Search Results for "algebraic"
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Showing 131 open source projects for "algebraic"
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Algebraic graphs
Algebraic graphs
Alga is a library for algebraic construction and manipulation of graphs in Haskell. See this Haskell Symposium paper and the corresponding talk for the motivation behind the library, the underlying theory and implementation details. We can give semantics to the constructors in terms of the pair (V, E) of graph vertices and edges. Alga can handle graphs comprising millions of vertices and billions of edges in a matter of seconds, which is fast enough for many applications. -
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Sundials.jl
Julia interface to Sundials, including a nonlinear solver
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. -
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HomotopyContinuation.jl
A Julia package for solving systems of polynomials
...Many models in the sciences and engineering are expressed as sets of real solutions to systems of polynomial equations. We can optimize any objective whose gradient is an algebraic function using homotopy methods by computing all critical points of the objective function. An important special case is when the objective function is the euclidean distance to a given point. An example of an non-algebraic objective function whose derivative is algebraic is the Kullback–Leibler divergence. Homotopy continuation methods allow us to study the conformation space of molecules as for example cyclooctane (CH₂)₈. ... -
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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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Flix
The Flix Programming Language
Flix is a statically typed programming language combining functional, imperative, and logic paradigms, with first‑class Datalog constraints and a polymorphic effect system. Designed to run on the JVM, Flix enforces purity tracking at compile time, supports algebraic data types, tail‑call elimination, and allows entire Datalog programs as values. -
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Catlab.jl
A framework for applied category theory in the Julia language
...Catlab provides a programming library and interactive interface for applications of category theory to scientific and engineering fields. It emphasizes monoidal categories due to their wide applicability but can support any categorical structure that is formalizable as a generalized algebraic theory. First and foremost, Catlab provides data structures, algorithms, and serialization for applied category theory. Macros offer a convenient syntax for specifying categorical doctrines and type-safe symbolic manipulation systems. Wiring diagrams (aka string diagrams) are supported through specialized data structures and can be serialized to and from GraphML (an XML-based format) and JSON. -
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DifferentialEquations.jl
Multi-language suite for high-performance solvers of equations
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 which routinely outperform the “standard” C/Fortran methods, and include algorithms optimized... -
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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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IronCalc
Main engine of the IronCalc ecosystem
IronCalc is a new, modern, work-in-progress spreadsheet engine and set of tools to work with spreadsheets in diverse settings. IronCalc is a lightweight, open-source computational engine designed for performing mathematical operations, formula calculations, and data-driven tasks. -
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MathLink.jl
Julia language interface for Mathematica/Wolfram Engine
This package provides access to Mathematica/Wolfram Engine via the MathLink library, now renamed to Wolfram Symbolic Transfer Protocol (WSTP). -
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C++ Library of Abstract Algebra concepts and arithmetic algorithms defined in terms of these concepts, using Instigate Generic Programming Methodology. Based on this library we plan to develop Linear Algebra and Optimization concepts and algorithms.
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CasADi
CasADi is a symbolic framework for numeric optimization
...These expression graphs, encapsulated in Function objects, can be evaluated in a virtual machine or exported to stand-alone C code. Initial value problems in ordinary or differential-algebraic equations (ODE/DAE) can be calculated using explicit or implicit Runge-Kutta methods or interfaces to IDAS/CVODES from the SUNDIALS suite. Derivatives are calculated using sensitivity equations, up to arbitrary order. -
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koka
Koka language compiler and interpreter
Koka is a strongly typed functional-style language with effect types and handlers. The core of Koka consists of a small set of well-studied language features, like first-class functions, a polymorphic type- and effect system, algebraic data types, and effect handlers. Each of these is composable and avoid the addition of “special” extensions by being as general as possible. Koka tracks the (side) effects of every function in its type, where pure and effectful computations are distinguished. The precise effect typing gives Koka rock-solid semantics backed by well-studied category theory, which makes Koka particularly easy to reason about for both humans and compilers. ... -
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Little Book of Linear Algebra
A concise, beginner-friendly introduction to the core ideas of linear
...The material is organized into chapters covering vectors, matrices, linear systems, vector spaces, eigenvalues/eigenvectors, and other central topics, each with worked examples and explanations. There is also a companion “LAB” section for hands-on exploration (e.g. using Python/NumPy) to help cement the connections between algebraic formulas and computational behavior. The exposition aims to sit between a pop-math summary and a heavy textbook: definitions and key theorems are stated cleanly, while proofs are sometimes omitted or sketched to keep the flow digestible. Because of its brevity and clarity, it's especially useful as a first pass for learners who want a solid map of the subject before diving into full textbooks. -
