Rewriting in mathematics, computer science and logic covers a wide range of non-deterministic methods of replacing subterms of a formula with other terms. This is a powerful general method for dealing with equation. A rewrite system is a set of equations over a given set of terms called rules that characterize a system of computation. Mathematics is the study of quantity, structure, space and change. ... Wikibooks Wikiversity has more about this subject: School of Computer Science Open Directory Project: Computer Science Collection of Computer Science Bibliographies Belief that title science in computer science is inappropriate Categories: Computer science | Academic disciplines ... Logic (from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy amongst philosophers (see below). ... In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables. ... In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables. ... Computation can be defined as finding a solution to a problem from given inputs by means of an algorithm. ...

The non-deterministic nature of a rewriting system indicates that it is not an algorithm for changing one term to another, but a set of possible substitutions. Flowcharts are often used to represent algorithms. ...

Rewrite systems provide a convenient method of automating theorem proving. If we begin with a set of equational hypotheses, then these may be used to formulate a set of rewrite rules. An example from school algebra goes under the heading collect like terms in an equation. There will usually be several ways to proceed, in collecting up and simplifying an equation Automated theorem proving (currently the most important subfield of automated reasoning) is the proving of mathematical theorems by a computer program. ... Algebra is a branch of mathematics which may be roughly characterized as a generalization and extension of arithmetic, in which symbols are employed to denote operations, and letters to represent number and quantity; it also refers to a particular kind of abstract algebra structure, the algebra over a field. ...

P(x) = Q(x)

in which P and Q are polynomials. After some application of the conventional rules of algebra we may end with an equation In mathematics, polynomial functions, or polynomials, are an important class of simple and smooth functions. ...

R(x) = 0.

This is something like a normal form, though we may well have different signs (at least) for R found by different routes. If we insist that R is monic there is actually a normal form (as is usually tacitly assumed) in which R(x) is written in terms of decreasing powers of x. The feature of this rewriting system that has some general application is that some unique result or normal form is obtainable; and naturally any serious computer algebra system will have to perform this simplification automatically. This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... In mathematics, a monic can refer to monic morphism – a special kind of morphism in category theory, monic polynomial – a polynomial whose leading coefficient is one. ... A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. ...

See also

• Confluence
• String rewriting
• Term rewriting
• Graph rewriting