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All the above multiplication algorithms can also be expanded to multiply polynomials. Alternatively the Kronecker substitution technique may be used to convert the problem of multiplying polynomials into a single binary multiplication. [31] Long multiplication methods can be generalised to allow the multiplication of algebraic formulae:
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.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
Advanced use of the rods can extract square roots. Napier's bones are not the same as logarithms, with which Napier's name is also associated, but are based on dissected multiplication tables. The complete device usually includes a base board with a rim; the user places Napier's rods and the rim to conduct multiplication or division.
The digital root of the result of this calculation is then compared with that of the result of the original calculation. If no mistake has been made in the calculations, these two digital roots must be the same. Examples in which casting-out-nines has been used to check addition, subtraction, multiplication, and division are given below.
The first Mental Calculations World Championship took place in 1998. This event repeats every year and now occurs online. It consists of a range of different tasks such as addition, subtraction, multiplication, division, irrational and exact square roots, cube roots and deeper roots, factorizations, fractions, and calendar dates. [2]
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