Related papers: A tutorial for the MAPLE ETA package

This article presents an open-source Python package for simulating micro-thermoelectric generators, based on the work by D. Beretta et al. (Sustainable Energy Fuels, 2017). Featuring a user-friendly graphical user interface and robust…

A route to evaluate exact sums represented by Dirichlet eta and beta functions, both of which are alternating and divergent at negative integer arguments, is advocated. It rests on precise polynomial extrapolations and stands as a…

In recent work, the author, in collaboration with Allen, Long, and Tu, developed the Explicit Hypergeometric Modularity Method (EHMM), which establishes the modularity of a large class of hypergeometric Galois representations in dimensions…

Enge and Schertz gave the method of using the double eta-quotient for the construction of elliptic curves over finite fields. In their method, it is necessary to count the number of rational points of elliptic curves corresponding to…

The MechElastic Python package evaluates the mechanical and elastic properties of bulk and 2D materials using the elastic coefficient matrix ($C_{ij}$) obtained from any ab-initio density-functional theory (DFT) code. The current version of…

One-loop functions with loop masses larger than external masses and momenta can always be expanded in terms of external masses and momenta. The precision requested for observables determines the number of the expansion terms retained in the…

In 2003, Kedlaya gave an algorithm to compute the zeta function associated to a hyperelliptic curve over a finite field, by computing the rigid cohomology of the curve. Edixhoven remarked that it is actually possible to compute the…

Proof assistants often call automated theorem provers to prove subgoals. However, each prover has its own proof calculus and the proof traces that it produces often lack many details to build a complete proof. Hence these traces are hard to…

A generalised Weber function is given by $\w_N(z) = \eta(z/N)/\eta(z)$, where $\eta(z)$ is the Dedekind function and $N$ is any integer; the original function corresponds to $N=2$. We classify the cases where some power $\w_N^e$ evaluated…

Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting.…

A brief introduction into Idempotent Mathematics and an idempotent version of Interval Analysis are presented. Some applications are discussed.

Let $q=e^{2\pi i\tau}$, $\Im\tau>0$, $x=e^{2\pi i\xi}\in\CC$ and $(x;q)_\infty=\prod_{n\ge 0}(1-xq^n)$. Let $(q,x)\mapsto(q^*,\iota_q x)$ be the classical modular substitution given by $q^*=e^{-2\pi i/\tau}$ and $\iota_q x=e^{2\pi…

We present the G-MAPLE (Generalised Modal Analysis from the Poles of the Laplace Expansion) software that allows decomposing data depending on a single parameter (such as time series data) into a set of exponential functions having complex…

This article is about a measurement analysis based approach to help software practitioners in managing the additional level complexities and variabilities in software product line applications. The architecture of the proposed approach i.e.…

Mathematica is a powerful application package for doing mathematics and is used almost in all branches of science. It has widespread applications ranging from quantum computation, statistical analysis, number theory, zoology, astronomy, and…

We define a zeta function woth respect to the twisted Grover matrix of a mixed digraph, and present an exponential expression and a determinant expression of this zeta function. As an application, we give a trace formula with respect to the…

The multiplication of a matrix by its transpose, $A^T A$, appears as an intermediate operation in the solution of a wide set of problems. In this paper, we propose a new cache-oblivious algorithm (ATA) for computing this product, based upon…

This work introduces a new software package `Sesame' for the numerical computation of classical semiconductor equations. It supports 1 and 2-dimensional systems and provides tools to easily implement extended defects such as grain…

The Matrix Element Method has proven to be a powerful method to optimally exploit the information available in detector data. Its widespread use is nevertheless impeded by its complexity and the associated computing time. MoMEMta, a C++…

Use of explicit integration methods for power electronic circuits with ideal switch models significantly improves simulation speed. The PLECS package [1] has effectively used this idea; however, the implementation details involved in PLECS…