters. Wiesbaden, Germany. doi:10.1007/978-3-658-25338-7. ISBN 978-3-658-25337-0. S2CID 128325519.{{cite book}}: CS1 maint: location missing publisher (link)
Keller 2019, pp. 50–51 Keller, Corina (2019). Chern-Simons theory and equivariant factorization algebras. BestMasters. Wiesbaden, Germany. doi:10.1007/978-3-658-25338-7. ISBN 978-3-658-25337-0. S2CID 128325519.{{cite book}}: CS1 maint: location missing publisher (link)
Keller 2019, pp. 58–59 Keller, Corina (2019). Chern-Simons theory and equivariant factorization algebras. BestMasters. Wiesbaden, Germany. doi:10.1007/978-3-658-25338-7. ISBN 978-3-658-25337-0. S2CID 128325519.{{cite book}}: CS1 maint: location missing publisher (link)
Golubitsky, Kondratieva & Ovchinnikov 2009 Golubitsky, O. D.; Kondratieva, M. V.; Ovchinnikov, A. I. (2009). "On the generalized Ritt problem as a computational problem". Journal of Mathematical Sciences. 163 (5): 515–522. arXiv:0809.1128. doi:10.1007/s10958-009-9689-3. S2CID 17503904.
Freitag, Sánchez & Simmons 2016 Freitag, James; Sánchez, Omar León; Simmons, William (2 June 2016). "On Linear Dependence Over Complete Differential Algebraic Varieties". Communications in Algebra. 44 (6): 2645–2669. arXiv:1401.6211. doi:10.1080/00927872.2015.1057828. S2CID 56218725.

springer.com

link.springer.com

Bronstein 2005, p. 76 Bronstein, Manuel (2005). Symbolic integration I : transcendental functions. Algorithms and Computation in Mathematics. Vol. 1 (2nd ed.). Berlin: Springer. doi:10.1007/b138171. ISBN 3-540-21493-3.
Li & Yuan 2019 Li, Wei; Yuan, Chun-Ming (February 2019). "Elimination Theory in Differential and Difference Algebra". Journal of Systems Science and Complexity. 32 (1): 287–316. doi:10.1007/s11424-019-8367-x. S2CID 255158214.
Ferro 2005 Ferro, Giuseppa Carrá (2005). "Generalized Differential Resultant Systems of Algebraic ODEs and Differential Elimination Theory". Differential equations with symbolic computation. Trends in Mathematics. Birkhäuser. pp. 343–350. doi:10.1007/3-7643-7429-2_18. ISBN 978-3-7643-7429-7.
Wu 2005b Wu, Wen-tsün (2005b). "On the Construction of Groebner Basis of a Polynomial Ideal Based on Riquier–Janet Theory". Differential equations with symbolic computation. Trends in Mathematics. Birkhäuser. pp. 351–368. doi:10.1007/3-7643-7429-2_20. ISBN 978-3-7643-7429-7.
Ferro & Gerdt 2003, p. 83 Ferro, Giuseppa Carrá; Gerdt, V. P. (2003). "Improved Kolchin–Ritt Algorithm". Programming and Computer Software. 29 (2): 83–87. doi:10.1023/A:1022996615890. S2CID 26280002.
Wu 2005a, p. 4 Wu, Wen-tsün (2005a). "On "Good" Bases of Algebraic-Differential Ideals". Differential equations with symbolic computation. Birkhäuser. pp. 343–350. doi:10.1007/3-7643-7429-2_19. ISBN 978-3-7643-7429-7.
Ferro & Gerdt 2003, p. 84 Ferro, Giuseppa Carrá; Gerdt, V. P. (2003). "Improved Kolchin–Ritt Algorithm". Programming and Computer Software. 29 (2): 83–87. doi:10.1023/A:1022996615890. S2CID 26280002.
Li & Yuan 2019, p. 294 Li, Wei; Yuan, Chun-Ming (February 2019). "Elimination Theory in Differential and Difference Algebra". Journal of Systems Science and Complexity. 32 (1): 287–316. doi:10.1007/s11424-019-8367-x. S2CID 255158214.
Boulier et al. 2009b Boulier, François; Lazard, Daniel; Ollivier, François; Petitot, Michel (April 2009b). "Computing representations for radicals of finitely generated differential ideals". Applicable Algebra in Engineering, Communication and Computing. 20 (1): 73–121. doi:10.1007/s00200-009-0091-7. S2CID 5482290.
Bronstein 2005, pp. 41, 51, 53, 102, 299, 309 Bronstein, Manuel (2005). Symbolic integration I : transcendental functions. Algorithms and Computation in Mathematics. Vol. 1 (2nd ed.). Berlin: Springer. doi:10.1007/b138171. ISBN 3-540-21493-3.
Keller 2019, p. 48 Keller, Corina (2019). Chern-Simons theory and equivariant factorization algebras. BestMasters. Wiesbaden, Germany. doi:10.1007/978-3-658-25338-7. ISBN 978-3-658-25337-0. S2CID 128325519.{{cite book}}: CS1 maint: location missing publisher (link)
Keller 2019, pp. 50–51 Keller, Corina (2019). Chern-Simons theory and equivariant factorization algebras. BestMasters. Wiesbaden, Germany. doi:10.1007/978-3-658-25338-7. ISBN 978-3-658-25337-0. S2CID 128325519.{{cite book}}: CS1 maint: location missing publisher (link)
Keller 2019, pp. 58–59 Keller, Corina (2019). Chern-Simons theory and equivariant factorization algebras. BestMasters. Wiesbaden, Germany. doi:10.1007/978-3-658-25338-7. ISBN 978-3-658-25337-0. S2CID 128325519.{{cite book}}: CS1 maint: location missing publisher (link)
Lam 1991, pp. 7–8 Lam, T. Y. (1991). A first course in noncommutative rings. Graduate Texts in Mathematics. Vol. 131. New York: Springer-Verlag. doi:10.1007/978-1-4419-8616-0. ISBN 0-387-97523-3.
Golubitsky, Kondratieva & Ovchinnikov 2009 Golubitsky, O. D.; Kondratieva, M. V.; Ovchinnikov, A. I. (2009). "On the generalized Ritt problem as a computational problem". Journal of Mathematical Sciences. 163 (5): 515–522. arXiv:0809.1128. doi:10.1007/s10958-009-9689-3. S2CID 17503904.

