메뉴 건너뛰기




Volumn 2630, Issue , 2003, Pages 40-87

Notes on triangular sets and triangulation-decomposition algorithms II: Differential systems

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; SURVEYING; TRIANGULATION;

EID: 27644560295     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45084-x_2     Document Type: Article
Times cited : (57)

References (75)
  • 4
    • 27644575753 scopus 로고    scopus 로고
    • Reasonning about surfaces using differential zero and ideal decomposition
    • J. Richet-Gebert and D. Wang, editors, ADG 2000, number 2061
    • P. Aubry and D. Wang. Reasonning about surfaces using differential zero and ideal decomposition. In J. Richet-Gebert and D. Wang, editors, ADG 2000, number 2061 in LNAI, pages 154-174, 2001.
    • (2001) LNAI , pp. 154-174
    • Aubry, P.1    Wang, D.2
  • 8
    • 1542268049 scopus 로고    scopus 로고
    • Symbolic Computation Group, University of Waterloo, Ontario, Canada
    • F. Boulier and E. Hubert. DIFFALG: description, help pages and examples of use. Symbolic Computation Group, University of Waterloo, Ontario, Canada, 1998. Now available at http://www.inria.fr/cafe/Evelyne.Hubert/webdiffalg.
    • (1998) DIFFALG: Description, Help Pages and Examples of Use
    • Boulier, F.1    Hubert, E.2
  • 9
    • 0029182270 scopus 로고
    • Representation for the radical of a finitely generated differential ideal
    • A. H. M. Levelt, editor, ACM Press, New York
    • F. Boulier, D. Lazard, F. Ollivier, and M. Petitot. Representation for the radical of a finitely generated differential ideal. In A. H. M. Levelt, editor, ISSAC'95. ACM Press, New York, 1995.
    • (1995) ISSAC'95
    • Boulier, F.1    Lazard, D.2    Ollivier, F.3    Petitot, M.4
  • 11
    • 0033659532 scopus 로고    scopus 로고
    • Computing canonical representatives of regular differential ideals
    • C. Traverse, editor, ACM-SIGSAM, ACM
    • F. Boulier and F. Lemaire. Computing canonical representatives of regular differential ideals. In C. Traverse, editor, ISSAC. ACM-SIGSAM, ACM, 2000.
    • (2000) ISSAC
    • Boulier, F.1    Lemaire, F.2
  • 13
    • 0346789752 scopus 로고    scopus 로고
    • Unmixed-dimensional decomposition of a finitely generated perfect differential ideal
    • D. Bouziane, A. Kandri Rody, and H. Maârouf. Unmixed-dimensional decomposition of a finitely generated perfect differential ideal. Journal of Symbolic Computation, 31(6):631-649, 2001.
    • (2001) Journal of Symbolic Computation , vol.31 , Issue.6 , pp. 631-649
    • Bouziane, D.1    Kandri Rody, A.2    Maârouf, H.3
  • 16
    • 0003368162 scopus 로고
    • Gröbner bases and differential algebra
    • AAECC, Springer-Verlag Berlin
    • G. Carra Ferro. Gröbner bases and differential algebra. In AAECC, volume 356 of Lecture Notes in Computer Science. Springer-Verlag Berlin, 1987.
    • (1987) Lecture Notes in Computer Science , vol.356
    • Carra Ferro, G.1
  • 17
    • 0002203411 scopus 로고
    • On term-orderings and rankings
    • Computational algebra (Fairfax, VA, 1993), number 151 Dekker, New York
    • G. Carrà Ferro and W. Y. Sit. On term-orderings and rankings. In Computational algebra (Fairfax, VA, 1993), number 151 in Lecture Notes in Pure and Applied Mathematics, pages 31-77. Dekker, New York, 1994.
    • (1994) Lecture Notes in Pure and Applied Mathematics , pp. 31-77
    • Carrà Ferro, G.1    Sit, W.Y.2
  • 19
    • 0042173311 scopus 로고
    • Sur les équations différentielles du troisième ordre et d'ordre supérieur dont l'intégrale générale a ses points critiques fixes
    • J. Chazy. Sur les équations différentielles du troisième ordre et d'ordre supérieur dont l'intégrale générale a ses points critiques fixes. Acta Mathematica, 34:317-385, 1911.
