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Lattice multiplication, also known as the Italian method, Chinese method, Chinese lattice, gelosia multiplication, [1] sieve multiplication, shabakh, diagonally or Venetian squares, is a method of multiplication that uses a lattice to multiply two multi-digit numbers.
Lattice, or sieve, multiplication is algorithmically equivalent to long multiplication. ... This formula can in some cases be used, to make multiplication tasks ...
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
Although the original problem asks for integer lattice points in a circle, there is no reason not to consider other shapes, for example conics; indeed Dirichlet's divisor problem is the equivalent problem where the circle is replaced by the rectangular hyperbola. [3]
Lattice-theoretic information about the lattice of subgroups can sometimes be used to infer information about the original group, an idea that goes back to the work of Øystein Ore (1937, 1938). For instance, as Ore proved , a group is locally cyclic if and only if its lattice of subgroups is distributive .
then the formulas for addition, multiplication, and multiplicative inverse are ... The set A is a ring (in fact a domain) and a lattice and is called the ring of ...
On the left, the lattice diagram of the field obtained from Q by adjoining the positive square roots of 2 and 3, together with its subfields; on the right, the corresponding lattice diagram of their Galois groups. In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory.
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
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