Publications Related to the RegularChains Library

Publications

Research articles

• A Short Contribution to the Theory of Regular Chains
  François Boulier, François Lemaire, Marc Moreno Maza, Adrien Poteaux
  Mathematics in Computer Science 15(2): 177-188, 2021.
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• Towards Extending Fulton's Algorithm for Computing Intersection Multiplicities Beyond the Bivariate Case
  Marc Moreno Maza, Ryan Sandford
  Proceedings of Computer Algebra in Scientific Computing - Lecture Notes in Computer Science, volume 12865, Springer, pages 232-251, 2021.
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• Multivariate Power Series in Maple
  Mohammadali Asadi, Alexander Brandt, Mahsa Kazemi, Marc Moreno Maza, Erik J. Postma
  Proceedings of the Maple Conference 2020, Springer, pages 28-66, 2020.
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• On the Extended Hensel Construction and its Application to the Computation of Real Limit Points
  Parisa Alvandi, Masoud Ataei, Mahsa Kazemi, Marc Moreno Maza
  Journal of Symbolic Computation 98: 120-162, 2020.
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• Complexity Estimates for Fourier-Motzkin Elimination
  Rui-Juan Jing, Marc Moreno Maza, Delaram Talaashrafi
  Proceedings of Computer Algebra in Scientific Computing - Lecture Notes in Computer Science, volume 12291, Springer, pages 282-306, 2020.
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• Comprehensive LU Factors of Polynomial Matrices
  Ana C. Camargos Couto, Marc Moreno Maza, David Linder, David J. Jeffrey, Robert M. Corless
  Proceedings of Mathematical Aspects of Computer and Information Sciences, MACIS 2019, Springer, pages 80-88, 2019.
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• Jordan Canonical Form with Parameters from Frobenius Form with Parameters
  Robert M. Corless, Marc Moreno Maza, Steven E. Thornton
  Proceedings of Mathematical Aspects of Computer and Information Sciences, MACIS 2017, Springer, pages 179-194, 2016.
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• Computing Limits of Real Multivariate Rational Functions
  Parisa Alvandi, Mahsa Kazemi, Marc Moreno Maza.
  Proceedings of International Symposium on Symbolic and Algebraic Computation, ISSAC 2016, ACM, pages 39-46, 2016.
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• Quantifier Elimination by Cylindrical Algebraic Decomposition Based on Regular Chains
  Changbo Chen, Marc Moreno Maza.
  Journal of Symbolic Computation 75: 74-93, 2016.
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• Regular Chains under Linear Changes of Coordinates and Applications
  Parisa Alvandi, Changbo Chen, Amir Hashemi, Marc Moreno Maza.
  Proceedings of Computer Algebra in Scientific Computing 2015 - Lecture Notes in Computer Science, volume 9301, Springer, pages 30-44.
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• A Standard Basis Free Algorithm for Computing the Tangent Cones of a Space Curve
  Parisa Alvandi, Marc Moreno Maza, Eric Schost, Paul Vrbik.
  Proceedings of Computer Algebra in Scientific Computing 2015 - Lecture Notes in Computer Science, volume 9301, Springer, pages 45-60.
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• Simplification of Cylindrical Algebraic Formulas
  Changbo Chen, Marc Moreno Maza.
  Proceedings of Computer Algebra in Scientific Computing 2015 - Lecture Notes in Computer Science, volume 9301, Springer, pages 119-134.
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• Simplification of Cylindrical Algebraic Formulas
  Changbo Chen, Marc Moreno Maza.
  Proceedings of Computer Algebra in Scientific Computing 2015 - Lecture Notes in Computer Science, volume 9301, Springer, pages 119-134.
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• Quantifier Elimination by Cylindrical Algebraic Decomposition Based on Regular Chains
  Changbo Chen, Marc Moreno Maza.
  To appear in the Journal of Symbolic Computation.
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• Real Quantifier Elimination in the RegularChains Library
  Changbo Chen, Marc Moreno Maza.
  Proceedings of ICMS 2014 - 4th International Congress, Seoul, South Korea, Lecture Notes in Computer Science, volume 8592, pages 283-290.
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• Cylindrical Algebraic Decomposition in the RegularChains Library
  Changbo Chen, Marc Moreno Maza.
