algebra jabr (#) Fr.: Algèbre 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. |
algebraic jabri (#) Fr.: algébrique Relating to, involving, or according to the laws of algebra. |
algebraic equation hamugeš-e jabri Fr.: équation algébrique An equation in the form of P = 0, where P is a → polynomial having a finite number of terms. |
algebraic function karyâ-ye jabri 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 P_{0}(x)y^{n} + P_{1}(x)y^{n - 1} + ... + P_{n}(x) = 0, where P_{0}(x), P_{1}(x), ..., P_{n}(x) are polynomials in x. |
algebraic number 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 x^{2} - 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 x^{2} + 1 = 0. |
associative algebra jabr-e âhazeši Fr.: algèbre associative An algebra whose multiplication is associative. → associative; → algebra. |
Boolean algebra 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. → Boolean; → algebra. The term Boolean algebra was first suggested by Sheffer in 1913. |
non-algebraic function karyâ-ye nâjabri Fr.: fonction non algébrique A → transcendental function. Examples are: exponential, logarithmic, and trigonometric functions. |