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A snippet of JavaScript code with keywords highlighted in different colors. The syntax of JavaScript is the set of rules that define a correctly structured JavaScript program. The examples below make use of the log function of the console object present in most browsers for standard text output.
The Shakespeare Programming Language (SPL) is an esoteric programming language designed by Jon Åslund and Karl Wiberg. [1] Like the Chef programming language, it is designed to make programs appear to be something other than programs — in this case, Shakespearean plays.
Legendre's three-square theorem states which numbers can be expressed as the sum of three squares; Jacobi's four-square theorem gives the number of ways that a number can be represented as the sum of four squares. For the number of representations of a positive integer as a sum of squares of k integers, see Sum of squares function.
The number of ways to write a natural number as sum of two squares is given by r 2 (n).It is given explicitly by = (() ())where d 1 (n) is the number of divisors of n which are congruent to 1 modulo 4 and d 3 (n) is the number of divisors of n which are congruent to 3 modulo 4.
For example, the function PT tests whether each row of ⍵ is a Pythagorean triplet (by testing whether the sum of squares equals twice the square of the maximum). PT ← { ( + / ⍵ * 2 ) = 2 × ( ⌈ / ⍵ ) * 2 } PT 3 4 5 1 x 4 5 3 3 11 6 5 13 12 17 16 8 11 12 4 17 15 8 PT x 1 0 1 0 0 1
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The explained sum of squares (ESS) is the sum of the squares of the deviations of the predicted values from the mean value of a response variable, in a standard regression model — for example, y i = a + b 1 x 1i + b 2 x 2i + ... + ε i, where y i is the i th observation of the response variable, x ji is the i th observation of the j th ...
In this example, the Gauss–Newton algorithm will be used to fit a model to some data by minimizing the sum of squares of errors between the data and model's predictions. In a biology experiment studying the relation between substrate concentration [S] and reaction rate in an enzyme-mediated reaction, the data in the following table were obtained.