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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 ...
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 .
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.
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}} .
Singmaster's conjecture is a conjecture in combinatorial number theory, named after the British mathematician David Singmaster who proposed it in 1971. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times).
Pascal and C were published c. 1970 –1972. Computer processors provide hardware support for procedural programming through a stack register and instructions for calling procedures and returning from them. Hardware support for other types of programming is possible, like Lisp machines or Java processors, but no attempt was commercially successful.
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.
Structured text, abbreviated as ST or STX, is one of the five languages supported by the IEC 61131-3 standard, designed for programmable logic controllers (PLCs). [1] [2] It is a high level language that is block structured and syntactically resembles Pascal, on which it is based. [3]