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A grid is drawn up, and each cell is split diagonally. The two multiplicands of the product to be calculated are written along the top and right side of the lattice, respectively, with one digit per column across the top for the first multiplicand (the number written left to right), and one digit per row down the right side for the second multiplicand (the number written top-down).
Napier's bones is a manually operated calculating device created by John Napier of Merchiston, Scotland for the calculation of products and quotients of numbers. The method was based on lattice multiplication, and also called rabdology, a word invented by Napier.
It is an extension of Napier's Bones, using two sets of rods to achieve multi-digit multiplication without the need to write down intermediate results, although some mental addition is still needed to calculate the result. The rods for the multiplicand are similar to Napier's Bones, with repetitions of the values.
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When done by hand, this may also be reframed as grid method multiplication or lattice multiplication. In software, this may be called "shift and add" due to bitshifts and addition being the only two operations needed. In 1960, Anatoly Karatsuba discovered Karatsuba multiplication, unleashing a flood of research into fast multiplication ...
The carry step of the multiplication can be performed at the final stage of the calculation (in bold), returning the final product of 45 × 256 = 11520. This is a variant of Lattice multiplication. The modern method of multiplication based on the Hindu–Arabic numeral system was first described by Brahmagupta. Brahmagupta gave rules for ...
There are 123 pages of text with 32 lines of print to a page. The pages are unnumbered, untrimmed and have wide margins. Some of the margins contain written notes. The size of the book is 14.5 cm by 20.6 cm. The book included information taken from the 1202 Liber Abaci, such as lattice multiplication.
A unital quantale is an idempotent semiring under join and multiplication. A unital quantale in which the identity is the top element of the underlying lattice is said to be strictly two-sided (or simply integral). A commutative quantale is a quantale whose multiplication is commutative.