Related papers: Automatic code generator for higher order integrat…
We present a program for the reduction of large systems of integrals to master integrals. The algorithm was first proposed by Laporta; in this paper, we implement it in MAPLE. We also develop two new features which keep the size of…
Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits, and reproduce the equilibrium…
An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as…
In this paper, we extend several time reversible numerical integrators to solve the Lorentz force equations from second order accuracy to higher order accuracy for relativistic charged particle tracking in electromagnetic fields. A fourth…
This paper tackles the challenge of teaching code semantics to Large Language Models (LLMs) for program analysis by incorporating code symmetries into the model architecture. We introduce a group-theoretic framework that defines code…
In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any…
Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor's algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary…
We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…
We present a method to obtain higher order integrals and polynomial algebras for two-dimensional superintegrable systems from creation and annihilation operators. All potentials with a second and a third order integrals of motion separable…
A common technique in the study of complex quantum-mechanical systems is to reduce the number of degrees of freedom in the Hamiltonian by using quasi-degenerate perturbation theory. While the Schrieffer--Wolff transformation achieves this…
Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltonian simulation methods. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates…
A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1,1) x…
In this paper, we are concerned with the construction and analysis of a new class of methods obtained as double jump compositions with complex coefficients and projection on the real axis. It is shown in particular that the new integrators…
The digital transformation of automation places new demands on data acquisition and processing in industrial processes. Logical relationships between acquired data and cyclic process sequences must be correctly interpreted and evaluated. To…
We proposed an algorithm that covers some cases of Hamilton Circuit Problem.
We describe a practical algorithm which computes the accepting automaton for the insertion encoding of a permutation class, whenever this insertion encoding is regular. This algorithm is implemented in the accompanying Maple package INSENC,…
We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its homogeneous self-dual embedding, and solving the…
The kinetic term of the $N$-body Hamiltonian system defined on the surface of the sphere is non-separable. As a result, standard explicit symplectic integrators are inapplicable. We exploit an underlying hierarchy in the structure of the…
A novel symplectic integrator for Hamiltonian equations on $S_2^n \times T^{\ast} \RR^m$ is developed and studied. Partitioned Runge--Kutta methods for Hamiltonian systems on products of Hamiltionian manifolds are studied, specifically,…
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…