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The factorial function is a common feature in scientific calculators. [73] It is also included in scientific programming libraries such as the Python mathematical functions module [74] and the Boost C++ library. [75]
In programming languages where functions are first-class objects (such as Lua, Python, or Perl [6]), automatic memoization can be implemented by replacing (at run-time) a function with its calculated value once a value has been calculated for a given set of parameters. The function that does this value-for-function-object replacement can ...
Lisp is a family of programming languages loosely inspired by mathematical notation and Alonzo Church's lambda calculus. Some dialects, such as Common Lisp, are primarily imperative but support functional programming. Others, such as Scheme, are designed for functional programming. In Scheme, the factorial function can be defined as follows:
In Python, a generator can be thought of as an iterator that contains a frozen stack frame. Whenever next() is called on the iterator, Python resumes the frozen frame, which executes normally until the next yield statement is reached. The generator's frame is then frozen again, and the yielded value is returned to the caller.
The translations shown above show that CPS is a global transformation. The direct-style factorial takes, as might be expected, a single argument; the CPS factorial& takes two: the argument and a continuation. Any function calling a CPS-ed function must either provide a new continuation or pass its own; any calls from a CPS-ed function to a non ...
Upon iteration, one may find that there are sets that shrink and converge towards a single point. In such a case, the point that is converged to is known as an attractive fixed point . Conversely, iteration may give the appearance of points diverging away from a single point; this would be the case for an unstable fixed point .
A fractional factorial design contains a carefully chosen subset of these combinations. The criterion for choosing the subsets is discussed in detail in the fractional factorial designs article. Formalized by Frank Yates , a Yates analysis exploits the special structure of these designs to generate least squares estimates for factor effects for ...
In computer programming, an iterator is an object that progressively provides access to each item of a collection, in order. [1] [2] [3]A collection may provide multiple iterators via its interface that provide items in different orders, such as forwards and backwards.