Related papers: Symbolic computations in differential geometry
The detection and classification of intersections between triangles are crucial tasks in a wide range of applications within Computer Graphics and Geometry Processing, including mesh Arrangements, mesh Booleans, and generic mesh processing…
In Computational Science, Engineering and Finance (CSEF) scripts typically serve as the "glue" between potentially highly complex and computationally expensive external subprograms. Differentiability of the resulting programs turns out to…
We overview the ensmallen numerical optimization library, which provides a flexible C++ framework for mathematical optimization of user-supplied objective functions. Many types of objective functions are supported, including general,…
Computer algebra systems play an important role in science as they facilitate the development of new theoretical models. The resulting symbolic equations are often implemented in a compiled programming language in order to provide fast and…
Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…
We demonstrate the use of computer algebra for facilitating the derivation of thin film reduced-order models. We focus on the weighted residual integral boundary layer (WRIBL) method, which has proven to be a very effective technique for…
To model deformation of anatomical shapes, non-linear statistics are required to take into account the non-linear structure of the data space. Computer implementations of non-linear statistics and differential geometry algorithms often lead…
This study extends the use of symbolic computation in Matrix Structural Analysis (MSA) to plane (2D) trusses, building on previous work that focused on continuous beams. An open-source MATLAB program, hosted on GitHub, was developed to…
$ $Deriving a robot's equation of motion typically requires placing multiple coordinate frames, commonly using the Denavit-Hartenberg convention to express the kinematic and dynamic relationships between segments. This paper presents an…
In this paper we describe the implementation of our C++ resistive magnetohydrodynamics solver. The framework developed facilitates the separation of the code implementing the specific numerical method and the physical model, on the one…
The aim of this work is to define and implement an extended C++ language to support the SIMD programming paradigm. The C++ programming language has been extended to express all the potentiality of an abstract SIMD machine consisting of a…
We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…
In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. However, it can be expensive, with worst case complexity doubly exponential in the…
IGUANA is a generic interactive visualisation framework based on a C++ component model. It provides powerful user interface and visualisation primitives in a way that is not tied to any particular physics experiment or detector design. The…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
We discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory of differential equations, geometric singularities can be…
We propose topology-aware feature partitioning into $k$ disjoint partitions for given scene features as a method for object-centric representation learning. To this end, we propose to use minimum $s$-$t$ graph cuts as a partitioning method…
The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…
This paper presents a generalised symbolic algorithm for solving systems of linear algebraic equations with multi-diagonal coefficient matrices. The algorithm is given in a pseudocode. A theorem which gives the condition for correctness of…