Publications related to Computing roots of polynomials over function fields of curves

Formal Verification of Integer Multipliers by Combining Gröbner Basis with Logic Reduction

Formal verification utilizing symbolic computer algebra has demonstrated the ability to formally verify large Galois field arithmetic circuits and basic architectures of integer arithmetic circuits. The technique models the circuit as Gröbner basis polynom ...

IEEE2016

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Michaël Unser, Daniel Andreas Schmitter, Ricard Delgado Gonzalo

Interpolatory basis functions are helpful to specify parametric curves or surfaces that can be modified by simple user-interaction. Their main advantage is a characterization of the object by a set of control points that lie on the shape itself (i.e., curv ...

2016

An Inner-Product Calculus for Periodic Functions and Curves

Michaël Unser, Daniel Andreas Schmitter, Anaïs Laure Marie-Thérèse Badoual

Our motivation is the design of efficient algorithms to process closed curves represented by basis functions or wavelets. To that end, we introduce an inner-product calculus to evaluate correlations and

L _{ 2 }

distances between such curves. In partic ...

2016

Polynomiality of Hurwitz numbers, Bouchard-Marino conjecture, and a new proof of the ELSV formula

Nicolas Gerson Orantin

In this paper we give a new proof of the ELSV formula. First, we refine an argument of Okounkov and Pandharipande in order to prove (quasi-)polynomiality of Hurwitz numbers without using the ELSV formula (the only way to do that before used the ELSV formul ...

Academic Press Inc Elsevier Science2015

Some remarks on representations of Yang-Mills algebras

In this article, we present some new properties of representations of Yang-Mills algebras. We first show that any free Lie algebra with m generators is a quotient of the Yang-Mills algebra ym(n) on n generators, for n ≥ 2m. We derive from this that any sem ...

2015

Asymptotics of action variables near semi-toric singularities

The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does n ...

Elsevier2015

Deciding Conditional Termination

We address the problem of conditional termination, which is that of defining the set of initial configurations from which a given program always terminates. First we define the dual set, of initial configurations from which a non-terminating execution exis ...

Tech Univ Braunschweig2014

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

2014

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

Jean-Christophe Mourrat

The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For s ...

Springer Heidelberg2014

Sums Of Squares In Algebraic Function Fields Over A Complete Discretely Valued Field

David Maximilian Grimm

A recently found local-global principle for quadratic forms over function fields of curves over a complete discretely valued field is applied to the study of quadratic forms, sums of squares, and related field invariants. ...

Pacific Journal Mathematics2014

Computing roots of polynomials over function fields of curves

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Formal Verification of Integer Multipliers by Combining Gröbner Basis with Logic Reduction

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

An Inner-Product Calculus for Periodic Functions and Curves

Polynomiality of Hurwitz numbers, Bouchard-Marino conjecture, and a new proof of the ELSV formula

Some remarks on representations of Yang-Mills algebras

Asymptotics of action variables near semi-toric singularities

Deciding Conditional Termination

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

Sums Of Squares In Algebraic Function Fields Over A Complete Discretely Valued Field

An Inner-Product Calculus for Periodic Functions and Curves

Formal Verification of Integer Multipliers by Combining Gröbner Basis with Logic Reduction

Asymptotics of action variables near semi-toric singularities

Some remarks on representations of Yang-Mills algebras

A Family of Smooth and Interpolatory Basis Functions for Parametric Curve and Surface Representation

Polynomiality of Hurwitz numbers, Bouchard-Marino conjecture, and a new proof of the ELSV formula

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Deciding Conditional Termination

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

Sums Of Squares In Algebraic Function Fields Over A Complete Discretely Valued Field