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Canadian Journal of Physics, ISSN 0008-4204, 2016, Volume 94, Issue 3, pp. 249 - 253
Journal Article
Michigan Mathematical Journal, ISSN 0026-2285, 2017, Volume 66, Issue 1, pp. 155 - 174
Using the theory of jet schemes, we give a new approach to the description of a minimal generating sequence of a divisorial valuations on A(2). For this... 
MATHEMATICS | BRANCHES | NEWTON-PUISEUX EXPANSION
Journal Article
JOURNAL OF SCIENTIFIC COMPUTING, ISSN 0885-7474, 02/2020, Volume 82, Issue 3
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2017, Volume 86, Issue 303, pp. 345 - 29
Journal Article
Annals of Operations Research, ISSN 0254-5330, 6/2016, Volume 241, Issue 1, pp. 515 - 573
Journal Article
Numerical Algorithms, ISSN 1017-1398, 05/2018, Volume 78, Issue 1, pp. 107 - 132
This paper is devoted to designing a practical algorithm to invert the Laplace transform by assuming that the transform possesses the Puiseux expansion at infinity... 
Bromwich integral | Gauss–Kronrod rule | Puiseux expansion | Inverse Laplace transform | Gauss–Legendre rule | Error estimate | MATHEMATICS, APPLIED | SERIES | Gauss-Legendre rule | TALBOTS METHOD | IMPLEMENTATION | EQUATIONS | NUMERICAL INVERSION | PRECISION | INTEGRALS | KRONROD QUADRATURE-RULES | GAUSS-LEGENDRE QUADRATURE | COMPUTATION | Gauss-Kronrod rule | Usage | Algorithms
Journal Article
Algebraic & geometric topology, ISSN 1472-2739, 2016, Volume 16, Issue 2, pp. 843 - 898
...; the Puiseux expansion naturally emerges. The corresponding DAHA superpolynomials are expected to coincide with the reduced ones in the Oblomkov-Shende-Rasmussen conjecture upon its generalization to arbitrary dominant weights... 
HOMFLY-PT polynomial | Iterated torus knot | Cabling | Khovanov-Rozansky homology | Double affine Hecke algebra | Jones polynomials | Macdonald polynomial | Generalized Jacobian | Puiseux expansion | Betti numbers | Plane curve singularity | SPRINGER | POLYNOMIALS | MATHEMATICS | STABLE PAIRS | FIBERS | COMPACTIFIED JACOBIANS | MATRIX FACTORIZATIONS | LINK HOMOLOGY | INVARIANTS | RATIONAL CURVES | SURFACES
Journal Article
Communications in Algebra, ISSN 0092-7872, 05/2016, Volume 44, Issue 5, pp. 2100 - 2109
We consider the problem of deciding whether a common solution to a multivariate polynomial equation system is isolated or not. We present conditions on a given... 
Algebraic varieties | Isolated points | Puiseux series | Curves | SYSTEM | MATHEMATICS | SET | DIMENSION | EQUIDIMENSIONAL DECOMPOSITION | Parametrization | Polynomials | Algebra | Vectors (mathematics) | Mathematical analysis
Journal Article
Revista Matemática Complutense, ISSN 1139-1138, 1/2015, Volume 28, Issue 1, pp. 227 - 252
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 01/2018, Volume 18, Issue 1, pp. 333 - 385
Journal Article
Communications in Algebra, ISSN 0092-7872, 05/2016, Volume 44, Issue 5, pp. 2118 - 2151
.... Each member of the family can be expressed via the Puiseux expansion. Studying the limits of suitably renormalized coefficients of the Puiseux expansions, we obtain... 
Parametric deformation | Primary: 14B07 | Puiseux expansion | Plane curve singularity | Secondary: 14H20 | MATHEMATICS | Parametrization | Obstructions | Algebra | Deformation | Singularities | Curves (geometry)
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 11/2015, Volume 14, Issue 9
The celebrated "Epimorphism Theorem" opened up several directions of research. In this survey article we highlight the known partial results and open questions... 
