# Category/Mathematics

- Aletheia
- In short, Aletheia is software for getting science published and into the hands of everyone, for free. It's a decentralised and distributed database used as a publishing platform for scientific research. So, Aletheia is software. But software without people is nothing. To comprehensively answer the question what is Aletheia, Aletheia is software surrounded by a community of people who want to change the world through open access to scientific knowledge. For a more in depth explanation, Aletheia is an Ethereum Blockchain application utilising IPFS for decentralised storage that anyone can upload documents to, download documents from, that also handles the academic peer review process. The application runs on individual PCs, all forming part of the IPFS database. This gives us an open source platform that cannot be bought out by the large publishers (and any derivitive works must also be open source) that should also be hard to take down due to the database being spread across the globe in multiple legal jurisdictions. Aletheia is designed to be a resilient platform run transparently by the community, not some black box corporation or editorial board, meaning all users can see the decisions Aletheia is making and have a stake in that decision making process if they so desire. By this nature, Aletheia is decentralised, it has no key person risk. Should the core group who invented Aletheia dissapear Aletheia won't cease to exist, it will continue to be run by the community. The community moderates content through various mechanisms (peer review, reputation scores etc.,) to ensure quality of content.

- Apophenia
- 'Apophenia' is a statistical library for C. It provides functions on the same level as those of the typical stats package (OLS, probit, singular value decomposition, &c.) but doesn't tie the user to an ad hoc language or environment. It uses the GNU Scientific Library for number crunching and SQLite for data management, so the library itself focuses on model estimation and quickly processing data.

- Aris
- A sequential proof program, designed to assist anyone interested in solving logical proofs. Aris supports both propositional and predicate logic, as well as Boolean algebra and arithmetical logic in the form of abstract sequences. It uses a predefined set of both inference and equivalence rules, however gives the user options to use older proofs as lemmas, including Isabelle's Isar proofs.

- Asymptote
- 'Asymptote' is a script-based vector graphics language for technical drawing, inspired by MetaPost but with an improved C++-like syntax. It provides for figures the same high-quality level of typesetting that LaTeX does for scientific text. It is a programming language, not just a graphics program, so it can use the best features of both scripts and GUIs. High-level graphics commands are implemented in the language itself, so they can be tailored to specific applications. Labels and equations are typeset with LaTeX for high-quality PostScript output.

- Autoclass
- AutoClass solves the problem of automatic discovery of classes in data (sometimes called clustering or unsupervised learning), as distinct from the generation of class descriptions from labeled examples (called supervised learning). It aims to discover the 'natural' classes in the data. AutoClass is applicable to observations of things that can be described by a set of attributes, without referring to other things. The data values corresponding to each attribute are limited to be either numbers or the elements of a fixed set of symbols. With numeric data, a measurement error must be provided.

- Bc
- 'Bc' is an arbitrary precision numeric processing language. Its syntax is similar to C, but differs in many substantial areas. It supports interactive execution of statements. 'Bc' is a utility included in the POSIX P1003.2/D11 draft standard. This version does not use the historical method of having bc be a compiler for the dc calculator (the POSIX document doesn't specify how bc must be implemented). This version has a single executable that both compiles the language and runs the resulting 'byte code.' The byte code is not the dc language.

- Besssugo
- besssugo is a free computational tool specifically designed to aid a cognizant expert—i.e. you, whether an engineer, scientist, technician, geek, etc—to build videos showing the result of a certain scientific calculation or whatever data can be computed or storied in a digital computer. Technically speaking, it is a plugin for the computational tool wasora, which provides means to parse and understand a high-level plain-text input file containing algebraic expressions, data for function interpolation, differential equations and output instructions amongst other facilities. Therefore, any mathematical computation which can be done by wasora—i.e. solving systems of differential-algebraic equations, multidimensional interpolation of scattered data, numerical integration and differentiation, etc.—can be combined with the facilities that besssugo provides to create visual representations in the form of animations.

- C-graph
- GNU C-Graph is a tool for visualizing the mathematical operation of convolution underlying natural phenomena susceptible to analysis in terms of engineering signals and systems theory. "C-Graph" is an abbreviation for "Convolution Graph". The package is derived from the BSc. Honours dissertation in Electrical Engineering "Interactive Computer Package Demonstrating: Sampling Convolution and the FFT", Adrienne Gaye Thompson, University of Aberdeen (1983). The package computes the linear convolution of two signals in the time domain then compares their circular convolution by demonstrating the convolution theorem. Each signal is modelled by a register of discrete values simulating samples of a signal, and the discrete Fourier transform (DFT) computed by means of the Fast Fourier Transform (FFT). GNU C-Graph is interactive, prompting the user to enter character or numerical values from the keyboard, dispensing with the learning curve for writing code. The software will be useful to students of signals and systems theory. C-Graph is written in contemporary Fortran. You can find pre-GNU development versions at: Code Art Now. Adrienne Gaye Thompson is the sole author of GNU C-Graph and looks forward to sharing further development with the Free software community.

- Cl-ana
- cl-ana is a library of modular utilities for reasonably high performance data analysis & visualization using Common Lisp. (Reasonably means I have to be able to use it for analyzing particle accelerator data). The library is made of various sublibraries and is designed in a very bottom-up way so that if you don't care about some feature you don't have to load it.
The functionality support so far are
- Tabular data analysis: Read-write of large datasets stored in HDF5 files are supported, along with ntuple datasets, CSVs, and in-memory data tables. Users can add their own table types by defining 4 methods and extending the table CLOS type.

- Histograms: Binned data analysis is supported with both contiguous and sparse histogram types; functional interface is provided via map (which allows reduce/fold) and filter.

- Plotting: Uses gnuplot for plotting dataset samples, plain-old lisp functions, histograms, strings-as-formulae, and anything else the user wishes to add via methods on a couple of generics.

- Fitting: Uses GSL for non-linear least squares fitting. Uses plain-old lisp functions as the fit functions and can fit against dataset samples, histograms, and whatever the user adds.

- Generic mathematics: CL doesn't provide extendable math functions, so cl-ana provides these as well as a convenient mechanism (a single function) for using these functions instead of the non-extendable versions. Already included are error propogation and quantities (values with units, e.g. 5 meters) as well as a GNU Octave-style handling of sequences (e.g. (+ (1 2) (3 4)) --> (4 6)).

- Coq
- A proof done with Coq is mechanically checked by the machine. In particular, Coq allows:
- to define functions or predicates,
- to state mathematical theorems and software specifications,
- to develop interactively formal proofs of these theorems,
- to check these proofs by a relatively small certification "kernel".

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