    • (1911) Acta Mathematica , vol.34 , pp. 317-385
    • Chazy, J.1
  • 20
    • 35248893511 scopus 로고    scopus 로고
    • Odetools: A maple package for studying and solving ordinary differential equations
    • incoming update of
    • E. S. Cheb-Terrab. Odetools: A maple package for studying and solving ordinary differential equations. http://lie.uwaterloo.ca/description/odetools, 1998. presented for the incoming update of "Handbook of Computer Algebra".
    • (1998) Handbook of Computer Algebra
    • Cheb-Terrab, E.S.1
  • 23
    • 27644459642 scopus 로고
    • Automated reasonning in differential geometry and mechanics using the characteristic set method. Part II. Mechanical theorem proving
    • S-C. Chou and X-S. Gao. Automated reasonning in differential geometry and mechanics using the characteristic set method. part II. mechanical theorem proving. Journal of Automated Reasonning, 10:173-189, 1993.
    • (1993) Journal of Automated Reasonning , vol.10 , pp. 173-189
    • Chou, S.-C.1    Gao, X.-S.2
  • 24
    • 0005144466 scopus 로고    scopus 로고
    • The classical, direct, and non-classical methods for symmetry reductions of nonlinear partial differential equations
    • Dedicated to Martin David Kruskal
    • P. A. Clarkson, D. K. Ludlow, and T. J. Priestley. The classical, direct, and non-classical methods for symmetry reductions of nonlinear partial differential equations. Methods and Applications of Analysis, 4(2):173-195, 1997. Dedicated to Martin David Kruskal.
    • (1997) Methods and Applications of Analysis , vol.4 , Issue.2 , pp. 173-195
    • Clarkson, P.A.1    Ludlow, D.K.2    Priestley, T.J.3
  • 25
    • 43949149919 scopus 로고
    • Symmetry reductions and exact solutions of a class of non-linear heat equations
    • P. A. Clarkson and E. L. Mansfield. Symmetry reductions and exact solutions of a class of non-linear heat equations. Physica, D70:250-288, 1994.
    • (1994) Physica , vol.D70 , pp. 250-288
    • Clarkson, P.A.1    Mansfield, E.L.2
  • 27
    • 38249014570 scopus 로고
    • Differential-algebraic decision methods and some applications to system theory
    • S. Diop. Differential-algebraic decision methods and some applications to system theory. Theoretical Computer Science, 98(1):137-161, 1992.
    • (1992) Theoretical Computer Science , vol.98 , Issue.1 , pp. 137-161
    • Diop, S.1
  • 29
    • 0003527787 scopus 로고
    • Commutative Algebra with a View toward Algebraic Geometry
    • Springer-Verlag New York
    • D. Eisenbud. Commutative Algebra with a View toward Algebraic Geometry. Graduate Texts in Mathematics. Springer-Verlag New York, 1994.
    • (1994) Graduate Texts in Mathematics
    • Eisenbud, D.1
  • 31
    • 1542268048 scopus 로고    scopus 로고
    • L. Guo, W. F. Keigher, P. J. Cassidy, and W. Y. Sit, editors. World Scientific Publishing Co.
    • L. Guo, W. F. Keigher, P. J. Cassidy, and W. Y. Sit, editors. Differential Algebra and Related Topics. World Scientific Publishing Co., 2002.
    • (2002) Differential Algebra and Related Topics
  • 33
    • 0001743074 scopus 로고    scopus 로고
    • Essential components of an algebraic differential equation
    • E. Hubert. Essential components of an algebraic differential equation. Journal of Symbolic Computation, 28(4-5):657-680, 1999.
    • (1999) Journal of Symbolic Computation , vol.28 , Issue.4-5 , pp. 657-680
    • Hubert, E.1
  • 34
    • 0034178810 scopus 로고    scopus 로고
    • Factorisation free decomposition algorithms in differential algebra
    • E. Hubert. Factorisation free decomposition algorithms in differential algebra. Journal of Symbolic Computation, 29(4-5):641-662, 2000.
    • (2000) Journal of Symbolic Computation , vol.29 , Issue.4-5 , pp. 641-662
    • Hubert, E.1
  • 38
    • 38249006658 scopus 로고
    • A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
    • M. Kalkbrener. A generalized Euclidean algorithm for computing triangular representations of algebraic varieties. Journal of Symbolic Computation, 15(2):143-167, 1993.
