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There are several advanced table formatting techniques to improve the display or editing of wikitables in Wikipedia. Most of the tips involve use of standard text-editors. While some special software packages exist, to allow customized editing, they are typically not available when travelling to other computers for wiki-editin
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of ...
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If p is an odd prime and p − 1 = 2 s d with s > 0 and d odd > 0, then for every a coprime to p, either a d ≡ 1 (mod p) or there exists r such that 0 ≤ r < s and a 2 r d ≡ −1 (mod p). This result may be deduced from Fermat's little theorem by the fact that, if p is an odd prime, then the integers modulo p form a finite field , in which ...
This eliminates the need to change representations and to encode new data structures and methods, which is traditionally required when augmenting linear algebra with quaternions. Rotors are universally applicable to any element of the algebra, not just vectors and other quaternions, but also lines, planes, circles, spheres, rays, and so on.
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
The denominator is exactly the volume of the primitive unit cell which is enclosed by the three primitive-vectors , and . In particular, we now know that d x 1 d x 2 d x 3 = a 1 a 2 a 3 a 1 ⋅ ( a 2 × a 3 ) ⋅ d x d y d z . {\displaystyle dx_{1}\,dx_{2}\,dx_{3}={\frac {a_{1}a_{2}a_{3}}{\mathbf {a} _{1}\cdot (\mathbf {a} _{2}\times \mathbf {a ...