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Addition-chain exponentiation

Index Addition-chain exponentiation

In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by positive integer powers that requires a minimal number of multiplications. [1]

15 relations: Addition chain, Addition-subtraction chain, Algorithm, Computer science, Donald Knuth, Dynamic programming, Elliptic curve, Exponentiation, Exponentiation by squaring, Integer, Mathematics, Negative number, NP-completeness, On-Line Encyclopedia of Integer Sequences, Optimal substructure.

Addition chain

In mathematics, an addition chain for computing a positive integer n can be given by a sequence of natural numbers v and a sequence of index pairs w such that each term in v is the sum of two previous terms, the indices of those terms being specified by w: Often only v is given since it is easy to extract w from v, but sometimes w is not uniquely reconstructible.

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Addition-subtraction chain

An addition-subtraction chain, a generalization of addition chains to include subtraction, is a sequence a0, a1, a2, a3,...

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Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

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Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.

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Dynamic programming

Dynamic programming is both a mathematical optimization method and a computer programming method.

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Elliptic curve

In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.

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Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

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Exponentiation by squaring

In mathematics and computer programming, exponentiating by squaring is a general method for fast computation of large positive integer powers of a number, or more generally of an element of a semigroup, like a polynomial or a square matrix.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Negative number

In mathematics, a negative number is a real number that is less than zero.

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NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

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On-Line Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.

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Optimal substructure

In computer science, a problem is said to have optimal substructure if an optimal solution can be constructed from optimal solutions of its subproblems.

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Addition chain exponentiation.

References

[1] https://en.wikipedia.org/wiki/Addition-chain_exponentiation

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