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Starting with Rado (1942), "independence functions" or "-functions" have been studied as one of many equivalent ways of axiomatizing matroids.An independence function maps a set of matroid elements to the number if the set is independent or if it is dependent; that is, it is the indicator function of the family of independent sets, essentially the same thing as an independence oracle.
Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...
Digits to the right of it are multiplied by 10 raised to a negative power or exponent. The first position to the right of the separator indicates 10 −1 (0.1), the second position 10 −2 (0.01), and so on for each successive position. As an example, the number 2674 in a base-10 numeral system is: (2 × 10 3) + (6 × 10 2) + (7 × 10 1) + (4 ...
In elementary arithmetic, a carry is a digit that is transferred from one column of digits to another column of more significant digits. It is part of the standard algorithm to add numbers together by starting with the rightmost digits and working to the left. For example, when 6 and 7 are added to make 13, the "3" is written to the same column ...
An oracle machine can perform all of the usual operations of a Turing machine, and can also query the oracle to obtain a solution to any instance of the computational problem for that oracle. For example, if the problem is a decision problem for a set A of natural numbers, the oracle machine supplies the oracle with a natural number, and the ...
This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a ...
Some programming languages such as Lisp, Python, Perl, Haskell, Ruby and Raku use, or have an option to use, arbitrary-precision numbers for all integer arithmetic. Although this reduces performance, it eliminates the possibility of incorrect results (or exceptions) due to simple overflow.
A weak separation oracle for K is an oracle that, given a vector y in Q n and a rational number d>0, returns one of the following:: [1]: 51 Assert that y is d -near K ; Find a vector a in Q n , normalized such that its maximum element is 1, such that a ⋅ y + d ≥ a ⋅ x {\displaystyle a\cdot y+d\geq a\cdot x} for all x that are d -deep in K .