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The Extended Pascal standard extends Pascal to support many things C supports, which the original standard Pascal did not, in a type safer manner. For example, schema types support (besides other uses) variable-length arrays while keeping the type-safety of mandatory carrying the array dimension with the array, allowing automatic run-time ...
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.
The first five layers of Pascal's 3-simplex (Pascal's pyramid). Each face (orange grid) is Pascal's 2-simplex (Pascal's triangle). Arrows show derivation of two example terms. In mathematics, Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem.
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]
Pascal is an imperative and procedural programming language, designed by Niklaus Wirth as a small, efficient language intended to encourage good programming practices using structured programming and data structuring.
Pic Micro Pascal a.k.a. PMP is a free Pascal cross compiler for PIC microcontrollers. It is intended to work with the Microchip Technology MPLAB suite installed; it has its own IDE (Scintilla-based) and it is a highly optimized compiler. It is intended to target 8-bit processors only: PIC10, PIC12, PIC16, PIC16 enhanced, PIC18.
In mathematics, Pascal's rule (or Pascal's formula) is a combinatorial identity about binomial coefficients.It states that for positive natural numbers n and k, + = (), where () is a binomial coefficient; one interpretation of the coefficient of the x k term in the expansion of (1 + x) n.