  Proceedings of ICMS 2014 - 4th International Congress, Seoul, South Korea, Lecture Notes in Computer Science, volume 8592, pages 425-433.
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• Doing Algebraic Geometry with the RegularChains Library
  Parisa Alvandi, Changbo Chen, Steffen Marcus, Marc Moreno Maza, Éric Schost, Paul Vrbik.
  Proceedings of ICMS 2014 - 4th International Congress, Seoul, South Korea, Lecture Notes in Computer Science, volume 8592, pages 472-479.
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• Solving Parametric Polynomial Systems by RealComprehensiveTriangularize
  Changbo Chen, Marc Moreno Maza.
  Proceedings of ICMS 2014 - 4th International Congress, Seoul, South Korea, Lecture Notes in Computer Science, volume 8592, pages 504-511.
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• Truth Table Invariant Cylindrical Algebraic Decomposition by Regular Chains
  Russell J. Bradford, Changbo Chen, James H. Davenport, Matthew England, Marc Moreno Maza, David J. Wilson.
  Proceedings of Computer Algebra in Scientific Computing - Lecture Notes in Computer Science, volume 8660, Springer, pages 44-59.
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• Problem Formulation for Truth-Table Invariant Cylindrical Algebraic Decomposition by Incremental Triangular Decomposition
  Russell J. Bradford, Changbo Chen, James H. Davenport, Matthew England, Marc Moreno Maza, David J. Wilson.
  Proceedings of Intelligent Computer Mathematics - International Conference, CICM 2014, Coimbra, Portugal, July 7, Lecture Notes in Computer Science, volume 8543, Springer, pages 45-60.
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• Computing the Limit Points of the Quasi-component of a Regular Chain in Dimension One
  Changbo Chen, Parisa Alvandi, Marc Moreno Maza.
  Proceedings of CASC 2013.
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• Triangular decomposition of semi-algebraic systems
  Changbo Chen, James H. Davenport, John P. May, Marc Moreno Maza, Bican Xia, Rong Xiao.
  Journal of Symbolic Computation. 49: 3-26, 2013.
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• Computing with semi-algebraic sets: Relaxation techniques and effective boundaries
  Changbo Chen, James H. Davenport, Marc Moreno Maza, Bican Xia, Rong Xiao.
  Journal of Symbolic Computation. 52: 72-96, 2013.
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• On Fulton's Algorithm for Computing Intersection Multiplicities
  Steffen Marcus, Marc Moreno Maza, Paul Vrbik.
  2012 Computer Algebra in Scientific Computing (CASC 2012), Springer Verlag, LNCS 6885, pages 198-211, 2012.
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• Inversion Modulo Zero-Dimensional Regular Chains
  Marc Moreno Maza, Éric Schost, Paul Vrbik.
  2012 Computer Algebra in Scientific Computing (CASC 2012), Springer Verlag, LNCS 6885, pages 224-235, 2012.
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• Generating Program Invariants via Interpolation
  Marc Moreno Maza, Rong Xiao.
  CoRR, abs/1201.5086, 2012.
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• Degree and dimension estimates for invariant ideals of P-solvable recurrences
  Marc Moreno Maza, Rong Xiao.
  Proc. of the 2012 Asian Symposium of Computer Mathematics (ASCM), to appear in LNAI, Springer, 23 pages, 2012.
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• An Incremental Algorithm for Computing Cylindrical Algebraic Decompositions
  Changbo Chen, Marc Moreno Maza
  Proc. of the 2012 Asian Symposium of Computer Mathematics (ASCM), to appear in LNAI, Springer, 21 pages, 2012.
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• On solving parametric polynomial systems
  Marc Moreno Maza, Bican Xia, Rong Xiao.
  J. of Mathematics in Computer Science. 5(4):457-473 (2012).
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• Algorithms for computing triangular decompositions of polynomial systems
  Changbo Chen and M. Moreno Maza.
  Journal of Symbolic Computation, 47(6): 610-642 (2012).
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• Solving semi-algebraic systems with the RegularChains library in Maple
  Changbo Chen, James H. Davenport, Francois Lemaire, Marc Moreno Maza, Nalina Phisanbut, Bican Xia, Rong Xiao, Yuzhen Xie.