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Peroxide
Rust numeric library with high performance and friendly syntax
...Peroxide uses a 1D data structure to represent matrices, making it straightforward to integrate with BLAS (Basic Linear Algebra Subprograms). This means that Peroxide can guarantee excellent performance for linear algebraic computations by leveraging the optimized routines provided by BLAS. For users familiar with numerical computing libraries like NumPy, MATLAB, or R, Rust's syntax might seem unfamiliar at first. This can make it more challenging to learn and use Rust libraries that heavily rely on Rust's unique features and syntax. -
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ModelingToolkit.jl
Modeling framework for automatically parallelized scientific ML
...It allows for users to give a high-level description of a model for symbolic preprocessing to analyze and enhance the model. Automatic symbolic transformations, such as index reduction of differential-algebraic equations, make it possible to solve equations that are impossible to solve with a purely numeric-based technique. ModelingToolkit.jl is a symbolic-numeric modeling package. Thus it combines some of the features from symbolic computing packages like SymPy or Mathematica with the ideas of equation-based modeling systems like the causal Simulink and the acausal Modelica. -
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Hasktorch
Tensors and neural networks in Haskell
Hasktorch is a powerful Haskell library for tensor computation and neural network modeling, built on top of libtorch (the backend of PyTorch). It brings differentiable programming, automatic differentiation, and efficient tensor operations into Haskell’s strongly typed functional paradigm. This project is in active development, so expect changes to the library API as it evolves. We would like to invite new users to join our Hasktorch discord space for questions and discussions.... -
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PureScript
A strongly-typed language that compiles to JavaScript
...Excellent tooling and editor support with instant rebuilds. An active community with many learning resources. Build real-world applications using functional techniques and expressive types, such as: Algebraic data types and pattern matching. Row polymorphism and extensible records. Higher kinded types and type classes with functional dependencies, as well as higher-rank polymorphism. Precompiled binaries are available for OSX, Linux, and Windows. The Pursuit package database hosts searchable documentation for PureScript packages. The recommended build tool for PureScript is Spago, which can be installed using npm. -
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DeepSeek Math
Pushing the Limits of Mathematical Reasoning in Open Language Models
DeepSeek-Math is DeepSeek’s specialized model (or dataset + evaluation) focusing on mathematical reasoning, symbolic manipulation, proof steps, and advanced quantitative problem solving. The repository is likely to include fine-tuning routines or task datasets (e.g. MATH, GSM8K, ARB), demonstration notebooks, prompt templates, and evaluation results on math benchmarks. The goal is to push DeepSeek’s performance in domains that require rigorous symbolic steps, calculus, linear algebra, number... -
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Scalaz
Principled Functional Programming in Scala
...Its type class–oriented design lets you write generic algorithms over capabilities rather than concrete types, improving reuse and testability. Scalaz also contributes optics, equality/ordering abstractions, and lawful instances with property-based tests to ensure algebraic laws hold. While the Scala ecosystem now includes sibling projects, Scalaz remains a deep toolbox for principled FP in Scala and a reference point for category-theory-inspired design on the JVM. -
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Catalyst.jl
Chemical reaction network and systems biology interface
Catalyst.jl is a symbolic modeling package for analysis and high-performance simulation of chemical reaction networks. Catalyst defines symbolic ReactionSystems, which can be created programmatically or easily specified using Catalyst's domain-specific language (DSL). Leveraging ModelingToolkit and Symbolics.jl, Catalyst enables large-scale simulations through auto-vectorization and parallelism. Symbolic ReactionSystems can be used to generate ModelingToolkit-based models, allowing the easy... -
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REDUCE
A Portable General-Purpose Computer Algebra System
REDUCE is an interactive system for general algebraic computations of interest to mathematicians, scientists and engineers. It can be used interactively for simple calculations but also provides a flexible and expressive user programming language. The development of the REDUCE computer algebra system was started in the 1960s by Anthony C. Hearn. Since then, many scientists from all over the world have contributed to its development. -
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Calcoo is a scientific calculator (with both RPN and algebraic modes) designed to provide maximum usability.
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chessPDFBrowser
Chess application whichs allows working with chess PDF books and PGNs.
Chess application which allows working with PDFs and PGNs. You can work with the chess games of the PDF and edit their tree of variants. Graphical environment. Standard PGN TAGs. PGN comments. Ocr like (Fen string detection from chess board position images). Connection to Uci chess engines (like stockfish). Position analysis, full game analysis. You can now play games against uci engines. pdf2pgn command line command included. Detailed documentation. Multilanguage... -
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Multifario is a C API for computing manifolds. The manifold is represented as an atlas of charts whose domains are balls. Multifario can compute implicitly defined manifolds and invariant manifolds. See also https://multifario.sourceforge.io/ Keywords: Continuation, Bifurcation.
