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Hecke.jl
Computational algebraic number theory
Hecke is a software package for algebraic number theory maintained by Claus Fieker, Tommy Hofmann and Carlo Sircana. It is written in julia and is based on the computer algebra packages Nemo and AbstractAlgebra. Hecke is part of the OSCAR project and the development is supported by the Deutsche Forschungsgemeinschaft DFG within the Collaborative Research Center TRR 195. -
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SpecialFunctions.jl
Special mathematical functions in Julia
Special mathematical functions in Julia, include Bessel, Hankel, Airy, error, Dawson, exponential (or sine and cosine) integrals, eta, zeta, digamma, inverse digamma, trigamma, and polygamma functions. Most of these functions were formerly part of Base in early versions of Julia. -
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BasicBSpline.jl
Basic (mathematical) operations for B-spline functions
Basic (mathematical) operations for B-spline functions and related things with Julia. -
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Integrals.jl
A common interface for quadrature and numerical integration
Integrals.jl is an instantiation of the SciML common IntegralProblem interface for the common numerical integration packages of Julia, including both those based upon quadrature as well as Monte-Carlo approaches. By using Integrals.jl, you get a single predictable interface where many of the arguments are standardized throughout the various integrator libraries. This can be useful for benchmarking or for library implementations since libraries that internally use a quadrature can easily... -
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Oscar.jl
A comprehensive open source computer algebra system for computations
Welcome to the OSCAR project, a visionary new computer algebra system that combines the capabilities of four cornerstone systems: GAP, Polymake, Antic and Singular. OSCAR requires Julia 1.6 or newer. In principle it can be installed and used like any other Julia package; doing so will take a couple of minutes. A comprehensive open source computer algebra system for computations in algebra, geometry, and number theory. -
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Symbolics.jl
Symbolic programming for the next generation of numerical software
Symbolics.jl is a high-performance symbolic computation library for the Julia programming language. It enables users to define, manipulate, and analyze mathematical expressions symbolically, with strong support for symbolic differentiation, simplification, equation solving, and code generation. Designed for use in scientific computing, machine learning, and engineering, Symbolics.jl integrates smoothly with Julia’s numerical ecosystem, allowing symbolic expressions to be compiled and... -
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SymbolicNumericIntegration.jl
SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals
SymbolicNumericIntegration.jl is a hybrid symbolic/numerical integration package that works on the Julia Symbolics expressions. -
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SuiteSparseGraphBLAS.jl
Sparse, General Linear Algebra for Graphs
A fast, general sparse linear algebra and graph computation package, based on SuiteSparse:GraphBLAS. -
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WaterLily.jl
Fast and simple fluid simulator in Julia
WaterLily.jl is a fluid dynamics simulation package in Julia that uses lattice Boltzmann methods (LBM) to simulate incompressible flows and fluid-structure interactions in two dimensions. It is designed for easy use and rapid prototyping of physical systems involving particles, obstacles, and hydrodynamic forces. The package is well-suited for educational purposes, computational physics research, and lightweight fluid simulations. -
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ControlSystems.jl
A Control Systems Toolbox for Julia
ControlSystems.jl is a Julia toolbox for control systems design and analysis, offering models in transfer-function and state-space representations, enabling construction of complex systems, simulation in time and frequency domains, and performance/stability evaluation. This toolbox works similar to that of other major computer-aided control systems design (CACSD) toolboxes. Systems can be created in either a transfer function or a state space representation. These systems can then be... -
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Dagger.jl
A framework for out-of-core and parallel execution
Dagger.jl is a framework for out-of-core and parallel computing in Julia that allows users to construct and execute dynamic task graphs. It is designed for large-scale, distributed, and memory-efficient computations. Dagger supports lazy evaluation and scheduling across multiple threads or machines, enabling high-performance workflows for data processing, scientific computing, and machine learning. -
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LazySets.jl
Scalable Symbolic-Numeric Set Computations
