Related papers: Exact Symbolic-Numeric Computation of Planar Algeb…
We enumerate plane complex algebraic curves of a given degree with one singularity of any given topological type. Our approach is to compute the homology classes of the corresponding equisingular strata in the parameter spaces of plane…
This paper presents two new direct symbolic-numerical algorithms for the transformation of Cartesian coordinates into geodetic coordinates considering the general case of a triaxial reference ellipsoid. The problem in both algorithms is…
Valiant introduced matchgate computation and holographic algorithms. A number of seemingly exponential time problems can be solved by this novel algorithmic paradigm in polynomial time. We show that, in a very strong sense, matchgate…
In this article we show how to compute a matrix representation and the implicit equation by means of the method developed in [Botbol: arXiv:1007.3437], using the computer algebra system Macaulay2 \cite{M2}. As it is probably the most…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
For causal discovery in the presence of latent confounders, constraints beyond conditional independences exist that can enable causal discovery algorithms to distinguish more pairs of graphs. Such constraints are not well-understood yet. In…
We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is…
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems to do with polynomial systems over the reals, but known to have worst-case computational…
Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. However, the estimation of the multiple nonlinear…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
We design polynomial size, constant depth (namely, $\mathsf{AC}^0$) arithmetic formulae for the greatest common divisor (GCD) of two polynomials, as well as the related problems of the discriminant, resultant, B\'ezout coefficients,…
We introduce beyond-worst-case analysis into symbolic computation. This is an extensive field which almost entirely relies on worst-case bit complexity, and we start from a basic problem in the field: isolating the real roots of univariate…
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…
The computational burden of probabilistic inference remains a hurdle for applying probabilistic programming languages to practical problems of interest. In this work, we provide a semantic and algorithmic foundation for efficient exact…
The paper introduces a novel representation for Generalized Planning (GP) problems, and their solutions, as C++ programs. Our C++ representation allows to formally proving the termination of generalized plans, and to specifying their…
In this paper we propose a direct and explicit realization of addition of divisors by means of an iterative reduction algorithm. Each iteration of the algorithm is the reduction of a degree $g+1$ divisor to a divisor of degree~$g$. Such an…
We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…
We apply numerical algebraic geometry to the invariant-theoretic problem of detecting symmetries between two plane algebraic curves. We describe an efficient equality test which determines, with "probability-one", whether or not two…
We present an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces.
In practice symmetries of combinatorial structures are computed by transforming the structure into an annotated graph whose automorphisms correspond exactly to the desired symmetries. An automorphism solver is then employed to compute the…