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Volumn 28, Issue 1-2, 1999, Pages 125-154

Triangular sets for solving polynomial systems: A comparative implementation of four methods

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EID: 0000631665     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1999.0270     Document Type: Article
Times cited : (57)

References (54)
  • 3
    • 0002820505 scopus 로고
    • Some examples for solving systems of algebraic equations by calculating Gröbner bases
    • Boege, W., Gebauer, R., Kredel, H. (1986). Some examples for solving systems of algebraic equations by calculating Gröbner bases. J. Symb. Comput., 2, 83-98.
    • (1986) J. Symb. Comput. , vol.2 , pp. 83-98
    • Boege, W.1    Gebauer, R.2    Kredel, H.3
  • 5
    • 0010082941 scopus 로고
    • Gsolve: A faster algorithm for solving systems of algebraic equations
    • Char, B. W., ed., New York, ACM Press
    • Bronstein, M. (1986). Gsolve: a faster algorithm for solving systems of algebraic equations. In Char, B. W., ed., Proceedings SYMSAC86, pp. 247-249. New York, ACM Press.
    • (1986) Proceedings SYMSAC86 , pp. 247-249
    • Bronstein, M.1
  • 8
    • 84962670416 scopus 로고
    • Ritt-Wu's decomposition algorithm and geometry theorem proving
    • LNCS Springer Verlag
    • Chou, S., Gao, X. (1990). Ritt-Wu's decomposition algorithm and geometry theorem proving. In Proceedings CADE-10, Kaiserslautern, Germany, LNCS 449, pp. 207-220, Springer Verlag.
    • (1990) Proceedings CADE-10, Kaiserslautern, Germany , vol.449 , pp. 207-220
    • Chou, S.1    Gao, X.2
  • 9
    • 84962715458 scopus 로고
    • Solving parametric algebraic systems
    • ACM Press, New York
    • Chou, S., Gao, X. (1992). Solving parametric algebraic systems. In Proceedings ISAAC'92 Berkeley, CA, pp. 335-341, ACM Press, New York.
    • (1992) Proceedings ISAAC'92 Berkeley, CA , pp. 335-341
    • Chou, S.1    Gao, X.2
  • 10
    • 0031232403 scopus 로고    scopus 로고
    • Converting bases with the Gröbner walk
    • Collart, S., Kalkbrener, M., Mall, D. (1997). Converting bases with the Gröbner walk. J. Symb. Comput., 24, 465-470.
    • (1997) J. Symb. Comput. , vol.24 , pp. 465-470
    • Collart, S.1    Kalkbrener, M.2    Mall, D.3
  • 12
    • 0010071304 scopus 로고
    • On implementing Buchberger's algorithm for Gröbner bases
    • Waterloo, B.W. Char
    • Czapor, S., Geddes, K. (1986). On implementing Buchberger's algorithm for Gröbner bases. In Proceedings SYMSAC'86, pp. 425-440. Waterloo, B.W. Char.
    • (1986) Proceedings SYMSAC'86 , pp. 425-440
    • Czapor, S.1    Geddes, K.2
  • 13
    • 85025486043 scopus 로고
    • About a new method method for computing in algebraic number fields
    • LNCS 204, Springer-Verlag
    • Della Dora, J., Discrescenzo, C., Duval, D. (1985). About a new method method for computing in algebraic number fields. In Proceedings EUROCAL 85, volume 2, LNCS 204, pp. 289-290. Springer-Verlag.
    • (1985) Proceedings EUROCAL 85 , vol.2 , pp. 289-290
    • Della Dora, J.1    Discrescenzo, C.2    Duval, D.3
  • 14
    • 85031678378 scopus 로고
    • Experimenting the Gröbner basis algorithm with the ALPI system
    • New York, ACM Press
    • Donati, L., Traverso, C. (1989). Experimenting the Gröbner basis algorithm with the ALPI system. Proceedings ISSAC'89, pp. 192-198. New York, ACM Press.
