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In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix. Some variants are commonly referred to as square-and-multiply algorithms or binary exponentiation.
A snippet of Python code with keywords highlighted in bold yellow font. The syntax of the Python programming language is the set of rules that defines how a Python program will be written and interpreted (by both the runtime system and by human readers). The Python language has many similarities to Perl, C, and Java. However, there are some ...
A metacharacter is a character that has a special meaning to a computer program, such as a shell interpreter or a regular expression (regex) engine.. In POSIX extended regular expressions, there are 14 metacharacters that must be escaped — preceded by a backslash (\) — in order to drop their special meaning and be treated literally inside an expression: opening and closing square brackets ...
Square (algebra), the result of multiplying something by itself; Quadrature (mathematics), the process of determining the area of a plane figure
The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 ...
As a running example, we consider a 10×10 magic square, where we have divided the square into four quarters. The quarter A contains a magic square of numbers from 1 to 25, B a magic square of numbers from 26 to 50, C a magic square of numbers from 51 to 75, and D a magic square of numbers from 76 to 100.
In 1980, Everett L. Johnson proposed using the quarter square method in a digital multiplier. [11] To form the product of two 8-bit integers, for example, the digital device forms the sum and difference, looks both quantities up in a table of squares, takes the difference of the results, and divides by four by shifting two bits to the right.
Marching Square Matlab algorithm – An easy to understand open-source marching square algorithm. implementation in Java; Marching Squares code in Java. Given a 2D data set and thresholds, returns GeneralPath[] for easy plotting. Meandering Triangles explanation and sample Python implementation.