LazySets.jl is a Julia package for calculus with convex sets. The aim is to provide a scalable library for solving complex set-based problems, such as those encountered in differential inclusions or reachability analysis techniques in the domain of formal verification. Typically, one is confronted with a set-based recurrence with a given initial set and/or input sets, and for visualization purposes, the final result has to be obtained through an adequate projection onto low dimensions. This... -
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FourierFlows.jl
Tools for building fast, hackable, pseudospectral equation solvers
This software provides tools for partial differential equations on periodic domains using Fourier-based pseudospectral methods. A central intent of the software's design is also to provide a framework for writing new, fast solvers for new physical problems. The code is written in Julia. -
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Yao
Extensible, Efficient Quantum Algorithm Design for Humans
An intermediate representation to construct and manipulate your quantum circuit and let you make own abstractions on the quantum circuit in native Julia. Yao supports both forward-mode (faithful gradient) and reverse-mode automatic differentiation with its builtin engine optimized specifically for quantum circuits. Top performance for quantum circuit simulations. Its CUDA backend and batched quantum register support can make typical quantum circuits even faster. Yao is designed to be... -
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KrylovKit.jl
Krylov methods for linear problems, eigenvalues, and singular values
A Julia package collecting a number of Krylov-based algorithms for linear problems, singular value and eigenvalue problems and the application of functions of linear maps or operators to vectors. -
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OrdinaryDiffEq.jl
High performance ordinary differential equation (ODE)
This is a suite for numerically solving differential equations written in Julia and available for use in Julia, Python, and R. The purpose of this package is to supply efficient Julia implementations of solvers for various differential equations. The well-optimized DifferentialEquations solvers benchmark as some of the fastest implementations, using classic algorithms and ones from recent research that routinely outperform the “standard” C/Fortran methods, and include algorithms optimized... -
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ITensors.jl
A Julia library for efficient tensor computations and tensor network
ITensors.jl is a high-performance Julia library for tensor network calculations, primarily used in quantum physics and computational science. It enables efficient manipulation of large, structured tensors with named indices and provides an intuitive interface for implementing algorithms like DMRG (Density Matrix Renormalization Group), TEBD (Time-Evolving Block Decimation), and more. ITensors.jl leverages Julia’s multiple dispatch and performance features to simplify the development of... -
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LabPlot
Data Visualization and Analysis
LabPlot is a FREE, open source and cross-platform Data Visualization and Analysis software accessible to everyone. -
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Kinetic.jl
Universal modeling and simulation of fluid mechanics upon ML
Kinetic is a computational fluid dynamics toolbox written in Julia. It aims to furnish efficient modeling and simulation methodologies for fluid dynamics, augmented by the power of machine learning. Based on differentiable programming, mechanical and neural network models are fused and solved in a unified framework. Simultaneous 1-3 dimensional numerical simulations can be performed on CPUs and GPUs. -
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MLPACK is a C++ machine learning library with emphasis on scalability, speed, and ease-of-use. Its aim is to make machine learning possible for novice users by means of a simple, consistent API, while simultaneously exploiting C++ language features to provide maximum performance and flexibility for expert users. * More info + downloads: https://mlpack.org * Git repo: https://github.com/mlpack/mlpack
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Bridge.jl
A statistical toolbox for diffusion processes
Statistics and stochastic calculus for Markov processes in continuous time, include univariate and multivariate stochastic processes such as stochastic differential equations or diffusions (SDE's) or Levy processes. -
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SLM-Topo
Topology optimisation designed for laser based additive manufacturing
In the selective laser melting process (SLM), components are built up layer by layer by incremental melting of metal powder with a laser beam. This process leads to locally inhomogeneous material properties of the manufactured components. By integrating these specific material properties of the SLM-process into a topology optimization, product developers can be supported in the design process by simulation. For this purpose, a topology optimization method is being developed which takes into...
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