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Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
the roots of this irreducible polynomial can be calculated as [5] 1 ± 2 1 / 6 , 1 ± − 1 ± 3 i 2 1 / 3 . {\displaystyle 1\pm 2^{1/6},1\pm {\frac {\sqrt {-1\pm {\sqrt {3}}i}}{2^{1/3}}}.} Even in the case of quartic polynomials , where there is an explicit formula for the roots, solving using the decomposition often gives a simpler form.
The TI-108 is a simple four-function calculator which uses single-step execution.. The immediate execution mode of operation (also known as single-step, algebraic entry system (AES) [7] or chain calculation mode) is commonly employed on most general-purpose calculators.
In arithmetic and algebra, the eighth power of a number n is the result of multiplying eight instances of n together. So: n 8 = n × n × n × n × n × n × n × n.. Eighth powers are also formed by multiplying a number by its seventh power, or the fourth power of a number by itself.
Unrooted binary trees with n + 5 / 2 labeled leaves. Each such tree may be formed from a tree with one fewer leaf, by subdividing one of the n tree edges and making the new vertex be the parent of a new leaf. Rooted binary trees with n + 3 / 2 labeled leaves. This case is similar to the unrooted case, but the number of edges ...
Instead of operating on multiples of 10, they are operated on 32-bit integers. Instead of higher bits being multiplied by ten, they are multiplied by 0x100000000 . This is usually done by either shifting to the left by 32 or putting the value into a specific register that represents the higher 32 bits.
In this case, the carrier density (in this context, also called the free electron density) can be estimated by: [5] n = N A Z ρ m m a {\displaystyle n={\frac {N_{\text{A}}Z\rho _{m}}{m_{a}}}} Where N A {\displaystyle N_{\text{A}}} is the Avogadro constant , Z is the number of valence electrons , ρ m {\displaystyle \rho _{m}} is the density of ...
Therefore, 49 = 7 2 and 15750 = 2 × 3 2 × 5 3 × 7 are both 7-smooth, while 11 and 702 = 2 × 3 3 × 13 are not 7-smooth. The term seems to have been coined by Leonard Adleman . [ 3 ] Smooth numbers are especially important in cryptography , which relies on factorization of integers. 2-smooth numbers are simply the powers of 2 , while 5 ...