A computer algebra system (CAS) 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.
In computer science, pattern matching is the act of checking a given sequence of tokens for the presence of the constituents of some pattern. In contrast to pattern recognition, the match usually has to be exact: "either it will or will not be a match." The patterns generally have the form of either sequences or tree structures. Uses of pattern matching include outputting the locations of a pattern within a token sequence, to output some component of the matched pattern, and to substitute the matching pattern with some other token sequence.
In computer science, model checking or property checking refers to the following problem: Given a model of a system, exhaustively and automatically check whether this model meets a given specification. Typically, one has hardware or software systems in mind, whereas the specification contains safety requirements such as the absence of deadlocks and similar critical states that can cause the system to crash. Model checking is a technique for automatically verifying correctness properties of finite-state systems.
A modeling language is any artificial language that can be used to express information or knowledge or systems in a structure that is defined by a consistent set of rules. The rules are used for interpretation of the meaning of components in the structure.
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, mathematically (mostly) correct type hierarchy.
In computing, a visual programming language (VPL) is any programming language that lets users create programs by manipulating program elements graphically rather than by specifying them textually. A VPL allows programming with visual expressions, spatial arrangements of text and graphic symbols, used either as elements of syntax or secondary notation. For example, many VPLs are based on the idea of "boxes and arrows", where boxes or other screen objects are treated as entities, connected by arrows, lines or arcs which represent relations.
A flowchart is a type of diagram that represents an algorithm, workflow or process. The flowchart shows the steps as boxes of various kinds, and their order by connecting the boxes with arrows. This diagrammatic representation illustrates a solution model to a given problem. Flowcharts are used in analyzing, designing, documenting or managing a process or program in various fields.
In computer science, a binary decision diagram (BDD) or branching program is a data structure that is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed representation of sets or relations. Unlike other compressed representations, operations are performed directly on the compressed representation, i.e. without decompression. Other data structures used to represent a Boolean function include negation normal form (NNF), and propositional directed acyclic graph (PDAG).
In computer science, symbolic execution (also symbolic evaluation) is a means of analyzing a program to determine what inputs cause each part of a program to execute. An interpreter follows the program, assuming symbolic values for inputs rather than obtaining actual inputs as normal execution of the program would, a case of abstract interpretation. It thus arrives at expressions in terms of those symbols for expressions and variables in the program, and constraints in terms of those symbols for the possible outcomes of each conditional branch.
Yacas is a general-purpose computer algebra system. The name is an acronym for Yet Another Computer Algebra System.
FORMAC, acronym of FORmula MAnipulation Compiler, was an early computer algebra system based on FORTRAN. It was developed by Jean E. Sammet.
Software visualization or software visualisation refers to the visualization of information of and related to software systems—either the architecture of its source code or metrics of their runtime behavior- and their development process by means of static, interactive or animated 2-D or 3-D visual representations of their structure, execution, behavior, and evolution.
ALTRAN was a FORTRAN extension providing rational algebra, developed by W.S. Brown, at Bell Labs around 1968.
Symbolic Manipulation Program, usually called SMP, was a computer algebra system designed by Chris A. Cole and Stephen Wolfram at Caltech circa 1979 and initially developed in the Caltech physics department under Wolfram's leadership with contributions from Geoffrey C. Fox, Jeffrey M. Greif, Eric D. Mjolsness, Larry J. Romans, Timothy Shaw, and Anthony E. Terrano. It was first sold commercially in 1981 by the Computer Mathematics Corporation of Los Angeles which later became part of Inference Corporation; Inference Corp. further developed the program and marketed it commercially from 1983 to 1988. SMP was essentially Version Zero of the more ambitious Mathematica system.
A structure editor, also structured editor or projectional editor, is any document editor that is cognizant of the document’s underlying structure. Structure editors can be used to edit hierarchical or marked up text, computer programs, diagrams, chemical formulas, and any other type of content with clear and well-defined structure. In contrast, a text editor is any document editor used for editing plain text files.
Incremental computing, also known as incremental computation, is a software feature which, whenever a piece of data changes, attempts to save time by only recomputing those outputs which depend on the changed data. When incremental computing is successful, it can be significantly faster than computing new outputs naively. For example, a spreadsheet software package might use incremental computation in its recalculation feature, to update only those cells containing formulas which depend on the changed cells.
In computational mathematics, 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.
Alan F. Blackwell is a New Zealand-British cognition scientist and professor at the Computer Laboratory, University of Cambridge, known for his work on diagrammatic representation, on data and language modelling, investment modelling, and end-user software engineering.
