منابع مشابه
Modular Arithmetic and Elementary Algebra
where z is an integer then gcd(a, b) = gcd(b, c). Indeed any divisor of a and b will divide c, and conversely any divisor of b and c will divide a. We can compute c by taking the remainder after dividing a by b, i.e. c is a mod b. (We will discuss the mod operation in greater details in the next section, but at this point, we only need the definition of c as the remainder of dividing a by b.) B...
متن کاملBasic Linear Algebra Operations in SLI Arithmetic
Symmetric level-index arithmetic was introduced to overcome recognized limitations of oating-point systems, most notably overrow and un-derrow. The original recursive algorithms for arithmetic operations could be parallelized to some extent, particularly when applied to extended sums or products, and a SIMD software implementation of some of these algorithms is described. The main purpose of th...
متن کاملSuccess and Failure in Arithmetic and Algebra
Arithmetic and algebra are central parts of the National Curriculum throughout the British Isles. In both of these there is a known and disconcerting level of failure, in algebra even more than in arithmetic. Why does this failure occur? Or, to look at the more positive side of the coin, why are some fortunate souls able to do these parts of mathematics almost without effort. By the conservatio...
متن کاملTropical Arithmetic & Algebra of Tropical Matrices
The purpose of this paper is to study the tropical algebra – the algebra over the tropical semi-ring. We start by introducing a third approach to arithmetic over the max-plus semi-ring which generalizes the two other concepts in use. Regarding this new arithmetic, matters of tropical matrices are discussed and the properties of these matrices are studied. These are the preceding phases toward t...
متن کاملTropical Arithmetic and Tropical Matrix Algebra
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial, notions of regularity and invertibility arise naturally for matrices over this semiring; we show that a tropical matrix is invertible if and only if it is r...
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ژورنال
عنوان ژورنال: Missouri Journal of Mathematical Sciences
سال: 1989
ISSN: 0899-6180
DOI: 10.35834/1989/0101022