  Proceedings of the Fourth Internationa Conference on Mathematical Aspects of Computer Science and Information Sciences (MACIS 2011), Edited by Stefan Raschau, pp. 38--51, 2011.
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• On solving parametric polynomial systems
  Marc Moreno Maza, Bican Xia, Rong Xiao.
  Proceedings of the Fourth Internationa Conference on Mathematical Aspects of Computer Science and Information Sciences (MACIS 2011), Edited by Stefan Raschau, pp. 205--215, 2011.
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• Computing with semi-algebraic sets represented by triangular decomposition
  Changbo Chen, James H. Davenport, M. Moreno Maza, Bican Xia, Rong Xiao.
  Proceedings of 2011 International Symposium on Symbolic and Algebraic Computation (ISSAC 2011), ACM Press, pp. 75--82, 2011.
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• Algorithms for computing triangular decompositions of polynomial systems
  Changbo Chen and M. Moreno Maza.
  Proceedings of 2011 International Symposium on Symbolic and Algebraic Computation (ISSAC 2011), ACM Press, pp. 83--90, 2011.
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• Semi-algebraic description of the equilibria of dynamical systems
  Changbo Chen and M. Moreno Maza.
  Proceedings of 2011 Computer Algebra in Scientific Computing (CASC 2011), Springer Verlag, LNCS 6885, pages 101-125, 2011.
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• Triangular decomposition of semi-algebraic systems
  Changbo Chen, James H. Davenport, John P. May, M. Moreno Maza, Bican Xia, Rong Xiao.
  Proceedings of 2010 International Symposium on Symbolic and Algebraic Computation (ISSAC 2010), ACM Press, pp. 187--194, 2010.
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• GCD Computations Modulo Regular Chains
  X. Li, M. Moreno Maza, W. Pan.
  Submitted to the Journal of Symbolic Computation.
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• Computations Modulo Regular Chains
  X. Li, M. Moreno Maza, W. Pan.
  Proceedings of ISSAC 2009, pages 239-246, ACM Press, New York, 2009
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• Computing Cylindrical Algebraic Decomposition via Triangular Decomposition
  C. Chen, M. Moreno Maza, B. Xia, L. Yang.
  Proceedings of ISSAC 2009, pages 95-102, ACM Press, New York, 2009
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• Computing Differential Characteristic Sets by Change of Ordering
  F. Boulier, F. Lemaire and M. Moreno Maza.
  Journal of Symbolic Computation Volume 45, Issue 1, Pages: 124-149, Janvier 2010.
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• Fast Arithmetic for Triangular Sets: from Theory to Practice
  X. Li, M. Moreno Maza and É Schost.
  Journal of Symbolic Computation, 44(7): 891-907, 2009
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• User Interface Design for Geometrical Decomposition Algorithms in Maple
  C. Chen, J. H. Davenport, J. May, M. Moreno Maza, B. Xia, R. Xiao and Y. Xie.
  Proceedings of Mathematical User-Interface, 12 pages, 2009
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• Real Root Isolation of Regular Chains
  F. Boulier, C. Chen, F.Lemaire and M. Moreno Maza.
  In Proceedings of the 2009 Asian Symposium on Computer Mathematics (ASCM 2009) Math-for-Industry, pp 15-29, 2009.
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• When does 〈T〉 Equal sat(T)?
  F. Lemaire, M. Moreno Maza, W. Pan and Y. Xie.
  Journal of Symbolic Computation, 46(12): 1291-1305, 2011.
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• Computing with Constructible Sets in Maple
  C. Chen, F. Lemaire, L. Liyun, M. Moreno Maza, W. Pan and Y. Xie.
  Submitted to J. of Symbolic Computation, 2009
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• Change of Ordering for Regular Chains in Positive Dimension
  X. Dahan, X. Jin, M. Moreno Maza and É Schost.
  Theoretical Computer Science, 392 (2008): 37­65, 2008
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• A Bound for the Rosenfeld-Gröbner Algorithm
  O. Golubitsky, M. Kondratieva, M. Moreno Maza and A. Ovchinnikov
  Journal of Symbolic Computation, 43(8): 582-610, 2008
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• On the Verification of Polynomial System Solvers
  C. Chen, M. Moreno Maza, W. Pan and Y. Xie
  Frontiers of Computer Science in China, Vol 2, Numb 1, pages 55-66, 2008
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• When does 〈T〉 Equal sat(T)?
