Relevant bibliographies by topics / Solving polynomial systems of equations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Solving polynomial systems of equations'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Solving polynomial systems of equations"

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Manocha, D. "Solving systems of polynomial equations." IEEE Computer Graphics and Applications 14, no. 2 (1994): 46–55. http://dx.doi.org/10.1109/38.267470.

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Moszyński, Krzysztof. "Remarks on polynomial methods for solving systems of linear algebraic equations." Applications of Mathematics 37, no. 6 (1992): 419–36. http://dx.doi.org/10.21136/am.1992.104521.

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LLIBRE, JAUME, and CLAUDIA VALLS. "POLYNOMIAL FIRST INTEGRALS FOR THE CHEN AND LÜ SYSTEMS." International Journal of Bifurcation and Chaos 22, no. 11 (2012): 1250262. http://dx.doi.org/10.1142/s0218127412502628.

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We characterize all the values of the parameters for which the Chen and Lü systems have polynomial first integrals by using weight homogeneous polynomials and the method of characteristics for solving partial differential equations. We improve previous results which were not complete.
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Wang, Dongming. "Solving polynomial equations: Characteristic sets and triangular systems." Mathematics and Computers in Simulation 42, no. 4-6 (1996): 339–51. http://dx.doi.org/10.1016/s0378-4754(96)00008-0.

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Serdyukova, S. I. "Solving large systems of polynomial equations using REDUCE." Programming and Computer Software 26, no. 1 (2000): 28–29. http://dx.doi.org/10.1007/bf02759175.

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Chukanov, Sergei Nikolaevich, and Ilya Stanislavovich Chukanov. "The Investigation of Nonlinear Polynomial Control Systems." Modeling and Analysis of Information Systems 28, no. 3 (2021): 238–49. http://dx.doi.org/10.18255/1818-1015-2021-3-238-249.

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The paper considers methods for estimating stability using Lyapunov functions, which are used for nonlinear polynomial control systems. The apparatus of the Gro¨bner basis method is used to assess the stability of a dynamical system. A description of the Gro¨bner basis method is given. To apply the method, the canonical relations of the nonlinear system are approximated by polynomials of the components of the state and control vectors. To calculate the Gro¨bner basis, the Buchberger algorithm is used, which is implemented in symbolic computation programs for solving systems of nonlinear polyno
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Raghavan, M., and B. Roth. "Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators." Journal of Mechanical Design 117, B (1995): 71–79. http://dx.doi.org/10.1115/1.2836473.

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Problems in mechanisms analysis and synthesis and robotics lead naturally to systems of polynomial equations. This paper reviews the state of the art in the solution of such systems of equations. Three well-known methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases are reviewed. The methods are illustrated by means of simple examples. We also review important kinematic analysis and synthesis problems and their solutions using these mathematical procedures.
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Raghavan, M., and B. Roth. "Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators." Journal of Vibration and Acoustics 117, B (1995): 71–79. http://dx.doi.org/10.1115/1.2838679.

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Problems in mechanisms analysis and synthesis and robotics lead naturally to systems of polynomial equations. This paper reviews the state of the art in the solution of such systems of equations. Three well-known methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases are reviewed. The methods are illustrated by means of simple examples. We also review important kinematic analysis and synthesis problems and their solutions using these mathematical procedures.
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Barotov, Dostonjon Numonjonovich, and Ruziboy Numonjonovich Barotov. "Polylinear Transformation Method for Solving Systems of Logical Equations." Mathematics 10, no. 6 (2022): 918. http://dx.doi.org/10.3390/math10060918.

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In connection with applications, the solution of a system of logical equations plays an important role in computational mathematics and in many other areas. As a result, many new directions and algorithms for solving systems of logical equations are being developed. One of these directions is transformation into the real continuous domain. The real continuous domain is a richer domain to work with because it features many algorithms, which are well designed. In this study, firstly, we transformed any system of logical equations in the unit n-dimensional cube Kn into a system of polylinear–poly
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Rojas, J. Maurice, and Yuyu Zhu. "A complexity chasm for solving sparse polynomial equations over p -adic fields." ACM Communications in Computer Algebra 54, no. 3 (2020): 86–90. http://dx.doi.org/10.1145/3457341.3457343.

