Related papers: FORM version 4.0
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
The long-standing aspiration for software reuse has made astonishing strides in the past few years. Many modern software development ecosystems now come with rich sets of publicly-available components contributed by the community.…
This work presents an updated version of the previously released freeware MAN (Modal Analysis of Nanoresonators) [Comput Phys Commun 284, 108627 (2023)], a software package designed to efficiently compute and normalize quasinormal modes…
Online forms are widely used to collect data from human and have a multi-billion market. Many software products provide online services for creating semi-structured forms where questions and descriptions are organized by pre-defined…
Generalized Additive Models (GAMs) have quickly become the leading choice for inherently-interpretable machine learning. However, unlike uninterpretable methods such as DNNs, they lack expressive power and easy scalability, and are hence…
We report on our experiences exploring state of the art Groebner basis computation. We investigate signature based algorithms in detail. We also introduce new practical data structures and computational techniques for use in both signature…
The capture calculus is an extension of System F<: that tracks free variables of terms in their type, allowing one to represent capabilities while limiting their scope. While previous calculi had mechanized soundness proofs -- notably…
This paper gives an overview of SCR3 -- a toolset designed to increase the usability of formal methods for software development. Formal requirements are specified in SCR3 in an easy to use and review format, and then used in checking…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
The symbolic manipulation program Schoonschip is being made freely available for a number of computers with Motorola 680x0 cpu's. It can run on machines with relatively modest memory and disk resources, and is designed to run as fast as…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Program transformation has gained a wide interest since it is used for several purposes: altering semantics of a program, adding features to a program or performing optimizations. In this paper we focus on program transformations at the…
UCLID5 is a tool for the multi-modal formal modeling, verification, and synthesis of systems. It enables one to tackle verification problems for heterogeneous systems such as combinations of hardware and software, or those that have…
In this work, a functional variant of the polynomial analogue of the classical Gandy's fixed point theorem is obtained. Sufficient conditions have been found to ensure that the complexity of the recursive function does not go beyond the…
The theme of symbolic computation in algebraic categories has become of utmost importance in the last decade since it enables the automatic modeling of modern algebra theories. On this theoretical background, the present paper reveals the…
The recently developed generalized Fourier-Galerkin method is complemented by a numerical continuation with respect to the kinetic energy, which extends the framework to the investigation of modal interactions resulting in folds of the…
Symbolic computation is an important approach in automated program analysis. Most state-of-the-art tools perform symbolic computation as interpreters and directly maintain symbolic data. In this paper, we show that it is feasible, and in…
The Business Process Modeling Notation (BPMN) is a widely used standard notation for defining intra- and inter-organizational workflows. However, the informal description of the BPMN execution semantics leads to different interpretations of…
Progress in the atomic-scale modelling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by either solving the electronic…
Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…