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Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Unsourced material may be challenged and removed. Find sources: "Computational complexity of mathematical operations" – news · newspapers · books · scholar · JSTOR ( April 2015 ) ( Learn how and when to remove this ...
Adding a fixed complex number to all complex numbers defines a translation in the complex plane, and multiplying by a fixed complex number is a similarity centered at the origin (dilating by the absolute value, and rotating by the argument).
Pascaline, 1642 – Blaise Pascal's arithmetic machine primarily intended as an adding machine which could add and subtract two numbers directly, as well as multiply and divide by repetition. Stepped Reckoner, 1672 – Gottfried Wilhelm Leibniz's mechanical calculator that could add, subtract, multiply, and divide.
In mathematics, more specifically in abstract algebra, the Frobenius theorem, proved by Ferdinand Georg Frobenius in 1877, characterizes the finite-dimensional associative division algebras over the real numbers. According to the theorem, every such algebra is isomorphic to one of the following: R (the real numbers) C (the complex numbers) H ...
The basic principle of Karatsuba's algorithm is divide-and-conquer, using a formula that allows one to compute the product of two large numbers and using three multiplications of smaller numbers, each with about half as many digits as or , plus some additions and digit shifts.
Unlike conventional modular reduction, which focuses on making the number smaller than N, Montgomery reduction focuses on making the number more divisible by R. It does this by adding a small multiple of N which is sophisticatedly chosen to cancel the residue modulo R. Dividing the result by R yields a much smaller number.
Addition and multiplication of split-complex numbers are then given by matrix addition and multiplication. The squared modulus of z is given by the determinant of the corresponding matrix. In fact there are many representations of the split-complex plane in the four-dimensional ring of 2x2 real matrices.
To subtract one number from another, the method of nine's complement was used. The only two differences between an addition and a subtraction are the position of the display bar (direct versus complement) and the way the first number is entered (direct versus complement). For a 10-digit wheel (N), the fixed outside wheel is numbered from 0 to 9 ...