메뉴 건너뛰기




Volumn 2630, Issue , 2003, Pages 1-39

Notes on triangular sets and triangulation-decomposition algorithms I: Polynomial systems

Author keywords

[No Author keywords available]

Indexed keywords

SURVEYING; TRIANGULATION;

EID: 33749566968     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45084-x_1     Document Type: Article
Times cited : (62)

References (55)
  • 4
    • 0000631665 scopus 로고    scopus 로고
    • Triangular sets for solving polynomial systems: A comparative implementation of four methods
    • P. Aubry and M. Moreno-Maza. Triangular sets for solving polynomial systems: a comparative implementation of four methods. Journal of Symbolic Computation, 28(1-2):125-154, 1999.
    • (1999) Journal of Symbolic Computation , vol.28 , Issue.1-2 , pp. 125-154
    • Aubry, P.1    Moreno-Maza, M.2
  • 7
    • 0038392359 scopus 로고    scopus 로고
    • Spécifications des algorithmes de triangulation de systèmes algébro-élémentaires
    • Ser. I
    • A. M. Bellido and V. Jalby. Spécifications des algorithmes de triangulation de systèmes algébro-élémentaires. C. R. Acad. Sci. Paris, Ser. I(334):155-159, 2001.
    • (2001) C. R. Acad. Sci. Paris , Issue.334 , pp. 155-159
    • Bellido, A.M.1    Jalby, V.2
  • 8
    • 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
  • 9
    • 0033659532 scopus 로고    scopus 로고
    • Computing canonical representatives of regular differential ideals
    • C. Traverso, editor, ACM-SIGSAM, ACM
    • F. Boulier and F. Lemaire. Computing canonical representatives of regular differential ideals. In C. Traverso, editor, ISSAC. ACM-SIGSAM, ACM, 2000.
    • (2000) ISSAC
    • Boulier, F.1    Lemaire, F.2
  • 10
    • 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
  • 13
    • 84962670416 scopus 로고
    • Ritt-wu's decomposition algorithm and geometry theorem proving
    • M. E. Stickel, editor, 10th International Conference on Automated Deduction, number 449 Springer-Verlag
    • S. C. Chou and X. S. Gao. Ritt-wu's decomposition algorithm and geometry theorem proving. In M. E. Stickel, editor, 10th International Conference on Automated Deduction, number 449 in Lecture Notes in Computer Sicences, pages 207-220. Springer-Verlag, 1990.
    • (1990) Lecture Notes in Computer Sicences , pp. 207-220
    • Chou, S.C.1    Gao, X.S.2
  • 14
    • 0041621982 scopus 로고
    • World Scientific Publishing Co. Inc., River Edge, NJ, Automated production of readable proofs for geometry theorems, With a foreword by Robert S. Boyer
    • S. C. Chou, X. S. Gao, and J. Z. Zhang. Machine proofs in geometry. World Scientific Publishing Co. Inc., River Edge, NJ, 1994. Automated production of readable proofs for geometry theorems, With a foreword by Robert S. Boyer.
    • (1994) Machine Proofs in Geometry
    • Chou, S.C.1    Gao, X.S.2    Zhang, J.Z.3
  • 16
    • 0004192435 scopus 로고
    • D. Reidel Publishing Co., Dordrecht, With a foreword by Larry Wos
    • S. C. Chou. Mechanical geometry theorem proving. D. Reidel Publishing Co., Dordrecht, 1988. With a foreword by Larry Wos.
    • (1988) Mechanical Geometry Theorem Proving
    • Chou, S.C.1
  • 17
    • 85025486043 scopus 로고
    • About a new method for computing in algebraic number fields
    • Proceedings of EUROCAL 85, number 204 Springer-Verlag
    • J. Della Dora, C. Dicrescenzo, and D. Duval. About a new method for computing in algebraic number fields. In Proceedings of EUROCAL 85, number 204 in Lecture Notes in Computer Science, pages 289-290. Springer-Verlag, 1985.
    • (1985) Lecture Notes in Computer Science , pp. 289-290
    • Della Dora, J.1    Dicrescenzo, C.2    Duval, D.3
  • 19
    • 25344457313 scopus 로고    scopus 로고
    • Technical Report 16, Laboratoire d'Arithmétique, de Calcul Formel et d'Optimisation, Limoges
    • S. Dellière. D. M. Wang simple systems and dynamic constructible closure. Technical Report 16, Laboratoire d'Arithmétique, de Calcul Formel et d'Optimisation, Limoges, http://www.unilim.fr/laco, 2000.
    • (2000) D. M. Wang Simple Systems and Dynamic Constructible Closure
    • Dellière, S.1
  • 22
    • 18044402323 scopus 로고    scopus 로고
    • On the links between triangular sets and dynamic constructible closure
    • S. Dellière. On the links between triangular sets and dynamic constructible closure. J. Pure Appl. Algebra, 163(1):49-68, 2001.
    • (2001) J. Pure Appl. Algebra , vol.163 , Issue.1 , pp. 49-68
    • Dellière, S.1
  • 24
    • 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
  • 26
    • 84962715458 scopus 로고
    • Solving parametric algebraic sytems
    • ACM Press, New York, NY, USA
    • X. S. Gao and S. C. Chou. Solving parametric algebraic sytems. In ISSAC 92, pages 335-341. ACM Press, New York, NY, USA, 1992.
    • (1992) ISSAC 92 , pp. 335-341
    • Gao, X.S.1    Chou, S.C.2
  • 29
