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If the exponent n is zero then the answer is 1. If the exponent is negative then we can reuse the previous formula by rewriting the value using a positive exponent. That is, = (). Together, these may be implemented directly as the following recursive algorithm:
In the floating-point case, a variable exponent would represent the power of ten to which the mantissa of the number is multiplied. Languages that support a rational data type usually allow the construction of such a value from two integers, instead of a base-2 floating-point number, due to the loss of exactness the latter would cause.
Assuming a channel coding setup as follows: the channel can transmit any of = messages, by transmitting the corresponding codeword (which is of length n). Each component in the codebook is drawn i.i.d. according to some probability distribution with probability mass function Q .
Inputs An integer b (base), integer e (exponent), and a positive integer m (modulus) Outputs The modular exponent c where c = b e mod m. Initialise c = 1 and loop variable e′ = 0; While e′ < e do Increment e′ by 1; Calculate c = (b ⋅ c) mod m; Output c; Note that at the end of every iteration through the loop, the equation c ≡ b e ...
In number theory, a frugal number is a natural number in a given number base that has more digits than the number of digits in its prime factorization in the given number base (including exponents). [1] For example, in base 10, 125 = 5 3, 128 = 2 7, 243 = 3 5, and 256 = 2 8 are frugal numbers (sequence A046759 in the OEIS).
This can be generalized to rational exponents of the form / by applying the power rule for integer exponents using the chain rule, as shown in the next step. Let y = x r = x p / q {\displaystyle y=x^{r}=x^{p/q}} , where p ∈ Z , q ∈ N + , {\displaystyle p\in \mathbb {Z} ,q\in \mathbb {N} ^{+},} so that r ∈ Q {\displaystyle r\in \mathbb {Q} } .
A snippet of Java code with keywords highlighted in bold blue font. The syntax of Java is the set of rules defining how a Java program is written and interpreted. The syntax is mostly derived from C and C++. Unlike C++, Java has no global functions or variables, but has data members which are also regarded as global variables.
map function, found in many functional programming languages, is one example of a higher-order function. It takes as arguments a function f and a collection of elements, and as the result, returns a new collection with f applied to each element from the collection.