    • (1989) Proceedings ISSAC'89 , pp. 192-198
    • Donati, L.1    Traverso, C.2
  • 15
    • 9144225010 scopus 로고
    • Esprit Scheme Project No. 6846. Has been extended to the FRISCO project
    • European Commission (1992). PoSSo - Polynomial System Solving Research Project. Esprit Scheme Project No. 6846. Has been extended to the FRISCO project.
    • (1992) PoSSo - Polynomial System Solving Research Project
  • 17
    • 25944479355 scopus 로고
    • Efficient computation of zero-dimensional Gröbner bases by change of ordering
    • Faugère, J.-C., Gianni, P., Lazard, D., Mora, T. (1993). Efficient computation of zero-dimensional Gröbner bases by change of ordering. J. Symb. Comput., 16, 329-344.
    • (1993) J. Symb. Comput. , vol.16 , pp. 329-344
    • Faugère, J.-C.1    Gianni, P.2    Lazard, D.3    Mora, T.4
  • 18
    • 9144273964 scopus 로고    scopus 로고
    • Design of nonseparable bidimensional wavelets and filter banks using Gröbner bases techniques
    • Theory and Applications of Filter Banks and Wavelets
    • Faugère, J.-C., Moreau de Saint-Martin, F., Rouillier, F. (1998). Design of nonseparable bidimensional wavelets and filter banks using Gröbner bases techniques. IEEE SP Trans. Signal Process., 46. Special Issue on Theory and Applications of Filter Banks and Wavelets.
    • (1998) IEEE SP Trans. Signal Process. , vol.46 , Issue.SPEC. ISSUE
    • Faugère, J.-C.1    Moreau De Saint-Martin, F.2    Rouillier, F.3
  • 19
    • 0010070016 scopus 로고
    • Efficient algorithms and bounds for Wu-Ritt characteristic sets
    • Proceedings MEGA'90, Lavorno, Italy, Birkhaüser
    • Gallo, G., Mishra, B. (1990). Efficient algorithms and bounds for Wu-Ritt characteristic sets. Proceedings MEGA'90, Lavorno, Italy, Progress in Mathematics 94, pp. 119-142, Birkhaüser.
    • (1990) Progress in Mathematics , vol.94 , pp. 119-142
    • Gallo, G.1    Mishra, B.2
  • 21
    • 85033813724 scopus 로고
    • "One sugar cube, please" or selection strategies in the Buchberger algorithm
    • New York, ACM Press
    • Giovinni, A., Mora, T., Niesi, G., Robbiano, L., Traverso, C. (1991). "One sugar cube, please" or selection strategies in the Buchberger algorithm. In Proceedings ISSAC'91, pp. 49-54. New York, ACM Press.
    • (1991) Proceedings ISSAC'91 , pp. 49-54
    • Giovinni, A.1    Mora, T.2    Niesi, G.3    Robbiano, L.4    Traverso, C.5
  • 24
    • 3643088632 scopus 로고
    • Triangular systems and factorized Gröbner bases
    • Cohen, G., Giusti, M. and Mora, T., eds, LNCS Springer Verlag
    • Gräbe, H.-G. (1995). Triangular systems and factorized Gröbner bases. In Proceedings AAECC 11, Paris, Cohen, G., Giusti, M. and Mora, T., eds, LNCS 948, pp. 248-261, Springer Verlag.
    • (1995) Proceedings AAECC 11, Paris , vol.948 , pp. 248-261
    • Gräbe, H.-G.1
  • 25
    • 0022476533 scopus 로고
    • A superexponential lower bound for Gröbner bases and Church Rosser commutative thue systems
    • Huynh, D. (1986). A superexponential lower bound for Gröbner bases and Church Rosser commutative thue systems. Inf. Control, 68, 196-206.
    • (1986) Inf. Control , vol.68 , pp. 196-206
    • Huynh, D.1
  • 29
    • 38249006658 scopus 로고
    • A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
    • Kalkbrener, M. (1993). A generalized Euclidean algorithm for computing triangular representations of algebraic varieties. J. Symb. Comput., 15, 143-167.
    • (1993) J. Symb. Comput. , vol.15 , pp. 143-167
    • Kalkbrener, M.1
  • 30
    • 0032210403 scopus 로고    scopus 로고
    • Algorithmic properties of polynomial rings
    • Kalkbrener, M. (1998). Algorithmic properties of polynomial rings. J. Symb. Comput., 26, 525-581.
