Search results
Results from the WOW.Com Content Network
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)!
For example, addition and division, the factorial and exponential function, and the function which returns the nth prime are all primitive recursive. [1] In fact, for showing that a computable function is primitive recursive, it suffices to show that its time complexity is bounded above by a primitive recursive function of the input size. [ 2 ]
The iteration form of the Eiffel loop can also be used as a boolean expression when the keyword loop is replaced by either all (effecting universal quantification) or some (effecting existential quantification). This iteration is a boolean expression which is true if all items in my_list have counts greater than three:
Hindu scholars have been using factorial formulas since at least 1150, when Bhāskara II mentioned factorials in his work Līlāvatī, in connection with a problem of how many ways Vishnu could hold his four characteristic objects (a conch shell, discus, mace, and lotus flower) in his four hands, and a similar problem for a ten-handed god. [4]
Iterating over a container is done using this form of loop: for e in c while w do # loop body od; The in c clause specifies the container, which may be a list, set, sum, product, unevaluated function, array, or object implementing an iterator. A for-loop may be terminated by od, end, or end do.
Using this formula to compute the values of all binomial coefficients generates an infinite array called Pascal's triangle. The same values can also be computed directly by a different formula that is not a recurrence, but uses factorials, multiplication and division, not just additions: =!!
Because the notation f n may refer to both iteration (composition) of the function f or exponentiation of the function f (the latter is commonly used in trigonometry), some mathematicians [citation needed] choose to use ∘ to denote the compositional meaning, writing f ∘n (x) for the n-th iterate of the function f(x), as in, for example, f ...
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.