In computing, a compiler is a computer program that translates computer code written in one programming language into another language. The name "compiler" is primarily used for programs that translate source code from a high-level programming language to a low-level programming language to create an executable program.
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.
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, formal language theory, the lambda calculus and type theory.
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 differentiable function F(x) such that
FORMAC, the FORmula MAnipulation Compiler, was the first computer algebra system to have significant use. It was developed by Jean E. Sammet and her team, as an extension of FORTRAN IV. The compiler was implemented as a preprocessor taking the FORMAC program and converting it to a FORTRAN IV program which was in turn compiled without further user intervention.
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.
John K. S. McKay was a British-Canadian mathematician and academic who worked at Concordia University, known for his discovery of monstrous moonshine, his joint construction of some sporadic simple groups, for the McKay conjecture in representation theory, and for the McKay correspondence relating certain finite groups to Lie groups.
The term "information algebra" refers to mathematical techniques of information processing. Classical information theory goes back to Claude Shannon. It is a theory of information transmission, looking at communication and storage. However, it has not been considered so far that information comes from different sources and that it is therefore usually combined. It has furthermore been neglected in classical information theory that one wants to extract those parts out of a piece of information that are relevant to specific questions.
Symbolic Manipulation Program, usually called SMP, was a computer algebra system designed by Chris A. Cole and Stephen Wolfram at Caltech circa 1979. It was initially developed in the Caltech physics department with contributions from Geoffrey C. Fox, Jeffrey M. Greif, Eric D. Mjolsness, Larry J. Romans, Timothy Shaw, and Anthony E. Terrano.
Speedcoding, Speedcode or SpeedCo was the first high-level programming language created for an IBM computer. The language was developed by John W. Backus in 1953 for the IBM 701 to support computation with floating point numbers.
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 of more than 1,000 domains and categories.
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.
AMBIT is a historical programming language that was introduced by Carlos Christensen of Massachusetts Computer Associates in 1964 for symbolic computation. The language was influenced by ALGOL 60 and is an early example of a pattern matching language for manipulation of strings . The acronym AMBIT stands for "Algebraic Manipulation by Identity Translation", but has also claimed "Acronym May Be Ignored Totally". AMBIT had dialects for manipulation of lists (AMBIT-L) and graphs (AMBIT-G) Both pioneered with data structure diagrams and visual programming as data and patterns were used to be represented by directed-graph diagrams. AMBIT/L was implemented for a PDP-10 computer and used to implement the interactive algebraic manipulation system IAM.
Cambridge Algebra System (CAMAL) is a computer algebra system written in Cambridge University by David Barton, Steve Bourne, and John Fitch. It was initially used for computations in celestial mechanics and general relativity. The foundation code was written in Titan computer assembler. In 1973, when Titan was replaced with an IBM370/85, it was rewritten in ALGOL 68C and then BCPL where it could run on IBM mainframes and assorted microcomputers.
Algebrator is a computer algebra system (CAS), which was developed in the late 1990s by Neven Jurkovic of Softmath, San Antonio, Texas. This is a CAS specifically geared towards algebra education. Beside the computation results, it shows step by step the solution process and context sensitive explanations.
ISSAC, the International Symposium on Symbolic and Algebraic Computation, is an academic conference in the field of computer algebra. ISSAC has been organized annually since 1988, typically in July. The conference is regularly sponsored by the Association for Computing Machinery special interest group SIGSAM, and the proceedings since 1989 have been published by ACM. ISSAC is considered as being one of the most influential conferences for the publication of scientific computing research.
FGLM is one of the main algorithms in computer algebra, named after its designers, Faugère, Gianni, Lazard and Mora. They introduced their algorithm in 1993. The input of the algorithm is a Gröbner basis of a zero-dimensional ideal in the ring of polynomials over a field with respect to a monomial order and a second monomial order. As its output, it returns a Gröbner basis of the ideal with respect to the second ordering. The algorithm is a fundamental tool in computer algebra and has been implemented in most of the computer algebra systems. The complexity of FGLM is O(nD3), where n is the number of variables of the polynomials and D is the degree of the ideal. There are several generalization and various applications for FGLM.
Deepak Kapur is a Distinguished Professor in the Department of Computer Science at the University of New Mexico.
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.