    • (1998) J. Symb. Comput. , vol.26 , pp. 525-581
    • Kalkbrener, M.1
  • 32
    • 0000069912 scopus 로고
    • A new method for solving algebraic systems of positive dimension
    • Lazard, D. (1991). A new method for solving algebraic systems of positive dimension. Discrete Appl. Math., 33, 147-160.
    • (1991) Discrete Appl. Math. , vol.33 , pp. 147-160
    • Lazard, D.1
  • 33
    • 0000167385 scopus 로고
    • Solving zero-dimensional algebraic systems
    • Lazard, D. (1992). Solving zero-dimensional algebraic systems. J. Symb. Comput., 15, 117-132.
    • (1992) J. Symb. Comput. , vol.15 , pp. 117-132
    • Lazard, D.1
  • 34
    • 9144234304 scopus 로고
    • An implementation of the characteristic set method for solving algebraic equations
    • Université Paris 6
    • Li, Z. (1995). An implementation of the characteristic set method for solving algebraic equations. In Proceedings POSSO Workshop on Software, Paris, France, Université Paris 6, pp. 107-122.
    • (1995) Proceedings POSSO Workshop on Software, Paris, France , pp. 107-122
    • Li, Z.1
  • 35
    • 9144225994 scopus 로고
    • An algorithm on finding all isolated zeros of polynomial equations
    • Liu, Z. (1989). An algorithm on finding all isolated zeros of polynomial equations. MM Research Preprints, 4, 63-76.
    • (1989) MM Research Preprints , vol.4 , pp. 63-76
    • Liu, Z.1
  • 36
    • 0001751788 scopus 로고
    • The complexity of the word problems for commutative semigroups and ideals
    • Mayr, E., Meyer, A. (1982). The complexity of the word problems for commutative semigroups and ideals. Adv. Math., 46, 305-329.
    • (1982) Adv. Math. , vol.46 , pp. 305-329
    • Mayr, E.1    Meyer, A.2
  • 37
    • 0001332043 scopus 로고
    • On decomposing systems of polynomial equations with finitely many solutions
    • Möller, H. M. (1993). On decomposing systems of polynomial equations with finitely many solutions. Appl. Algebra Eng. Commun. Comput., 4 217-230.
    • (1993) Appl. Algebra Eng. Commun. Comput. , vol.4 , pp. 217-230
    • Möller, H.M.1
  • 39
    • 0005430478 scopus 로고    scopus 로고
    • A new algorithm for computing triangular decompositions of algebraic varieties
    • NAG Ltd, Oxford, U.K.
    • Moreno Maza, M. (1998). A new algorithm for computing triangular decompositions of algebraic varieties. Technical Report TR 4/98, NAG Ltd, Oxford, U.K.
    • (1998) Technical Report TR 4/98
    • Moreno Maza, M.1
  • 40
    • 84955583152 scopus 로고
    • Polynomial gcd computations over towers of algebraic extensions
    • Springer
    • Moreno Maza, M., Rioboo, R. (1995). Polynomial gcd computations over towers of algebraic extensions. Proceedings AAECC-11, pp. 365-382. Springer.
    • (1995) Proceedings AAECC-11 , pp. 365-382
    • Moreno Maza, M.1    Rioboo, R.2
  • 44
    • 0030268743 scopus 로고    scopus 로고
    • Hilbert functions and the Buchberger algorithm
    • Traverso, C. (1996). Hilbert functions and the Buchberger algorithm. J. Symb. Comput., 22, 355-376.
    • (1996) J. Symb. Comput. , vol.22 , pp. 355-376
    • Traverso, C.1
  • 45
    • 0041776563 scopus 로고
    • On Wu's method for solving systems of algebraic equations
    • Johannes Kepler University, Linz, Austria
    • Wang, D. M. (1991). On Wu's method for solving systems of algebraic equations. Technical Report RISC-LINZ Series no 91-52.0, Johannes Kepler University, Linz, Austria.
