The branch of mathematics which deals with the properties and relations of numbers using symbols (usually letters of the alphabet) to represent numbers or members of a specified set; the generalization and extension of arithmetic.
Algebra, from M.L., from Ar. al jabr "reunion of broken bones," the first known use in the title of a book by the Persian mathematician and astronomer Abu Ja'far Mohammad ibn Musa al-Khwarizmi (c780-c850), who worked in Baghdad under the patronage of Caliph Al-Mamun. The full title of the tratise was Hisab al-Jabr w'al-Muqabala "Arithmetic of Completion and Balancing." → algorithm.
Jabr, from Ar. al jabr, as above.
Relating to, involving, or according to the laws of algebra.
Fr.: équation algébrique
An equation in the form of P = 0, where P is a → polynomial having a finite number of terms.
Fr.: fonction algébrique
A function expressed in terms of → polynomials and/or roots of polynomials. In other words, any function y = f(x) which satisfies an equation of the form P0(x)yn + P1(x)yn - 1 + ... + Pn(x) = 0, where P0(x), P1(x), ..., Pn(x) are polynomials in x.
adad-e jabri (#)
Fr.: nombre algébrique
A number, → real or → complex, that is a → root of a → non-zero polynomial equation whose → coefficients are all → rational. For example, the root x of the polynomial x2 - 2x + 1 = 0 is an algebraic number, because the polynomial is non-zero and the coefficients are rational numbers. The imaginary number i is algebraic, because it is the solution to x2 + 1 = 0.
Fr.: algèbre associative
An algebra whose multiplication is associative.
jabr-e Booli (#)
Fr.: algèbre de Boole
Any of a number of possible systems of mathematics that deals with → binary digits instead of numbers. In Boolean algebra, a binary value of 1 is interpreted to mean → true and a binary value of 0 means → false. Boolean algebra can equivalently be thought of as a particular type of mathematics that deals with → truth values instead of numbers.
Fr.: fonction non algébrique
A → transcendental function. Examples are: exponential, logarithmic, and trigonometric functions.