  F. Lemaire, M. Moreno Maza, W. Pan and Y. Xie
  Proceedings of ISSAC 2008, pages 207-214, ACM Press, New York, NY, USA, 2008
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• The Complete Root Classification of a Parametric Polynomial on an Interval
  S. Liang, D.J. Jeffrey, M. Moreno Maza
  Proceedings of ISSAC 2008, pages 189-196, ACM Press, New York, 2008
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• On the Representation of Constructible Sets
  C. Chen, L. Li, M. Moreno Maza, W. Pan and Y. Xie
  Proceedings of Milestones in Computer Algebra 2008, pages 103-108, Trinidad and Tobago, 2008
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• The ConstructibleSetTools and ParametricSystemsTools Modules of the RegularChains Library in Maple
  C. Chen, F. Lemaire, L. Liyun, M. Moreno Maza, W. Pan and Y. Xie
  Proceedings of the International Conference on Computational Science and Applications, IEEE Computer Society, pages 342-352, 2008
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• On Approximate Triangular Decompositions in Dimension Zero
  M. Moreno Maza, G. Reid, R. Scott and W. Wu
  Journal of Symbolic Computation, 42(7):693-716, 2007
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• On Approximate Linearized Triangular Decompositions
  M. Moreno Maza, G. Reid, R. Scott and W. Wu
  book chapter of Advances on Symbolic-Numeric Computation, edited by D. M. Wang and L. Zhi, p. 268-287, Springer, 2007
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• Component-level Parallelization of Triangular Decompositions
  M. Moreno Maza and Y. Xie
  Proceedings of Parallel Symbolic Computation'07, pages 69-77, ACM Press, New York, NY, USA, 2007
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• Comprehensive Triangular Decomposition
  C. Chen, F. Lemaire, O. Golubitsky, M. Moreno Maza and W. Pan
  Proceedings of CASC 2007: Computer Algebra in Scientific Computing, pages 73-101, Lecture Notes in Computer Science, vol. 4770, Springer-Verlag, 2007
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• On the Verification of Polynomial System Solvers
  C. Chen, M. Moreno Maza, W. Pan and Y. Xie
  Proceedings of the Fifth Asian Workshop on Foundations of Software, pages 116-144, University of Xiamen, China, 2007
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• Efficient Computations of Irredundant Triangular Decompositions with the RegularChains Library
  C. Chen, F. Lemaire, M. Moreno Maza, W. Pan and Y. Xie
  Proceedings of Computer Algebra Systems and Their Applications'07, Y. Shi et al. (Eds.): ICCS 2007, Part II, LNCS 4488, pp. 268­271, Springer-Verlag Berlin Heidelberg 2007
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• Tutorial: Triangular Decompositions of Polynomial Systems: from Theory to Practice
  M. Moreno Maza
  Proceedings of ISSAC'06, page 8, ACM Press, 2006
  Extended abstract in PDF   Slides in PDF
• Brief Announcement: An Implementation Report for Parallel Triangular Decompositions
  Moreno Maza, M. and Xie, Y
  Proceedings of 19th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), page 235, ACM Press, 2006
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• Change of Ordering for Regular Chains in Positive Dimension
  X. Dahan, X. Jin, M. Moreno Maza and É Schost
  Proceedings of Algebraic Geometry and Geometric Modelling'06, pages 49-53, Universidad de Barcelona, 2006
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• Parallelization of Triangular Decompositions
  M. Moreno Maza and Y. Xie
  Proceedings of Algebraic Geometry and Geometric Modelling'06, pages 96-100, Universidad de Barcelona, 2006
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• Bounds and Algebraic Algorithms in Differential Algebra: the Ordinary Case
  O. Golubitsky, M. Kondratieva, M. Moreno Maza and A. Ovchinnikov
  Proceedings of the 9th Intern. Conf. on Intelligent Systems and Computer Science'06, pages 7-11, Faculty of Mechanics and Mathematics, Moscow State University, 2006
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• Change of Ordering for Regular Chains in Positive Dimension
  X. Dahan, X. Jin, M. Moreno Maza and É Schost
  Proceedings of Maple Conference 2006, pages 26-24, Maplesoft, 2006
