| Developer | Waldek Hebisch + independent group of people |
|---|---|
| Stable release | 1.3.11 / 1 July 2024 |
| Implementation language | SPAD, Aldor, Boot, Common Lisp |
| OS | Cross-platform |
| License | Modified BSD License |
| Filename extensions | .spad, .input, .as |
| Website | fricas |
FriCAS is a general purpose computer algebra system with a strong focus on mathematical research and development of new algorithms. It comprises an interpreter, a compiler and a still-growing library [1] of more than 1,000 domains and categories.
FriCAS provides a strongly typed high-level programming language called SPAD and a similar interactive language that uses type-inferencing for convenience. Aldor was intentionally developed being the next generation compiler for the Axiom CAS and its forks. FriCAS (optionally) allows running Aldor programs. Both languages share a similar syntax and a sophisticated (dependent) type system. [2] [3] [4]
FriCAS is comprehensively documented and available as source code and as a binary distribution for the most common platforms. Compiling the sources requires besides other prerequisites a Common Lisp environment (whereby many of the major implementations are supported and freely available as open source).
FriCAS runs on many POSIX platforms such as Linux, macOS, Unix, BSD as well as under Cygwin and Microsoft Windows (WSL).
Two computer algebra systems named Scratchpad were developed by IBM. The first one was started in 1965 by James Griesmer [5] at the request of Ralph Gomory, and written in Fortran. [6] The development of this software was stopped before any public release. The second Scratchpad, originally named Scratchpad II, was developed from 1977 on, at Thomas J. Watson Research Center, under the direction of Richard Dimick Jenks. [7]
The design is principally due to Richard D. Jenks (IBM Research), James H. Davenport (University of Bath), Barry M. Trager (IBM Research), David Y.Y. Yun (Southern Methodist University) and Victor S. Miller (IBM Research). Early consultants on the project were David Barton (University of California, Berkeley) and James W. Thatcher (IBM Research). Implementation included Robert Sutor (IBM Research), Scott C. Morrison (University of California, Berkeley), Christine J. Sundaresan (IBM Research), Timothy Daly (IBM Research), Patrizia Gianni (University of Pisa), Albrecht Fortenbacher (Universitaet Karlsruhe), Stephen M. Watt (IBM Research and University of Waterloo), Josh Cohen (Yale University), Michael Rothstein (Kent State University), Manuel Bronstein (IBM Research), Michael Monagan (Simon Fraser University), Jonathan Steinbach (IBM Research), William Burge (IBM Research), Jim Wen (IBM Research), William Sit (City College of New York), and Clifton Williamson (IBM Research) [8]
Scratchpad II was renamed Axiom when IBM decided, circa 1990, to make it a commercial product. A few years later, it was sold to NAG. In 2001, it was withdrawn from the market and re-released to Tim Daly under the Modified BSD License. In 2007, Axiom was forked as FriCAS by Waldek Hebisch following encouragement from Tim Daly [9] to resolve disagreements about project goals. [10]
FriCAS has a largely complete implementation of the Risch–Bronstein–Trager algorithm. [11]
Another useful feature is stream:
)set stream calculate 5 exp_series := series(exp x, x=0)
Type: UnivariatePuiseuxSeries(Expression(Integer),x,0)
So any coefficient may be retrieved, for instance :
coefficient(exp_series,40)
Type: Expression(Integer)
The exponential function is a mathematical function denoted by or . Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the operation of taking powers of a number, but various modern definitions allow it to be rigorously extended to all real arguments , including irrational numbers. Its ubiquitous occurrence in pure and applied mathematics led mathematician Walter Rudin to consider the exponential function to be "the most important function in mathematics".
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.
Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language. It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and others. A toolbox, MapleSim, adds functionality for multidomain physical modeling and code generation.
Maxima is a powerful software package for performing computer algebra calculations in mathematics and the physical sciences. It is written in Common Lisp and runs on all POSIX platforms such as macOS, Unix, BSD, and Linux, as well as under Microsoft Windows and Android. It is free software released under the terms of the GNU General Public License (GPL).
GNU TeXmacs is a scientific word processor and typesetting component of the GNU Project. It originated as a variant of GNU Emacs with TeX functionalities, though it shares no code with those programs, while using TeX fonts. It is written and maintained by Joris van der Hoeven and a group of developers. The program produces structured documents with a WYSIWYG user interface. New document styles can be created by the user. The editor provides high-quality typesetting algorithms and TeX and other fonts for publishing professional looking documents.
In symbolic computation, the Risch algorithm is a method of indefinite integration used in some computer algebra systems to find antiderivatives. It is named after the American mathematician Robert Henry Risch, a specialist in computer algebra who developed it in 1968.
In mathematics, an involution, involutory function, or self-inverse function is a function f that is its own inverse,
Axiom is a free, general-purpose computer algebra system. It consists of an interpreter environment, a compiler and a library, which defines a strongly typed hierarchy.
Aldor is a programming language. It is the successor of A# as the extension language of the Axiom computer algebra system.
In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e. to find a formula for a differentiable function F(x) such that
A♯ is an object-oriented functional programming language distributed as a separable component of Version 2 of the Axiom computer algebra system. A# types and functions are first-class values and can be used freely together with an extensive library of data structures and other mathematical abstractions. A key design guideline for A# was suitability of compiling to portable and efficient machine code. It is distributed as free and open-source software under a BSD-like license.
SageMath is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, group theory, differentiable manifolds, numerical analysis, number theory, calculus and statistics.
The scale space representation of a signal obtained by Gaussian smoothing satisfies a number of special properties, scale-space axioms, which make it into a special form of multi-scale representation. There are, however, also other types of "multi-scale approaches" in the areas of computer vision, image processing and signal processing, in particular the notion of wavelets. The purpose of this article is to describe a few of these approaches:
In applied mathematics, a transcendental equation is an equation over the real numbers that is not algebraic, that is, if at least one of its sides describes a transcendental function. Examples include:
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes exact computation with expressions containing variables that have no given value and are manipulated as symbols.
Stephen M. Watt, a computer scientist and mathematician, is past Dean of the Faculty of Mathematics and Professor in the David R. Cheriton School of Computer Science at the University of Waterloo, Ontario, Canada.
IBM Quantum Platform is an online platform allowing public and premium access to cloud-based quantum computing services provided by IBM. This includes access to a set of IBM's prototype quantum processors, a set of tutorials on quantum computation, and access to an interactive textbook. As of February 2021, there are over 20 devices on the service, six of which are freely available for the public. This service can be used to run algorithms and experiments, and explore tutorials and simulations around what might be possible with quantum computing.
Patrizia M. Gianni is an Italian mathematician specializing in computer algebra. She is known for her early research on Gröbner bases including her discovery of the FGLM algorithm for changing monomial orderings in Gröbner bases, and for her development of the components of the Axiom computer algebra system concerning polynomials and rational functions.
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