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An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
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 ...
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).
The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory.One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value.
Free Pascal Compiler (FPC) is an open-source Object Pascal compiler that supports many Pascal dialects, including Turbo Pascal 7, Delphi, and others. Currently, FPC can generate code for IA-32 , x86-64 , PowerPC , SPARC , and ARM processors, and for several operating systems, including Microsoft Windows , Linux , FreeBSD , Classic Mac OS , and ...
We can see this either as a sum of the number of coefficients of an (n − 1) th component ((m − 1)-simplex) of Pascal's m-simplex with the number of coefficients of an nth component ((m − 2)-simplex) of Pascal's (m − 1)-simplex, or by a number of all possible partitions of an nth power among m exponents.
A Pascal matrix can actually be constructed by taking the matrix exponential of a special subdiagonal or superdiagonal matrix. The example below constructs a 7 × 7 Pascal matrix, but the method works for any desired n × n Pascal matrices. The dots in the following matrices represent zero elements.
Turbo Pascal – "TURBO.EXE" up to version 7, and Turbo Pascal for Windows ("TPW") and Turbo Pascal for Macintosh. Pure Pascal and HiSPeed Pascal 2 Pascal language Environment for the Atari ST range of computers. Borland Pascal 7 – A professional version of Turbo Pascal line which targeted both DOS and Windows.