worldcat.org

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Morrison 1999 Morrison, Sally (1 October 1999). "The Differential Ideal [ P ] : M∞" (PDF). Journal of Symbolic Computation. 28 (4): 631–656. doi:10.1006/jsco.1999.0318. ISSN 0747-7171.
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Sit 2002, pp. 3–4 Sit, William Y. (2002). "The Ritt-Kolchin theory for differential polynomials". In Guo, Li; Cassidy, Phyllis J; Keigher, William F; Sit, William Y (eds.). Differential algebra and related topics: proceedings of the International Workshop, Newark Campus of Rutgers, the State University of New Jersey, 2-3 November 2000. River Edge, NJ: World Scientific. doi:10.1142/4768. ISBN 981-02-4703-6.
Sit 2002, p. 6 Sit, William Y. (2002). "The Ritt-Kolchin theory for differential polynomials". In Guo, Li; Cassidy, Phyllis J; Keigher, William F; Sit, William Y (eds.). Differential algebra and related topics: proceedings of the International Workshop, Newark Campus of Rutgers, the State University of New Jersey, 2-3 November 2000. River Edge, NJ: World Scientific. doi:10.1142/4768. ISBN 981-02-4703-6.
Sit 2002, p. 4 Sit, William Y. (2002). "The Ritt-Kolchin theory for differential polynomials". In Guo, Li; Cassidy, Phyllis J; Keigher, William F; Sit, William Y (eds.). Differential algebra and related topics: proceedings of the International Workshop, Newark Campus of Rutgers, the State University of New Jersey, 2-3 November 2000. River Edge, NJ: World Scientific. doi:10.1142/4768. ISBN 981-02-4703-6.