    • (1993) Journal of Symbolic Computation , vol.15 , Issue.2 , pp. 143-167
    • Kalkbrener, M.1
  • 40
    • 1542268047 scopus 로고    scopus 로고
    • Commentaries by Armand Borel, Michael F. Singer, Bruno Poizat, Alexandru Buium and Phyllis J. Cassidy, Edited and with a preface by Hyman Bass, Buium and Cassidy. American Mathematical Society, Providence, RI
    • E. Kolchin. Selected works of Ellis Kolchin with commentary. Commentaries by Armand Borel, Michael F. Singer, Bruno Poizat, Alexandru Buium and Phyllis J. Cassidy, Edited and with a preface by Hyman Bass, Buium and Cassidy. American Mathematical Society, Providence, RI, 1999.
    • (1999) Selected Works of Ellis Kolchin with Commentary
    • Kolchin, E.1
  • 41
    • 0003263342 scopus 로고
    • Differential Algebra and Algebraic Groups
    • Academic Press, New York-London
    • E. R. Kolchin. Differential Algebra and Algebraic Groups, volume 54 of Pure and Applied Mathematics. Academic Press, New York-London, 1973.
    • (1973) Pure and Applied Mathematics , vol.54
    • Kolchin, E.R.1
  • 42
    • 0000167385 scopus 로고
    • Solving zero dimensional algebraic systems
    • D. Lazard. Solving zero dimensional algebraic systems. Journal of Symbolic Computation, 15:117-132, 1992.
    • (1992) Journal of Symbolic Computation , vol.15 , pp. 117-132
    • Lazard, D.1
  • 44
    • 34249756641 scopus 로고
    • Mechanical theorem proving in the local theory of surfaces
    • Z. Li. Mechanical theorem proving in the local theory of surfaces. Annals of Mathematics and Artificial Intelligence, 13(1-2):25-46, 1995.
    • (1995) Annals of Mathematics and Artificial Intelligence , vol.13 , Issue.1-2 , pp. 25-46
    • Li, Z.1
  • 45
    • 0242648854 scopus 로고    scopus 로고
    • Coherent, regular and simple system in zero decompositions of partial differential systems
    • Z. Li and D. Wang. Coherent, regular and simple system in zero decompositions of partial differential systems. Systems Sciences and Mathematical Sciences, 12 suppl, 1999.
    • (1999) Systems Sciences and Mathematical Sciences , vol.12 , Issue.SUPPL.
    • Li, Z.1    Wang, D.2
  • 49
    • 0032477225 scopus 로고    scopus 로고
    • Nonclassical reductions of a 3+1-cubic nonlinear Schrödinger system
    • E. L. Mansfield, G. J. Reid, and P. A. Clarkson. Nonclassical reductions of a 3+1-cubic nonlinear Schrödinger system. Computer Physics Communications, 115:460-488, 1998.
    • (1998) Computer Physics Communications , vol.115 , pp. 460-488
    • Mansfield, E.L.1    Reid, G.J.2    Clarkson, P.A.3
  • 50
    • 0034759097 scopus 로고    scopus 로고
    • Differential algebra methods for the study of the structural identifiability of rational function state-space models in the biosciences
    • G. Margaria, E. Riccomagno, M. J. Chappell, and H. P. Wynn. Differential algebra methods for the study of the structural identifiability of rational function state-space models in the biosciences. Mathematical Biosciences, 174(1):1-26, 2001.
    • (2001) Mathematical Biosciences , vol.174 , Issue.1 , pp. 1-26
    • Margaria, G.1    Riccomagno, E.2    Chappell, M.J.3    Wynn, H.P.4
  • 53
    • 35248837565 scopus 로고
    • Canonical bases: Relations with standard bases, finiteness conditions and application to tame automorphisms
    • Costiglioncello, editor, Birkhauser, August
    • F. Ollivier. Canonical bases : Relations with standard bases, finiteness conditions and application to tame automorphisms. In Costiglioncello, editor, MEGA'90. Birkhauser, August 1990.
    • (1990) MEGA'90
    • Ollivier, F.1
  • 54
    • 0003686926 scopus 로고
    • Applications of Lie Groups to Differential Equations
    • Number 107 Springer-Verlag, New York
    • P. Olver. Applications of Lie Groups to Differential Equations. Number 107 in Graduate texts in Mathematics. Springer-Verlag, New York, 1986.