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The applications of solving systems of polynomial equations are legion: The real case permeates all of non-linear optimization as well as numerous problems in engineering. The p -adic case leads to many classical questions in number theory, and is close to many applications in cryptography, coding theory, and computational number theory. As such, it is important to understand the complexity of solving systems of polynomial equations over local fields. Furthermore, the complexity of solving structured systems --- such as those with a fixed number of monomial terms or invariance with respect to
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Dissertations / Theses on the topic "Solving polynomial systems of equations"

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Wise, Steven M. "POLSYS_PLP: A Partitioned Linear Product Homotopy Code for Solving Polynomial Systems of Equations." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36933.

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Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked, and in the handling of singular solutions, have made probability-one homotopy methods even more practical. This thesis describes the theory behind and performance of the new code POLSYS_PLP, which consists of Fortran 90 modules f
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Bard, Gregory V. "Algorithms for solving linear and polynomial systems of equations over finite fields with applications to cryptanalysis." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/7202.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.<br>Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Mohamed, Mohamed Saied Emam. "Improved Strategies for Solving Multivariate Polynomial Equation Systems over Finite Fields." Phd thesis, TU Darmstadt, 2011. https://tuprints.ulb.tu-darmstadt.de/2622/4/Mohamed-Diss.pdf.

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One of the important research problems in cryptography is the problem of solving multivariate polynomial equations over finite fields. The hardness of solving this problem is the measure of the security of many public key cryptosystems as well as of many symmetric cryptosystems, like block and stream ciphers. In recent years, algebraic cryptanalysis has been presented as a method of attacking cryptosystems. This method consists in solving multivariate polynomial systems. Therefore, developing algorithms for solving such systems is a hot research topic. Over the recent years, several algori
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Mohamed, Mohamed Saied Emam [Verfasser], Johannes [Akademischer Betreuer] Buchmann, and Jintai [Akademischer Betreuer] Ding. "Improved Strategies for Solving Multivariate Polynomial Equation Systems over Finite Fields / Mohamed Saied Emam Mohamed. Betreuer: Johannes Buchmann ; Jintai Ding." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2011. http://d-nb.info/1105562581/34.

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Vu, Thi Xuan. "Homotopy algorithms for solving structured determinantal systems." Electronic Thesis or Diss., Sorbonne université, 2020. http://www.theses.fr/2020SORUS478.

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Les systèmes polynomiaux multivariés apparaissant dans de nombreuses applications ont des structures spéciales et les systèmes invariants apparaissent dans un large éventail d'applications telles que dans l’optimisation polynomiale et des questions connexes en géométrie algébrique réelle. Le but de cette thèse est de fournir des algorithmes efficaces pour résoudre de tels systèmes structurés. Afin de résoudre le premier type de systèmes, nous concevons des algorithmes efficaces en utilisant les techniques d’homotopie symbolique. Alors que les méthodes d'homotopie, à la fois numériques et symbo
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Paramanathan, Pamini. "Systems of polynomial equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ64880.pdf.

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Vanatta, Natalie. "Solving multi-variate polynomial equations in a finite field." Monterey, California: Naval Postgraduate School, 2013. http://hdl.handle.net/10945/34756.

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Approved for public release; distribution is unlimited<br>Solving large systems of multivariate polynomial equations is an active area of mathematical research, as these polynomials are used in many fields of science. The objective of this research is to advance the development of algebraic methods to attack the mathematical foundations of modern-day encryption methods, which can be modeled as a system of multivariate polynomial equations over a finite field. Our techniques overcome the limitations of previous methods. Additionally, a model is proposed to estimate the time required to solve la
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Stoffel, Joshua David. "Lagrange-Chebyshev Based Single Step Methods for Solving Differential Equations." University of Akron / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=akron1335299082.

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Parts, Inga. "Piecewise polynomial collocation methods for solving weakly singular integro-differential equations /." Online version, 2005. http://dspace.utlib.ee/dspace/bitstream/10062/851/5/parts.pdf.

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Cifuentes, Pardo Diego Fernando. "Exploiting chordal structure in systems of polynomial equations." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/92972.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (pages 79-81).<br>Chordal structure and bounded treewidth allow for efficient computation in linear algebra, graphical models, constraint satisfaction and many other areas. Nevertheless, it has not been studied whether chordality migh
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Books on the topic "Solving polynomial systems of equations"

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1962-, Sturmfels Bernd, ed. Solving systems of polynomial equations. American Mathematical Society, 2002.

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Alexander, Morgan. Solving polynomial systems using continuation for engineering and scientific problems. Prentice-Hall, 1987.

