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Macsyma Inc
Macsyma (; "Project MAC's SYmbolic MAnipulator") is one of the oldest general-purpose computer algebra systems still in wide use. It was originally developed from 1968 to 1982 at MIT's Project MAC. In 1982, Macsyma was licensed to Symbolics and became a commercial product. In 1992, Symbolics Macsyma was spun off to Macsyma, Inc., which continued to develop Macsyma until 1999. That version is still available for Microsoft's Windows XP operating system. The 1982 version of MIT Macsyma remained available to academics and US government agencies, and it is distributed by the US Department of Energy (DOE). That version, DOE Macsyma, was maintained by Bill Schelter. Under the name of Maxima, it was released under the GPL in 1999, and remains under active maintenance. Development The project was initiated in July, 1968 by Carl Engelman, William A. Martin (front end, expression display, polynomial arithmetic) and Joel Moses (simplifier, indefinite integration: heuristic/Risch). Martin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algebra System
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. Computer algebra systems may be divided into two classes: specialized and general-purpose. The specialized ones are devoted to a specific part of mathematics, such as number theory, group theory, or teaching of elementary mathematics. General-purpose computer algebra systems aim to be useful to a user working in any scientific field that requires manipulation of mathematical expressions. To be useful, a general-purpose computer algebra system must include various features such as: *a user interface ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pattern Matching
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 (if any) 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 (i.e., search and replace). Sequence patterns (e.g., a text string) are often described using regular expressions and matched using techniques such as backtracking. Tree patterns are used in some programming languages as a general tool to process data based on its structure, e.g. C#, F#, Haskell, ML, Python, Ruby, Rust, Scala, Swift and the symbolic mathematics language Mathematica have special syntax for expressing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number a+bi, is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Differential Equation
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast with the term partial differential equation which may be with respect to ''more than'' one independent variable. Differential equations A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^+b(x)=0, where , ..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of the unknown function of the variable . Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formula Editor
A formula editor is a computer program that is used to typeset mathematical formulas and mathematical expressions. Formula editors typically serve two purposes: * They allow word processing and publication of technical content either for print publication, or to generate raster images for web pages or screen presentations. * They provide a means for users to specify input to computational systems that is easier to read and check than plain text input and output from computational systems that is easy to understand or ready for publication. Content for formula editors can be provided manually using a markup language,e.g. TeX or MathML, via a point-and-click GUI, or as computer generated results from symbolic computations such as Mathematica. Typical features include the ability to nest fractions, radicals, superscripts, subscripts, overscripts and underscripts together with special characters such as mathematical symbols, arrows and scalable parentheses. Some systems are ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LispM
Lisp machines are general-purpose computers designed to efficiently run Lisp as their main software and programming language, usually via hardware support. They are an example of a high-level language computer architecture, and in a sense, they were the first commercial single-user workstations. Despite being modest in number (perhaps 7,000 units total as of 1988) Lisp machines commercially pioneered many now-commonplace technologies, including effective garbage collection, laser printing, windowing systems, computer mice, high-resolution bit-mapped raster graphics, computer graphic rendering, and networking innovations such as Chaosnet. Several firms built and sold Lisp machines in the 1980s: Symbolics (3600, 3640, XL1200, MacIvory, and other models), Lisp Machines Incorporated (LMI Lambda), Texas Instruments ( Explorer, MicroExplorer), and Xerox (Interlisp-D workstations). The operating systems were written in Lisp Machine Lisp, Interlisp (Xerox), and later partly in Common Lis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multics
Multics ("Multiplexed Information and Computing Service") is an influential early time-sharing operating system based on the concept of a single-level memory.Dennis M. Ritchie, "The Evolution of the Unix Time-sharing System", Communications of the ACM, Vol. 17, 1984, pp. 365-375. Nathan Gregory writes that Multics "has influenced all modern operating systems since, from microcomputers to mainframes." Initial planning and development for Multics started in 1964, in Cambridge, Massachusetts. Originally it was a cooperative project led by MIT ( Project MAC with Fernando Corbató) along with General Electric and Bell Labs. It was developed on the GE 645 computer, which was specially designed for it; the first one was delivered to MIT in January 1967. GE offered their earlier 635 systems with an early timesharing system known as "Mark I" and intended to offer the 645 with Multics as a larger successor. Bell withdrew from the project in 1969 as it became clear it would not deliver ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-commutative
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of the property that says something like or , the property can also be used in more advanced settings. The name is needed because there are operations, such as division (mathematics), division and subtraction, that do not have it (for example, ); such operations are ''not'' commutative, and so are referred to as ''noncommutative operations''. The idea that simple operations, such as the multiplication (mathematics), multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. A similar property exists for binary relations; a binary relation is said to be symmetric relation, symmetric if the relation appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Summation
In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined. Summations of infinite sequences are called series. They involve the concept of limit, and are not considered in this article. The summation of an explicit sequence is denoted as a succession of additions. For example, summation of is denoted , and results in 9, that is, . Because addition is associative and commutative, there is no need of parentheses, and the result is the same irrespective of the order of the summands. Summation of a sequence of only one element results in this element itself. Summation of an empty sequence (a sequence with no elements), by convention, results in 0. Very often, the elem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bill Gosper
Ralph William Gosper Jr. (born April 26, 1943), known as Bill Gosper, is an American mathematician and programmer. Along with Richard Greenblatt, he may be considered to have founded the hacker community, and he holds a place of pride in the Lisp community. The Gosper curve and the Gosper's algorithm are named after him. Becoming a hacker In high school, Gosper was interested in model rockets until one of his friends was injured in a rocketry accident and contracted a fatal brain infection.. Gosper enrolled in MIT in 1961, and he received his bachelor's degree in mathematics from MIT in 1965 despite becoming disaffected with the mathematics department because of their anti-computer attitude. In his second year at MIT, Gosper took a programming course from John McCarthy and became affiliated with the MIT AI Lab. His contributions to computational mathematics include HAKMEM and the MIT Maclisp system. He made major contributions to Macsyma, Project MAC's computer algebra syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Genesereth
Michael Genesereth (born 1948) is an American logician and computer scientist, who is most known for his work on computational logic and applications of that work in enterprise management, computational law, and general game playing. Genesereth is professor in the Computer Science Department at Stanford University and a professor by courtesy in the Stanford Law School. His 1987 textbook on Logical Foundations of Artificial Intelligence remains one of the key references on Symbolic artificial intelligence. He is the author of the influential Game Description Language (GDL) and Knowledge Interchange Format (KIF), the latter of which led to the ISO Common Logic standard. Education Genesereth received a B.S. in Physics (1972) from Massachusetts Institute of Technology, and both an M.S. (1974) and Ph.D. (1978) in Applied Mathematics from Harvard University. As a graduate student, he worked on the Macsyma computer algebra system and wrote his dissertation on an automated advisor for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating-point Arithmetic
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: 12.345 = \underbrace_\text \times \underbrace_\text\!\!\!\!\!\!^ In practice, most floating-point systems use base two, though base ten ( decimal floating point) is also common. The term ''floating point'' refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