    • 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
  • 31
    • 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
  • 32
    • 0032210403 scopus 로고    scopus 로고
    • Algorithmic properties of polynomial rings
    • November
    • M. Kalkbrener. Algorithmic properties of polynomial rings. Journal of Symbolic Computation, 26(5):525-582, November 1998.
    • (1998) Journal of Symbolic Computation , vol.26 , Issue.5 , pp. 525-582
    • Kalkbrener, M.1
  • 33
    • 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
  • 34
    • 0000069912 scopus 로고
    • A new method for solving algebraic systems of positive dimension
    • D. Lazard. A new method for solving algebraic systems of positive dimension. Discrete and Applied Mathematics, 33:147-160, 1991.
    • (1991) Discrete and Applied Mathematics , vol.33 , pp. 147-160
    • Lazard, D.1
  • 35
    • 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
  • 36
    • 0032099036 scopus 로고    scopus 로고
    • Triviality and dimension of a system of algebraic differential equations
    • H. Maârouf, A. Kandri Rody, and M. Ssafini. Triviality and dimension of a system of algebraic differential equations. Journal of Automated Reasoning, 20(3):365-385, 1998.
    • (1998) Journal of Automated Reasoning , vol.20 , Issue.3 , pp. 365-385
    • Maârouf, H.1    Kandri Rody, A.2    Ssafini, M.3
  • 40
    • 0037570310 scopus 로고    scopus 로고
    • n
    • Polynomial elimination - algorithms and applications
    • n. Journal of Symbolic Computation, 28(1-2):213-223, 1999. Polynomial elimination - algorithms and applications.
    • (1999) Journal of Symbolic Computation , vol.28 , Issue.1-2 , pp. 213-223
    • Richardson, D.1
  • 41
    • 0043025485 scopus 로고
    • Manifolds of functions defined by systems of algebraic differential equations
    • J. F. Ritt. Manifolds of functions defined by systems of algebraic differential equations. Transaction of the American Mathematical Society, 32:569-598, 1930.
    • (1930) Transaction of the American Mathematical Society , vol.32 , pp. 569-598
    • Ritt, J.F.1
  • 42
    • 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
  • 43
    • 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
  • 47
    • 0003282797 scopus 로고    scopus 로고
    • Computational Methods in Commutative Algebra and Algebraic Geometry
    • Springer, Berlin
    • W. V. Vasconcelos. Computational Methods in Commutative Algebra and Algebraic Geometry, volume 2 of Algorithms and Computation in Mathematics. Springer, Berlin, 1998.
    • (1998) Algorithms and Computation in Mathematics , vol.2
    • Vasconcelos, W.V.1
  • 49
    • 0003161187 scopus 로고
    • An elimination method for polynomial systems
    • August
    • D. Wang. An elimination method for polynomial systems. Journal of Symbolic Computation, 16(2):83-114, August 1993.
    • (1993) Journal of Symbolic Computation , vol.16 , Issue.2 , pp. 83-114
    • Wang, D.1
  • 50
    • 0032016328 scopus 로고    scopus 로고
    • Decomposing polynomial systems into simple systems
    • D. Wang. Decomposing polynomial systems into simple systems. Journal of Symbolic Computation, 25(3):295-314, 1998.
    • (1998) Journal of Symbolic Computation , vol.25 , Issue.3 , pp. 295-314
    • Wang, D.1
  • 52
    • 0011620090 scopus 로고    scopus 로고
    • Computing triangular systems and regular systems
    • D. Wang. Computing triangular systems and regular systems. Journal of Symbolic Computation, 30(2):221-236, 2000.
    • (2000) Journal of Symbolic Computation , vol.30 , Issue.2 , pp. 221-236
    • Wang, D.1
  • 53
    • 0003343439 scopus 로고
    • On the decision problem and the mechanization of theorem-proving in elementary geometry
    • W. T. Wu. On the decision problem and the mechanization of theorem-proving in elementary geometry. Sci. Sinica, 21(2):159-172, 1978.
    • (1978) Sci. Sinica , vol.21 , Issue.2 , pp. 159-172
    • Wu, W.T.1
  • 54
    • 0004114491 scopus 로고
    • Springer-Verlag, Vienna, Basic principles, Translated from the 1984 Chinese original by Xiao Fan Jin and Dong Ming Wang
    • W. T. Wu. Mechanical theorem proving in geometries. Springer-Verlag, Vienna, 1994. Basic principles, Translated from the 1984 Chinese original by Xiao Fan Jin and Dong Ming Wang.
    • (1994) Mechanical Theorem Proving in Geometries
    • Wu, W.T.1
  • 55
    • 0242480577 scopus 로고    scopus 로고
    • Kluwer Academic Publishers Group, Dordrecht, Mechanical geometry theorem-proving, mechanical geometry problem-solving and polynomial equations-solving
    • W. T. Wu. Mathematics mechanization. Kluwer Academic Publishers Group, Dordrecht, 2000. Mechanical geometry theorem-proving, mechanical geometry problem-solving and polynomial equations-solving.
    • Mathematics Mechanization , vol.2000
    • Wu, W.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.