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Sidi, Avram. Efficient implementation of minimal polynominal and reduced rank extrapolation methods. NASA Lewis Research Center, Institute for Computational Mechanics in Propulsion, 1990.

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Bronstein, Manuel, Arjeh M. Cohen, Henri Cohen, et al., eds. Solving Polynomial Equations. Springer-Verlag, 2005. http://dx.doi.org/10.1007/b138957.

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Wen-tsün, Wu. Mathematics mechanization: Mechanical geometry theorem-proving, mechanical geometry problem-solving, and polynomial equations-solving. Kluwer Academic Publishers, 2000.

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Gruevski, Trpe. Algorithms for solving the polynomial algebraic equations of any power. Company Samojlik, 2000.

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Bernd, Fischer. Polynomial based iteration methods for symmetric linear systems. Society for Industrial and Applied Mathematics, 2011.

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Greenbaum, Anne. Iterative methods for solving linear systems. Society for Industrial and Applied Mathematics, 1997.

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Pielczyk, Andreas. Numerical methods for solving systems of quasidifferentiable equations. A. Hain, 1991.

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Hallett, Andrew Hughes. Hybrid algorithms with automatic switching for solving nonlinear equation systems. Dept. of Economics, Fraser of Allander Institute, University of Strathclyde, 1996.

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Book chapters on the topic "Solving polynomial systems of equations"

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Mishra, Bhubaneswar. "Solving Systems of Polynomial Equations." In Algorithmic Algebra. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-4344-1_4.

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Sommese, Andrew J., Jan Verschelde, and Charles W. Wampler. "Solving Polynomial Systems Equation by Equation." In Algorithms in Algebraic Geometry. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-75155-9_8.

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Joswig, Michael, and Thorsten Theobald. "Solving Systems of Polynomial Equations Using Gröbner Bases." In Universitext. Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4817-3_10.

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Ishteva, Mariya, and Philippe Dreesen. "Solving Systems of Polynomial Equations—A Tensor Approach." In Large-Scale Scientific Computing. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97549-4_38.

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Tu, Xinghan, and Xiaohua Peng. "Solving the System of Fuzzy Polynomial Equations." In Advances in Intelligent and Soft Computing. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14880-4_18.

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Sottile, Frank. "From Enumerative Geometry to Solving Systems of Polynomial Equations." In Computations in Algebraic Geometry with Macaulay 2. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04851-1_6.

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Courtois, Nicolas, Alexander Klimov, Jacques Patarin, and Adi Shamir. "Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations." In Advances in Cryptology — EUROCRYPT 2000. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-45539-6_27.

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Ivanyos, Gábor, and Miklos Santha. "On Solving Systems of Diagonal Polynomial Equations Over Finite Fields." In Frontiers in Algorithmics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19647-3_12.

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Grigoriev, Dima. "Polynomial Complexity of Solving Systems of Few Algebraic Equations with Small Degrees." In Computer Algebra in Scientific Computing. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02297-0_11.

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Buchinskiy, Ivan M., Matvei V. Kotov, and Alexander V. Treier. "On the Complexity of the Problem of Solving Systems of Tropical Polynomial Equations of Degree Two." In Communications in Computer and Information Science. Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-73365-9_5.

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Conference papers on the topic "Solving polynomial systems of equations"

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Widdershoven, Raphael, Nico Vervliet, and Lieven De Lathauwer. "A Bézoutian-Based Method for Solving Overdetermined Systems of Polynomial Equations." In 2024 32nd European Signal Processing Conference (EUSIPCO). IEEE, 2024. http://dx.doi.org/10.23919/eusipco63174.2024.10715262.

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Babadzanjanz, L. K., I. Yu Pototskaya, Yu Yu Pupysheva, and V. S. Korolev. "EXPENDITURE OPTIMAL CONTROL FOR A SATELLITE MOVING CLOSE TO THE LIBRATION POINT." In SGEM International Multidisciplinary Scientific GeoConference 24. STEF92 Technology, 2024. https://doi.org/10.5593/sgem2024/6.1/s28.64.

