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Use of a user-defined function sq(x) in Microsoft Excel. The named variables x & y are identified in the Name Manager. The function sq is introduced using the Visual Basic editor supplied with Excel. Subroutine in Excel calculates the square of named column variable x read from the spreadsheet, and writes it into the named column variable y.
Formulas in the B column multiply values from the A column using relative references, and the formula in B4 uses the SUM() function to find the sum of values in the B1:B3 range. A formula identifies the calculation needed to place the result in the cell it is contained within. A cell containing a formula, therefore, has two display components ...
This popular sorting algorithm has an average-case performance of O(n log(n)), which contributes to making it a very fast algorithm in practice. But given a worst-case input, its performance degrades to O(n 2). Also, when implemented with the "shortest first" policy, the worst-case space complexity is instead bounded by O(log(n)).
The DFA can be constructed explicitly and then run on the resulting input string one symbol at a time. Constructing the DFA for a regular expression of size m has the time and memory cost of O(2 m), but it can be run on a string of size n in time O(n). Note that the size of the expression is the size after abbreviations, such as numeric ...
An n-bit LUT can encode any n-input Boolean function by storing the truth table of the function in the LUT. This is an efficient way of encoding Boolean logic functions, and LUTs with 4-6 bits of input are in fact the key component of modern field-programmable gate arrays (FPGAs) which provide reconfigurable hardware logic capabilities.
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
A closed formula, also ground formula or sentence, is a formula in which there are no free occurrences of any variable. If A is a formula of a first-order language in which the variables v 1, …, v n have free occurrences, then A preceded by ∀v 1 ⋯ ∀v n is a universal closure of A.
Variable names must be italicized explicitly, and superscripts and subscripts must use an explicit tag or template. Except for short formulas, the source of a formula typically has more markup overhead and can be difficult to read. The common practice of most members of WikiProject mathematics is the following: