Search Results - complexity. 68W30 Symbolic computation and algebraic computation

Decision problem for a class of univariate Pfaffian functions by Barbagallo, María Laura, Jeronimo, Gabriela, Sabia, Juan

“… We present a new symbolic procedure solving this problem with a computable complexity based on the computation of suitable Sturm sequences…”
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A quasi-linear irreducibility test in K[[x]][y] by Poteaux, Adrien, Weimann, Martin

“…We provide an irreducibility test in the ring K [ [ x ] ] [ y ] whose complexity is quasi-linear with respect to the discriminant valuation, assuming the input…”
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Schur Polynomials Do Not Have Small Formulas If the Determinant does not by Chaugule, Prasad, Kumar, Mrinal, Limaye, Nutan, Mohapatra, Chandra Kanta, She, Adrian, Srinivasan, Srikanth

“…). In recent years, they have also shown up in various incarnations in Computer Science, e.g, quantum computation Hallgren et al. (2000); O'Donnell & Wright (2015…”
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Computing roadmaps in unbounded smooth real algebraic sets II: Algorithm and complexity by Prébet, Rémi, Safey El Din, Mohab, Schost, Éric

“…A roadmap for an algebraic set V defined by polynomials with coefficients in the field Q of rational numbers is an algebraic curve contained in V whose intersection with all connected components of V∩Rn is connected…”
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Bounds for Polynomials on Algebraic Numbers and Application to Curve Topology by Diatta, Daouda Niang, Diatta, Sény, Rouillier, Fabrice, Roy, Marie-Françoise, Sagraloff, Michael

“… } be the real planar algebraic curve implicitly defined as the vanishing set of  P . We give a deterministic algorithm to compute the topology of V R ( P…”
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Using Machine Learning to Improve Cylindrical Algebraic Decomposition by Huang, Zongyan, England, Matthew, Wilson, David J., Bridge, James, Davenport, James H., Paulson, Lawrence C.

“…Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields…”
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Algebraic diagonals and walks: Algorithms, bounds, complexity by Bostan, Alin, Dumont, Louis, Salvy, Bruno

“… It is classical that in this case DiagF is an algebraic function. We propose an algorithm that computes an annihilating polynomial for DiagF…”
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Algorithmic Reduction of Biological Networks with Multiple Time Scales by Kruff, Niclas, Lüders, Christoph, Radulescu, Ovidiu, Sturm, Thomas, Walcher, Sebastian

“…We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical…”
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Real root finding for low rank linear matrices by Henrion, Didier, Naldi, Simone, Din, Mohab Safey El

“… that intersects each connected component of the low rank real algebraic set. The complexity of our algorithm is studied thoroughly…”
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Dimension results for extremal-generic polynomial systems over complete toric varieties by Bender, Matías, Spaenlehauer, Pierre-Jean

“…We study polynomial systems with prescribed monomial supports in the Cox ring of a toric variety built from a complete polyhedral fan. We present combinatorial…”
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A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations by Seiler, Werner M., Seiß, Matthias, Sturm, Thomas

“…We discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic…”
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Computing the equisingularity type of a pseudo-irreducible polynomial by Poteaux, Adrien, Weimann, Martin

“…Germs of plane curve singularities can be classified accordingly to their equisingularity type. For singularities over C , this important data coincides with…”
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On the complexity of skew arithmetic by van der Hoeven, Joris

“…In this paper, we study the complexity of several basic operations on linear differential operators with polynomial coefficients…”
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Cylindrical Algebraic Sub-Decompositions by Wilson, D. J., Bradford, R. J., Davenport, J. H., England, M.

“…Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets…”
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Linear programming using limited-precision oracles by Gleixner, Ambros, Steffy, Daniel E.

“… When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations…”
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Deterministic root finding over finite fields using Graeffe transforms by Grenet, Bruno, van der Hoeven, Joris, Lecerf, Grégoire

“… This algorithm allows for the efficient computation of Graeffe transforms of arbitrary orders…”
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On computing absolutely irreducible components of algebraic varieties with parameters by Ayad, Ali

“…This paper presents a new algorithm for computing absolutely irreducible components of n -dimensional algebraic varieties defined implicitly by parametric homogeneous polynomial equations…”
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Multi-point evaluation in higher dimensions by van der Hoeven, Joris, Schost, Éric

“… ; one particularly important example is the algebra of truncated power series . Similarly to what is known for multi-point evaluation and interpolation in the univariate case, our algorithms have quasi-linear time complexity…”
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Certified simultaneous isotopic approximation of algebraic curves via subdivision by Burr, Michael, Byrd, Michael

“…We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of algebraic curves in the plane…”
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Condition number based complexity estimate for solving polynomial systems by She, Zhikun, Xia, Bican, Zheng, Zhiming

“…By modifying and combining algorithms in symbolic and numerical computation, we propose a real-root-counting based method for deciding the feasibility of systems of polynomial equations…”
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