    • (1991) Technical Report RISC-LINZ Series No 91-52.0
    • Wang, D.M.1
  • 46
    • 9144263181 scopus 로고
    • Some improvements on Wu's method for solving systems of algebraic equations
    • Wu, W.-T. and Cheng, M.-D., eds, Institute of Systems Science, Academia Sinica
    • Wang, D. M. (1992). Some improvements on Wu's method for solving systems of algebraic equations. In Wu, W.-T. and Cheng, M.-D., eds, Proceedings of the Int. Workshop on Math. Mechanisation, Beijing, China. Institute of Systems Science, Academia Sinica.
    • (1992) Proceedings of the Int. Workshop on Math. Mechanisation, Beijing, China
    • Wang, D.M.1
  • 47
    • 0346297660 scopus 로고
    • An elimination method based on Siedenberg's theory and its applications
    • Eysette, F. and Galligo, A., eds, Boston, Birkhaüser
    • Wang, D. M. (1993a). An elimination method based on Siedenberg's theory and its applications. In Eysette, F. and Galligo, A., eds, Comptutational Algebraic Geometry, pp. 301-328. Boston, Birkhaüser.
    • (1993) Comptutational Algebraic Geometry , pp. 301-328
    • Wang, D.M.1
  • 48
    • 0003161187 scopus 로고
    • An elimination method for polynomial systems
    • Wang, D. M. (1993b). An elimination method for polynomial systems. J. Symb. Comput., 16, 83-114.
    • (1993) J. Symb. Comput. , vol.16 , pp. 83-114
    • Wang, D.M.1
  • 49
    • 0000370913 scopus 로고
    • An implementation of the characteristic set method in Maple
    • Pfalzgraf, J. and Wang, D. M., eds, Wien, Springer
    • Wang, D. M. (1995). An implementation of the characteristic set method in Maple. In Pfalzgraf, J. and Wang, D. M., eds, Automated Practical Reasoning: Algebraic Approaches, pp. 187-201. Wien, Springer.
    • (1995) Automated Practical Reasoning: Algebraic Approaches , pp. 187-201
    • Wang, D.M.1
  • 50
    • 0030285766 scopus 로고    scopus 로고
    • Solving polynomial equations: Characteristic sets and triangular systems
    • Wang, D. M. (1996). Solving polynomial equations: characteristic sets and triangular systems. Math. Comput. Simul., 42, 339-345.
    • (1996) Math. Comput. Simul. , vol.42 , pp. 339-345
    • Wang, D.M.1
  • 51
    • 0032016328 scopus 로고    scopus 로고
    • Decomposing polynomial systems into simple systems
    • Wang, D. M. (1998). Decomposing polynomial systems into simple systems. J. Symb. Comput., 25, 295-314.
    • (1998) J. Symb. Comput. , vol.25 , pp. 295-314
    • Wang, D.M.1
  • 52
    • 0002557822 scopus 로고
    • On zeros of algebraic equations - An application of Ritt principle
    • Wu, W. T. (1986). On zeros of algebraic equations - an application of Ritt principle. Kexue Tongbao, 31, 1-5.
    • (1986) Kexue Tongbao , vol.31 , pp. 1-5
    • Wu, W.T.1
  • 53
    • 0002971341 scopus 로고
    • A zero structure theorem for polynomial equations solving
    • Wu, W. T. (1987). A zero structure theorem for polynomial equations solving. MM Research Preprints, 1, 2-12.
    • (1987) MM Research Preprints , vol.1 , pp. 2-12
    • Wu, W.T.1
  • 54
    • 0342478350 scopus 로고
    • Searching dependency between algebraic equations: An algorithm applied to automated reasoning
    • Johnson, J., McKee, S. and Vella, A., eds, Oxford, Oxford University Press
    • Yang, L., Zhang, J. (1994). Searching dependency between algebraic equations: an algorithm applied to automated reasoning. In Johnson, J., McKee, S. and Vella, A., eds, Artificial Intelligence in Mathematics, pp. 147-156. Oxford, Oxford University Press.
    • (1994) Artificial Intelligence in Mathematics , pp. 147-156
    • Yang, L.1    Zhang, J.2


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