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Devised by Niklaus Wirth in the late 1960s and early 1970s, Pascal is a programming language.Originally produced by Borland Software Corporation, Embarcadero Delphi is composed of an IDE, set of standard libraries, and a Pascal-based language commonly called either Object Pascal, Delphi Pascal, or simply 'Delphi' (Embarcadero's current documentation refers to it as 'the Delphi language (Object ...
Each Pascal's m-simplex is a semi-infinite object, which consists of an infinite series of its components. Let ∧ {\displaystyle \wedge } m n denote its n th component, itself a finite ( m − 1) - simplex with the edge length n , with a notational equivalent n m − 1 {\displaystyle \vartriangle _{n}^{m-1}} .
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, [1] India, [2] China, Germany, and Italy.
Pascal-P5, created outside the Zürich group, accepts the full Pascal language and includes ISO 7185 compatibility. Pascal-P6 is a follow on to Pascal-P5 that along with other features, aims to be a compiler for specific CPUs, including AMD64. UCSD Pascal branched off Pascal-P2, where Kenneth Bowles used it to create the interpretive UCSD p-System.
Object Pascal is an extension of the Pascal language that was developed at Apple Computer by a team led by Larry Tesler in consultation with Niklaus Wirth, the inventor of Pascal. [2] It is descended from an earlier object-oriented version of Pascal named Clascal , which was available on the Lisa computer.
Pascal's pyramid's first five layers. Each face (orange grid) is Pascal's triangle. Arrows show derivation of two example terms. In mathematics, Pascal's pyramid is a three-dimensional arrangement of the trinomial numbers, which are the coefficients of the trinomial expansion and the trinomial distribution. [1]
In matrix theory and combinatorics, a Pascal matrix is a matrix (possibly infinite) containing the binomial coefficients as its elements. It is thus an encoding of Pascal's triangle in matrix form. There are three natural ways to achieve this: as a lower-triangular matrix , an upper-triangular matrix , or a symmetric matrix .
Animation of generator using depth-first search A different animation of a generator using depth-first search. This algorithm, also known as the "recursive backtracker" algorithm, is a randomized version of the depth-first search algorithm.