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  2. Comparison of code generation tools - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_code...

    Several code generation DSLs (attribute grammars, tree patterns, source-to-source rewrites) Active DSLs represented as abstract syntax trees DSL instance Well-formed output language code fragments Any programming language (proven for C, C++, Java, C#, PHP, COBOL) gSOAP: C / C++ WSDL specifications

  3. Falling and rising factorials - Wikipedia

    en.wikipedia.org/wiki/Falling_and_rising_factorials

    These symbols are collectively called factorial powers. [2] The Pochhammer symbol, introduced by Leo August Pochhammer, is the notation (), where n is a non-negative integer. It may represent either the rising or the falling

  4. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    Many other notable functions and number sequences are closely related to the factorials, including the binomial coefficients, double factorials, falling factorials, primorials, and subfactorials. Implementations of the factorial function are commonly used as an example of different computer programming styles, and are included in scientific ...

  5. Double factorial - Wikipedia

    en.wikipedia.org/wiki/Double_factorial

    These are counted by the double factorial 15 = (6 − 1)‼. In mathematics, the double factorial of a number n, denoted by n‼, is the product of all the positive integers up to n that have the same parity (odd or even) as n. [1] That is,

  6. Factorial number system - Wikipedia

    en.wikipedia.org/wiki/Factorial_number_system

    The factorial number system is a mixed radix numeral system: the i-th digit from the right has base i, which means that the digit must be strictly less than i, and that (taking into account the bases of the less significant digits) its value is to be multiplied by (i − 1)!

  7. TomSym - Wikipedia

    en.wikipedia.org/wiki/TomSym

    TomSym is complete modeling environment in Matlab with support for most built-in mathematical operators in Matlab. It is a combined modeling, compilation and interface to the TOMLAB solvers. The matrix derivative of a matrix function is a fourth rank tensor - that is, a matrix each of whose entries is a matrix. Rather than using four ...

  8. Factorization of polynomials over finite fields - Wikipedia

    en.wikipedia.org/wiki/Factorization_of...

    It follows that, to compute in a finite field of non prime order, one needs to generate an irreducible polynomial. For this, the common method is to take a polynomial at random and test it for irreducibility. For sake of efficiency of the multiplication in the field, it is usual to search for polynomials of the shape x n + ax + b. [citation ...

  9. Multiplicative partitions of factorials - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_partitions...

    Multiplicative partitions of factorials are expressions of values of the factorial function as products of powers of prime numbers. They have been studied by Paul Erdős and others. [1] [2] [3] The factorial of a positive integer is a product of decreasing integer factors, which can in turn be factored into prime numbers.