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Satellite motion control in the vicinity of the libration point with expenditure criteria is considered. Expenditure optimization is natural in the case, where it is necessary to keep mechanical system in the neighborhood of the equilibrium point for a long time. Disturbing factors from time to time distort this system unacceptably far from the equilibrium point, and we need to extinguish these deviations, using fuel or another resource, which reserves are limited. Optimization of the satellite motion control according to this criterion is important not only from the economic and technical sid
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Sahba, Farshid, Amin Sahba, Rmin Sahba, and Vahideh Hashempour. "A Model Based on Genetic Algorithm for Solving Polynomial Equations." In 2024 IEEE 15th Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON). IEEE, 2024. http://dx.doi.org/10.1109/uemcon62879.2024.10754782.

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Iori, Tomoyuki. "Controlled Invariant Sets for Polynomial Systems Defined by Non-polynomial Equations." In 2024 IEEE 63rd Conference on Decision and Control (CDC). IEEE, 2024. https://doi.org/10.1109/cdc56724.2024.10886422.

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Shen, Zhan, and Kexin Li. "Analog Circuit for Solving Linear Ordinary Differential Equations." In 2024 IEEE 6th International Conference on Power, Intelligent Computing and Systems (ICPICS). IEEE, 2024. https://doi.org/10.1109/icpics62053.2024.10796335.

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Canny, J. F., E. Kaltofen, and L. Yagati. "Solving systems of nonlinear polynomial equations faster." In the ACM-SIGSAM 1989 international symposium. ACM Press, 1989. http://dx.doi.org/10.1145/74540.74556.

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Mourrain, Bernard, and Victor Y. Pan. "Asymptotic acceleration of solving multivariate polynomial systems of equations." In the thirtieth annual ACM symposium. ACM Press, 1998. http://dx.doi.org/10.1145/276698.276862.

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Zjavka, Ladislav, and Vaclav Snasel. "Composing and Solving General Differential Equations Using Extended Polynomial Networks." In 2015 International Conference on Intelligent Networking and Collaborative Systems (INCOS). IEEE, 2015. http://dx.doi.org/10.1109/incos.2015.28.

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Faugère, Jean-Charles, and Sajjad Rahmany. "Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases." In the 2009 international symposium. ACM Press, 2009. http://dx.doi.org/10.1145/1576702.1576725.

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Nor, Hafizudin Mohamad, Ahmad Izani Md. Ismail, and Ahmad Abdul Majid. "Linear fixed point function for solving system of polynomial equations." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882474.

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Reports on the topic "Solving polynomial systems of equations"

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Baader, Franz, Pavlos Marantidis, and Alexander Okhotin. Approximately Solving Set Equations. Technische Universität Dresden, 2016. http://dx.doi.org/10.25368/2022.227.

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Unification with constants modulo the theory ACUI of an associative (A), commutative (C) and idempotent (I) binary function symbol with a unit (U) corresponds to solving a very simple type of set equations. It is well-known that solvability of systems of such equations can be decided in polynomial time by reducing it to satisfiability of propositional Horn formulae. Here we introduce a modified version of this problem by no longer requiring all equations to be completely solved, but allowing for a certain number of violations of the equations. We introduce three different ways of counting the
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Schnabel, Robert B., and Paul D. Frank. Solving Systems of Nonlinear Equations by Tensor Methods. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada169927.

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Zhang, Xiaodong, Richard H. Byrd, and Robert B. Schnabel. Parallel Methods for Solving Nonlinear Block Bordered Systems of Equations. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada217062.

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Bader, Brett William. Tensor-Krylov methods for solving large-scale systems of nonlinear equations. Office of Scientific and Technical Information (OSTI), 2004. http://dx.doi.org/10.2172/919158.

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Li, Guangye. The Secant/Finite Difference Algorithm for Solving Sparse Nonlinear Systems of Equations. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada453093.

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Varga, Richard S. Investigation on Improved Iterative Methods for Solving Sparse Systems of Linear Equations. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada187046.

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Varga, Richard S. Investigations on Improved Iterative Methods for Solving Sparse Systems of Linear Equations. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada166170.

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Marcus, Martin H. An Improved Method for Solving Systems of Linear Equations in Frequency Response Problems. Defense Technical Information Center, 2004. http://dx.doi.org/10.21236/ada422723.

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Blue, James L. B2DE -- a program for solving systems of partial differential equations in two dimensions. National Bureau of Standards, 1986. http://dx.doi.org/10.6028/nbs.ir.86-3411.

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Dennis, Jr, Li J. E., and Guangye. The Combined Schubert/Secant Finite-Difference Algorithm for Solving Sparse Nonlinear Systems of Equations. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada453834.

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