相关论文: Volume computation for polytopes and partition fun…

Taking partial traces for computing reduced density matrices, or related functions, is a ubiquitous procedure in the quantum mechanics of composite systems. In this article, we present a thorough description of this function and analyze the…

Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial…

By introducing a class of meromorphic functions with certain ramification structures on $\Bbb{CP}^1$, a new method for the determination of the Legendre representation of elliptic curves with complex multiplication is introduced. These…

In this paper, we derive a simple recursion formula for the Weil-Petersson volumes of moduli spaces of hyperbolic surfaces with boundaries. This formula demonstrates the polynomiality of the volume functions. By constructing the Laplace…

In this article, using a known method, a computation is performed of the derivatives of the microcanonical entropy, with respect to the energy up to the 4-th order, using a Laplace transform technique, and adapted it to the case where the…

We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…

In this paper, we propose a new algebraic winding number and prove that it computes the number of complex roots of a polynomial in a rectangle, including roots on edges or vertices with appropriate counting. The definition makes sense for…

The calculation and manipulation of large multi-variable rational functions is a key bottleneck in multi-loop calculations. In these conference proceedings, based on my article [Chawdhry (2023) arXiv:2312.03672], I present a technique to…

We examine two different ways of encoding a counting function, as a rational generating function and explicitly as a function (defined piecewise using the greatest integer function). We prove that, if the degree and number of input…

The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…

In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our…

We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.

Some integrals of matrix spaces over a quaternionic field have been calculated in this work. The associated volume of hyperbolic matrix spaces over a quaternionic field has also been calculated by making use of these integrals, and it is of…

Motivated by string theory connection, a covariant procedure for perturbative calculation of the partition function of the two-dimensional generalized $\sigma$-model is considered. The importance of a consistent regularization of the…

We present a mathematical analysis of transformations used in fast calculation of inverse square root for single-precision floating-point numbers. Optimal values of the so called magic constants are derived in a systematic way, minimizing…

A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…

In this paper, we introduce and analyze multidimensional vector-valued Laplace transform of functions with values in sequentially complete locally convex spaces. A great number of our results seem to be new even for the functions with…

We present a systematic method for determining the two-loop effective Lagrangian resulting from integrating out a set of heavy particles in an ultraviolet scalar theory. We prove that the matching coefficients are entirely determined from…

It is the aim of this work to identify and illustrate the potential and weaknesses of the computer algebra system Maple in the area of the Calculus of Variations: a classical area of mathematics that studies the methods for finding maximum…

We experimentally study the fundamental problem of computing the volume of a convex polytope given as an intersection of linear inequalities. We implement and evaluate practical randomized algorithms for accurately approximating the…