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# Algebraic

of, occurring in, or utilizing .
Mathematics. of or relating to an element that is the root of a polynomial equation with coefficients from some given field:
is algebraic over the field of real numbers.
using arbitrary letters or symbols in place of the letters, symbols, or numbers of an actual application.
Historical Examples

It possesses the same merits in relation to Geometry that the atomic theory has in relation to algebraic calculus.
Aids to Reflection Samuel Taylor Coleridge

His specialty was the solution of algebraic problems mentally.
A Budget of Paradoxes, Volume I (of II) Augustus De Morgan

algebraic investigation required writing: but the weaver’s hands being engaged he could not write.
Notes and Queries, Number 57, November 30, 1850 Various

To attain it, we should have to reason naked in a desert with algebraic symbols.
Shelley, Godwin and Their Circle H. N. Brailsford

Yet there may not be any limit to algebraic or mathematical determinations.
The Mystery of Space Robert T. Browne

Hence the failure of attempts to apply arithmetical or algebraic formulae to logic.
The Republic Plato

She now trusted he would not have the effrontery to fly in the face of an algebraic paradox.
The Art of Amusing Frank Bellew

Then he remembered, as if recalling some algebraic formula, “I’m in love.”
Erik Dorn Ben Hecht

An equation admits of description in two ways:— It may be regarded purely as an algebraic expression, or as a geometrical locus.
Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7 Various

Yes: it enables us to subject the formulæ to algebraic manipulation.
Logic, Inductive and Deductive William Minto

of or relating to algebra: an algebraic expression
using or relating to finite numbers, operations, or relationships

1660s, from algebra + -ic. Earlier was algebraical (1570s).

language
An early system on MIT’s Whirlwind.
[CACM 2(5):16 (May 1959)].
(1995-01-24)
theory
In domain theory, a complete partial order is algebraic if every element is the least upper bound of some chain of compact elements. If the set of compact elements is countable it is called omega-algebraic.
[Significance?]
(1995-04-25)

Tagged:

• Algebraic compiler and translator

algebraic compiler and translator language (ACT 1) A language and compiler for the Royal McBee LGP-30, designed around 1959, apparently by Clay S. Boswell, Jr, and programmed by Mel Kaye. (http://ed-thelen.org/comp-hist/lgp-30-man.html) (2008-08-04)

• Algebraic data type

algebraic data type programming (Or “sum of products type”) In functional programming, new types can be defined, each of which has one or more constructors. Such a type is known as an algebraic data type. E.g. in Haskell we can define a new type, “Tree”: data Tree = Empty | Leaf Int | Node Tree […]

• Algebraic equation

an equation in the form of a polynomial having a finite number of terms and equated to zero, as 2 x 3 + 4 x 2 − x + 7 = 0. Historical Examples He felt as he had when puzzling over the unknown quantity in an algebraic equation. Jerome, A Poor Man Mary E. […]

• Algebraic extension

a field containing a given field such that every element in the first field is algebraic over the given field.

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