An Etymological Dictionary of Astronomy and Astrophysics
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Relating to, involving, or according to the laws of algebra.

→ algebra + → -ic.

An equation in the form of P = 0, where P is a → polynomial having a finite number of terms.

→ algebra; → equation.

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)y^{n - 1} + ... + P_n(x) = 0, where P₀(x), P₁(x), ..., P_n(x) are polynomials in x.

→ algebraic + → function.

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.

→ algebraic; → number.

A → transcendental function. Examples are: exponential, logarithmic, and trigonometric functions.

→ non-; → algebraic + → function.