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• Well Known Theorems on Triangular Systems and the D5 Principle
  F. Boulier, F. Lemaire and M. Moreno Maza
  Proceedings of Transgressive Computing 2006, J.-G. Dumas et al., editors, Granada, Spain, 2006
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• On the Complexity of the D5 Principle
  X. Dahan, M. Moreno Maza, É. Schost, and Y. Xie
  Proceedings of Transgressive Computing 2006, J.-G. Dumas et al., editors, Granada, Spain, 2006
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• Primary Decomposition of Zero-dimensional Ideals: Putting Monico's Algorithm into Practice
  M. Moreno Maza, É. Schost, and W. Zhou
  Proceedings of Transgressive Computing 2006, J.-G. Dumas et al., editors, Granada, Spain, 2006
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• Making a Sophisticated Symbolic Solver Available to Different Communities of Users
  F. Lemaire, M. Moreno Maza and Y. Xie
  Proceedings of Asian Technology Conference in Mathematics'06, Polytechnic University of Hong Kong, 2006
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• On Approximate Triangular Decompsoitions I. Dimension Zero
  M. Moreno Maza and G. Reid and R. Scott and W. Wu
  Proceedings of Symbolic-Numeric Computation'05, D. M. Wang and L. Zhi editors, Xi'an, China, 2005
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• On Approximate Triangular Decompositions II. Linear Systems
  M. Moreno Maza and G. Reid and R. Scott and W. Wu
  Proceedings of Symbolic-Numeric Computation'05, D. M. Wang and L. Zhi editors, Xi'an, China, 2005
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• Lifting Techniques for Triangular Decompositions
  X. Dahan, M. Moreno Maza, É. Schost, W. Wu and Y. Xie
  Proceedings of ISSAC'05, Beijing, China, ACM Press, 2005
  Distinguished Student Author Award
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• The RegularChains Library in Maple 10
  F. Lemaire and M. Moreno Maza and Y. Xie
  Proceedings of Maple Summer Conference'05, Ilias S. Kotsireas editor, Waterloo, Canada, 2005
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• A New Henselian Construction and its Application to Polynomial GCDs over Direct Products of Fields
  F. Boulier, M. Moreno Maza and C.Oancea
  Proceedings of EACA'04, Universidad de Santander, Spain, 2004
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• Equiprojectable Decompositions of Zero-dimensional Varieties
  X. Dahan, M. Moreno Maza, É. Schost, W. Wu and Y. Xie
  Proceedings of International Conference on Poynomial System Solving, University of Paris 6, France, 2004
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• PARDI !
  F. Boulier, F.Lemaire and M. Moreno Maza
  Proceedings of ISSAC 2001, pages 38-47, ACM Press, 2001
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• Well Known Theorems on Triangular Systems
  F. Boulier, F. Lemaire and M. Moreno Maza
  Tech. Rep. LIFL 2001-09, Univ. of Lille 1, 2001
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• PARDI !
  F. Boulier, F. Lemaire and M. Moreno Maza
  Tech. Rep. LIFL 2001-011, Univ. of Lille 1, 2001
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• On Triangular Decompositions of Algebraic Varieties
  M. Moreno Maza
  Presented at the MEGA-2000 conference, Bath, UK, June 2000
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• On the Theories of Triangular Sets
  P. Aubry, D. Lazard, M. Moreno Maza
  Journal of Symbolic Computation, 28(1-2):105-124, 1999
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• Triangular Sets for Solving Polynomial Systems: A Comparative Implementation of Four Methods
  P. Aubry and M. Moreno Maza
  Journal of Symbolic Computation, 28(1-2):125-154, 1999
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• Calculs de Pgcd au-dessus des Tours d'Extensions Simples et Résolution des Systèmes d'Équations Algébriques
  M. Moreno Maza
  PhD Thesis, Universit'e Paris 6, France, 1997
  PS.GZ
• Polynomial GCD Computations over Towers of Algebraic Extensions
  M. Moreno Maza and R. Rioboo
  Proceedings of AAECC-11, pages 365-382. Springer, 1995
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