Epimorphism theorem | affine fibrations | cancellation problem | Polynomial rings | linearization problem | embedding problem | MATHEMATICS, APPLIED | TOPOLOGICAL PROOF | AFFINE RATIONAL DOMAINS | CANCELLATION THEOREM | NEWTON-PUISEUX EXPANSION | CODIMENSION-ONE | MATHEMATICS | LINEAR PLANES | VARIABLES | EMBEDDINGS | POLYNOMIAL ALGEBRAS | TSCHIRNHAUSEN TRANSFORMATION
Journal Article
Journal of Algebra, ISSN 0021-8693, 2011, Volume 343, Issue 1, pp. 143 - 159
We generalize Abhyankar–Mohʼs theory of approximate roots of polynomials to the case of approximate roots of non-characteristic degrees of an irreducible... 
Approximate roots of polynomials | Characteristic sequences | MATHEMATICS | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | NEWTON-PUISEUX EXPANSION
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 11/2015, Volume 14, Issue 9
This paper contains a complete and self-contained proof of the AMS theorem. The main tool is a new algorithm producing an irreducible dependence for a pair of... 
degree semigroup | Abhyankar-Moh-Suzuki theorem | minimal polynomial dependence | MATHEMATICS, APPLIED | NEWTON-PUISEUX EXPANSION | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | MINIMAL POLYNOMIALS | CURVES | MATHEMATICS | AFFINE PLANE | LINE | ROOTS | EMBEDDINGS
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2000, Volume 69, Issue 231, pp. 1167 - 1182
In this paper we present a refined version of the Newton polygon process to compute the Puiseux expansions of an algebraic function defined over the rational function field... 
Integers | Algebra | Mathematical theorems | Algorithms | Polynomials | Algebraic functions | Logarithms | Coefficients | Power series | Polygons | Algebraic function | Puiseux expansion | Newton polygon complexity | Newton polygon | complexity | MATHEMATICS, APPLIED | algebraic function | THEOREM | FACTORING POLYNOMIALS | ALGORITHM | NUMBER-FIELDS
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 11/2015, Volume 14, Issue 9
In this work we deal with dicritical divisors, curvettes and polynomials. These objects have been one of the main research interests of Abhyankar during his... 
Dicritical divisor | special pencil | INFINITY | MATHEMATICS | MATHEMATICS, APPLIED | GENERIC INCARNATIONS | NEWTON-PUISEUX EXPANSION | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | JACOBIAN PROBLEM | CURVES | QUADRATIC TRANSFORMS | Mathematics - Algebraic Geometry
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 10/2010, Volume 266, Issue 2, pp. 243 - 264
... at in nity · ojasiewicz exponent at in nity · Puiseux expansion at in nity · Real approximation of complex curves Mathematics Subject Classi cation (2000) Primary 32C99... 
Łojasiewicz inequality at infinity | Primary 32C99 | Secondary 14R25 | 32A20 | Łojasiewicz exponent at infinity | Mathematics, general | Mathematics | Puiseux expansion at infinity | Real approximation of complex curves | 32S05 | MATHEMATICS | EXPONENT | Lojasiewicz inequality at infinity | Lojasiewicz exponent at infinity
Journal Article
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2013, Volume 65, Issue 1, pp. 169 - 182
We introduce the notion of an approximate Jacobian Newton diagram which is the Jacobian Newton diagram of the morphism (f((k)), f), where f is a branch and... 
Jacobian Newton diagram | Approximate root | Irreducible plane curve | MATHEMATICS | DISCRIMINANT | SINGULARITIES | approximate root | PUISEUX EXPANSION | irreducible plane curve | GENERALIZED TSCHIRNHAUSEN TRANSFORMATION | POLAR INVARIANTS | Mathematics - Algebraic Geometry
Journal Article
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