What is a residue number theory?

The word residue is used in a number of different contexts in mathematics. Two of the most common uses are the complex residue of a pole, and the remainder of a congruence. The number in the congruence is called the residue of (mod ). The residue of large numbers can be computed quickly using congruences.

What is meant by residue number system?

A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. Other applications of multi-modular arithmetic include polynomial greatest common divisor, Gröbner basis computation and cryptography.

What is residue arithmetic?

Carry independent arithmetic (called residue arithmetic) is possible within some limits. This residue arithmetic representation is a way of approaching a famous bound on the speed at which addition and multiplication can be performed.

What is RNS algorithm?

Abstract. A new and efficient number theoretic algorithm for evaluating signs of determinants is proposed. The algorithm uses computations over small finite rings. It is devoted to a variety of computational geometry problems, where the necessity of evaluating signs of determinants of small matrices often arises.

What is the definition of a residue numeral system?

Definition. A residue numeral system is defined by a set of k integers called the moduli, which are generally supposed to be pairwise coprime (that is, any two of them have a greatest common divisor equal to one). referred to as the moduli. Residue number systems have been defined for non-coprime moduli,…

Why is the residue number system called multi modular arithmetic?

Residue number system. This representation is allowed by the Chinese remainder theorem, which asserts that, if N is the product of the moduli, there is, in an interval of length N, exactly one integer having any given set of modular values. The arithmetic of a residue numeral system is also called multi-modular arithmetic .

What happens to a residue system when M is odd?

In this case, if M is odd, each set of residues represents exactly one integer of absolute value at most M . For adding, subtracting and multiplying numbers represented in a residue number system, it suffices to perform the same modular operation on each pair of residues. More precisely, if

Is the residue number system a pairwise coprime moduli?

called the moduli, which are generally supposed to be pairwise coprime (that is, any two of them have a greatest common divisor equal to one). referred to as the moduli. Residue number systems have been defined for non-coprime moduli, but are not commonly used because of worse properties.