Related papers: Computation of Differential Chow Forms for Prime D…

We use homotopy theory to define certain rational coefficients characteristic numbers with integral values, depending on a given prime number q and positive integer t. We prove the first nontrivial degree formula and use it to show that…

We develop an algorithm to compute Fourier expansions of vector valued modular for Weil representations. As an application, we compute explicit linear equivalences of special divisors on modular varieties of orthogonal type. We define three…

A scheme for approximating the kernel $w$ of the fractional $\alpha$-integral by a linear combination of exponentials is proposed and studied. The scheme is based on the application of a composite Gauss-Jacobi quadrature rule to an integral…

This paper is devoted to studying difference indices of quasi-prime difference algebraic systems. We define the quasi dimension polynomial of a quasi-prime difference algebraic system. Based on this, we give the definition of the difference…

A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…

We show that the degree of a graded lattice ideal of dimension 1 is the order of the torsion subgroup of the quotient group of the lattice. This gives an efficient method to compute the degree of this type of lattice ideals.

We present a new probabilistic algorithm to compute modular polynomials modulo a prime. Modular polynomials parameterize pairs of isogenous elliptic curves and are useful in many aspects of computational number theory and cryptography. Our…

We describe first-degree prime ideals of biquadratic extensions in terms of first-degree prime ideals of two underlying quadratic fields. The identification of the prime divisors is given by numerical conditions involving their ideal norms.…

A precise estimation of the computational complexity in Shor's factoring algorithm under the condition that the large integer we want to factorize is composed by the product of two prime numbers, is derived by the results related to number…

There are well known algorithms to compute the class group of the maximal order $\mathcal{O}_K$ of a number field $K$ and the group of invertible ideal classes of a non-maximal order $R$. In this paper we explain how to compute also the…

Let $J\subset I$ be monomial ideals. We show that the Stanley depth of $I/J$ can be computed in a finite number of steps. We also introduce the $\fdepth$ of a monomial ideal which is defined in terms of prime filtrations and show that it…

We develop a probabilistic algorithm for computing elimination ideals of likelihood equations, which is for larger models by far more efficient than directly computing Groebner bases or the interpolation method proposed in the first…

Discrete maximum principles in the approximation of partial differential equations are crucial for the preservation of qualitative properties of physical models. In this work we enforce the discrete maximum principle by performing a simple…

Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szanto. In this paper, we give the first complete bounds for the…

Let $\Delta$ denote the discriminant of a generic binary $d$-ic. We show that for $d \ge 3$, the Jacobian ideal of $\Delta$ is perfect of height 2. Moreover, we describe its SL_2-equivariant minimal resolution, and the associated invariant…

We are concerned with the numerical solution obtained by splitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative coefficients. It…

A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters.…

A large system of ordinary differential equations is approximated by a parabolic partial differential equation with dynamic boundary condition and a different one with Robin boundary condition. Using the theory of differential operators…

An optimization based state and parameter estimation method is presented where the required Jacobian matrix of the cost function is computed via automatic differentiation. Automatic differentiation evaluates the programming code of the cost…

We consider the problem of differentially private selection. Given a finite set of candidate items and a quality score for each item, our goal is to design a differentially private mechanism that returns an item with a score that is as high…