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In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations ...
The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. Because it is often taught in mathematics education at the level of primary school or elementary school , this algorithm is sometimes called the grammar school method.
Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13. The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.
to implement multiplication as a sequence of table look ups for the log g (a) and g y functions and an integer addition operation. This exploits the property that every finite field contains generators. In the Rijndael field example, the polynomial x + 1 (or {03}) is one such generator.
The group {1, −1} above and the cyclic group of order 3 under ordinary multiplication are both examples of abelian groups, and inspection of the symmetry of their Cayley tables verifies this. In contrast, the smallest non-abelian group, the dihedral group of order 6, does not have a symmetric Cayley table.
Multiplication table of quaternion group as a subgroup of SL(2,C). The entries are represented by sectors corresponding to their arguments: 1 (green), i (blue), −1 (red), − i (yellow). The two-dimensional irreducible complex representation described above gives the quaternion group Q 8 as a subgroup of the general linear group GL ( 2 ...