SYNO | exponentiation | involution |
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Usage Examples English
- When units occur in exponentiation, such as in square and cubic forms, any multiplier prefix is considered part of the unit, and thus included in the exponentiation.
- All three of the above algebraic groups are used by the GMP-ECM package, which includes efficient implementations of the two-stage procedure, and an implementation of the PRAC group-exponentiation algorithm which is rather more efficient than the standard binary exponentiation approach.
- At the same time, the inverse problem of discrete exponentiation is not difficult (it can be computed efficiently using exponentiation by squaring, for example).
- The idea is based on iterated exponentiation in much the same way that exponentiation is iterated multiplication.
- The definition of exponentiation can be extended to allow any real or complex exponent.
- is provided by addition-chain exponentiation. However, this requires designing a specific algorithm for each exponent, and the computation needed for designing these algorithms are difficult (NP-complete), so exponentiation by squaring is generally preferred for effective computations.
- In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number of multiplications.
- (To carry out these modular exponentiations, one could use a fast exponentiation algorithm like binary or addition-chain exponentiation).
- When units occur in exponentiation, such as in square and cubic forms, any multiples-prefix is considered part of the unit, and thus included in the exponentiation.
- This might be carried out indefinitely to represent [...] as iterated exponentiation of iterated exponentiation for any "a", "n" and "b" (although it clearly becomes rather cumbersome).
- The use of the caret for exponentiation can be traced back to ALGOL 60, [...] which expressed the exponentiation operator as an upward-pointing arrow, intended to evoke the superscript notation common in mathematics.
- For even size cubes [...] (see exponentiation).
- In particular, whether or not the index β is a limit ordinal, [...] is a fixed point not only of base ω exponentiation but also of base δ exponentiation for all ordinals [...].
- Encryption under ElGamal requires two exponentiations; however, these exponentiations are independent of the message and can be computed ahead of time if needed.
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Contains translations by TU Chemnitz and Mr Honey's Business Dictionary (German-English only).
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