    • (1986) Graduate Texts in Mathematics
    • Olver, P.1
  • 55
    • 84972029082 scopus 로고
    • Algorithms for reducing a system of pde to standard form, determining the dimension of its solution space and calculating its taylor series solution
    • G. J. Reid. Algorithms for reducing a system of pde to standard form, determining the dimension of its solution space and calculating its taylor series solution. European Journal Of Applied Mathematics, 2:293-318, 1991.
    • (1991) European Journal of Applied Mathematics , vol.2 , pp. 293-318
    • Reid, G.J.1
  • 56
    • 84971844577 scopus 로고
    • Finding abstract Lie symmetry algebras of differential equations without integrating determining equations
    • G. J. Reid. Finding abstract Lie symmetry algebras of differential equations without integrating determining equations. European Journal of Applied Mathematics, 2(4):319-340, 1991.
    • (1991) European Journal of Applied Mathematics , vol.2 , Issue.4 , pp. 319-340
    • Reid, G.J.1
  • 57
    • 0030364642 scopus 로고    scopus 로고
    • Reduction of systems of nonlinear partial differential equations to simplified involutive forms
    • G. J. Reid, A. D. Wittkopf, and A. Boulton. Reduction of systems of nonlinear partial differential equations to simplified involutive forms. Eur. J. ofAppl. Math., 7:604 - 635, 1996.
    • (1996) Eur. J. Of Appl. Math. , vol.7 , pp. 604-635
    • Reid, G.J.1    Wittkopf, A.D.2    Boulton, A.3
  • 59
    • 0003247880 scopus 로고
    • Differential Equations from the Algebraic Standpoint
    • J. F. Ritt. Differential Equations from the Algebraic Standpoint. Amer. Math. Soc. Colloq. Publ., 1932.
    • (1932) Amer. Math. Soc. Colloq. Publ.
    • Ritt, J.F.1
  • 60
    • 0002159569 scopus 로고
    • On the singular solutions of algebraic differential equations
    • J. F. Ritt. On the singular solutions of algebraic differential equations. Annals of Mathematics, 37(3):552-617, 1936.
    • (1936) Annals of Mathematics , vol.37 , Issue.3 , pp. 552-617
    • Ritt, J.F.1
  • 61
    • 0003360236 scopus 로고
    • Differential Algebra
    • American Mathematical Society, Reprinted by Dover Publications, Inc
    • J. F. Ritt. Differential Algebra, volume XXXIII of Colloquium publications. American Mathematical Society, 1950. Reprinted by Dover Publications, Inc (1966).
    • (1950) Colloquium Publications , vol.33
    • Ritt, J.F.1
  • 68
    • 0346789353 scopus 로고    scopus 로고
    • Computer algebra and differential equations - An overview
    • W. Seiler. Computer algebra and differential equations - an overview. mathPAD 7, 7:34-49, 1997.
    • (1997) MathPAD 7 , vol.7 , pp. 34-49
    • Seiler, W.1
  • 71
    • 35248856122 scopus 로고    scopus 로고
    • HIDAES (Higher Index Differential Algebraic Equations Solver)
    • Technical report, LMC-IMAG
    • J. Visconti. HIDAES (Higher Index Differential Algebraic Equations Solver). Software and test set. Technical report, LMC-IMAG, http://www-lmc.imag.fr/CF/ LOGICIELS/page_dae.html, 1999.
    • (1999) Software and Test Set
    • Visconti, J.1
  • 73
    • 0346794374 scopus 로고    scopus 로고
    • An elimination method for differential polynomial systems. I
    • D. Wang. An elimination method for differential polynomial systems. I. Systems Science and Mathematical Sciences, 9(3):216-228, 1996.
    • (1996) Systems Science and Mathematical Sciences , vol.9 , Issue.3 , pp. 216-228
    • Wang, D.1
  • 74
    • 1542297985 scopus 로고    scopus 로고
    • CECM - Simon Fraser University - Vancouver
    • A. Witkopf and G. Reid. The RIF package. CECM - Simon Fraser University - Vancouver, http://www.cecm.sfu.ca/wittkopf/rif.html.
    • The RIF Package
    • Witkopf, A.1    Reid, G.2
  • 75
    • 2342612062 scopus 로고
    • Mechanical theorem proving of differential geometries and some of its applications in mechanics
    • W. T. Wu. Mechanical theorem proving of differential geometries and some of its applications in mechanics. Journal of Automated Reasoning, 7(2):171-191, 1991.
    • (1991) Journal of Automated Reasoning , vol.7 , Issue.2 , pp. 171-191
    • Wu, W.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.