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Montgomery modular multiplication relies on a special representation of numbers called Montgomery form. The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab ...
A template for displaying common fractions of the form int+num/den nicely. It supports 0–3 anonymous parameters with positional meaning. Template parameters Parameter Description Type Status leftmost part 1 Denominator if only parameter supplied. Numerator if 2 parameters supplied. Integer if 3 parameters supplied. If no parameter is specified the template will render a fraction slash only ...
Order of operations. In mathematicsand computer programming, the order of operationsis a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations. The rank of an operation is called its precedence, and an ...
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator ( b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
Fixed-point arithmetic. In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of dollar). More generally, the term may refer to ...
A fractional ideal of is an - submodule of such that there exists a non-zero such that . The element can be thought of as clearing out the denominators in , hence the name fractional ideal. The principal fractional ideals are those -submodules of generated by a single nonzero element of . A fractional ideal is contained in if and only if it is ...
e. In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded. The construction of the field of fractions is modeled on the relationship between the integral domain of integers and the field of rational numbers. Intuitively, it consists of ratios between integral domain elements.
A FRACTRAN program is an ordered list of positive fractions together with an initial positive integer input n. The program is run by updating the integer n as follows: for the first fraction f in the list for which nf is an integer, replace n by nf; repeat this rule until no fraction in the list produces an integer when multiplied by n, then halt.
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