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Polynomiality properties of tropical refined invariants [PDF]
Tropical refined invariants of toric surfaces constitute a fascinating interpolation between real and complex enumerative geometries via tropical geometry.
Brugallé, Erwan +1 more
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Polynomial decomposition algorithms
\textit{M. Fried} and \textit{R. MacRae} [Math. Ann. 180, 220--226 (1969; Zbl 0185.28803)] proved the following theorem: Let \(f,g,p,q\) be univariate polynomials over an arbitrary field \(k\). Then \(p(x)-q(z)\) divides \(f(x)-g(z)\) if and only if there exists a polynomial \(F(t)\) over \(k\) such that \(f(t)=F(p(t))\) and \(g(t)=F(q(t)).\) The ...
David R. Barton, Richard Zippel
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Polynomiality properties of tropical refined invariants
24 Figures, 44 pages. V2: minor revisionsTropical refined invariants of toric surfaces constitute a fascinating interpolation between real and complex enumerative geometries via tropical geometry.
Brugallé, Erwan +1 more
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Division algorithms for Bernstein polynomials [PDF]
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Busé, Laurent, Goldman, Ron
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Convergence analysis of an Inexact Infeasible Interior Point method for Semidefinite Programming [PDF]
In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima,Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993).
Pieraccini, Sandra, Bellavia, S
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Polynomial decomposition algorithms
A polynomial \(f\) over a commutative ring is said to be decomposable if it has a non-trivial functional decomposition \(f=g\circ h\). Previous algorithms to check decomposability were exponential-time in the worst case and only worked over fields of characteristic 0.
Dexter Kozen, Susan Landau 0001
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Algorithmic Computation of Polynomial Amoebas [PDF]
We present algorithms for computation and visualization of amoebas, their contours, compactified amoebas and sections of three-dimensional amoebas by two-dimensional planes. We also provide method and an algorithm for the computation of~polynomials whose amoebas exhibit the most complicated topology among all polynomials with a fixed Newton polytope ...
D. V. Bogdanov +2 more
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Interpolation by lattice polynomial functions: A polynomial time algorithm [PDF]
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Quentin Brabant +2 more
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Quasi-polynomiality of monotone orbifold Hurwitz numbers and Grothendieck's dessins d'enfants [PDF]
We prove quasi-polynomiality for monotone and strictly monotone orbifold Hurwitz numbers. The second enumerative problem is also known as enumeration of a special kind of Grothendieck's dessins d'enfants or $r$-hypermaps.
R.Kramer +6 more
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Quantum algorithms for the Jones polynomial [PDF]
This paper gives a generalization of the AJL algorithm and unitary braid group representation for quantum computation of the Jones polynomial to continuous ranges of values on the unit circle of the Jones parameter. We show that our 3-strand algorithm for the Jones polynomial is a special case of this generalization of the AJL algorithm.
Kauffman, Louis H. +1 more
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