English Dictionary: algebraic | by the DICT Development Group |
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From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Alcove \Al"cove\ (?; 277), n. [F. alc[93]ve, Sp. or Pg. alcoba, from Ar. al-quobbah arch, vault, tent.] 1. (Arch.) A recessed portion of a room, or a small room opening into a larger one; especially, a recess to contain a bed; a lateral recess in a library. 2. A small ornamental building with seats, or an arched seat, in a pleasure ground; a garden bower. --Cowper. 3. Any natural recess analogous to an alcove or recess in an apartment. The youthful wanderers found a wild alcove. --Falconer. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Alexipharmac \A*lex`i*phar"mac\, Alexipharmacal \A*lex`i*phar"ma*cal\, a. & n. [See {Alexipharmic}.] Alexipharmic. [Obs.] | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Alexipharmac \A*lex`i*phar"mac\, Alexipharmacal \A*lex`i*phar"ma*cal\, a. & n. [See {Alexipharmic}.] Alexipharmic. [Obs.] | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Alexipharmic \A*lex`i*phar"mic\, Alexipharmical \A*lex`i*phar"mic*al\, a. [Gr. [?] keeping off poison; [?] to keep off + [?] drug, poison: cf. F. alexipharmaque.] (Med.) Expelling or counteracting poison; antidotal. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Alexipharmic \A*lex`i*phar"mic\, n. (Med.) An antidote against poison or infection; a counterpoison. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Alexipharmic \A*lex`i*phar"mic\, Alexipharmical \A*lex`i*phar"mic*al\, a. [Gr. [?] keeping off poison; [?] to keep off + [?] drug, poison: cf. F. alexipharmaque.] (Med.) Expelling or counteracting poison; antidotal. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Alexipyretic \A*lex`i*py*ret"ic\, a. [Gr. [?] + [?] burning heat, fever, [?] fire.] (Med.) Serving to drive off fever; antifebrile. -- n. A febrifuge. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Algebra \Al"ge*bra\, n. [LL. algebra, fr. Ar. al-jebr reduction of parts to a whole, or fractions to whole numbers, fr. jabara to bind together, consolidate; al-jebr w'almuq[be]balah reduction and comparison (by equations): cf. F. alg[8a]bre, It. & Sp. algebra.] 1. (Math.) That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols. It is applicable to those relations that are true of every kind of magnitude. 2. A treatise on this science. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Mathematics \Math`e*mat"ics\, n. [F. math[82]matiques, pl., L. mathematica, sing., Gr. [?] (sc. [?]) science. See {Mathematic}, and {-ics}.] That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations. Note: Mathematics embraces three departments, namely: 1. {Arithmetic}. 2. {Geometry}, including {Trigonometry} and {Conic Sections}. 3. {Analysis}, in which letters are used, including {Algebra}, {Analytical Geometry}, and {Calculus}. Each of these divisions is divided into pure or abstract, which considers magnitude or quantity abstractly, without relation to matter; and mixed or applied, which treats of magnitude as subsisting in material bodies, and is consequently interwoven with physical considerations. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Algebraic \Al`ge*bra"ic\, Algebraical \Al`ge*bra"ic*al\, a. Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings. {Algebraic curve}, a curve such that the equation which expresses the relation between the co[94]rdinates of its points involves only the ordinary operations of algebra; -- opposed to a transcendental curve. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Algebraic \Al`ge*bra"ic\, Algebraical \Al`ge*bra"ic*al\, a. Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings. {Algebraic curve}, a curve such that the equation which expresses the relation between the co[94]rdinates of its points involves only the ordinary operations of algebra; -- opposed to a transcendental curve. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Function \Func"tion\, n. [L. functio, fr. fungi to perform, execute, akin to Skr. bhuj to enjoy, have the use of: cf. F. fonction. Cf. {Defunct}.] 1. The act of executing or performing any duty, office, or calling; per formance. [bd]In the function of his public calling.[b8] --Swift. 2. (Physiol.) The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body. 3. The natural or assigned action of any power or faculty, as of the soul, or of the intellect; the exertion of an energy of some determinate kind. As the mind opens, and its functions spread. --Pope. 4. The course of action which peculiarly pertains to any public officer in church or state; the activity appropriate to any business or profession. Tradesmen . . . going about their functions. --Shak. The malady which made him incapable of performing his regal functions. --Macaulay. 5. (Math.) A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x^{2}, 3^{x}, Log. x, and Sin. x, are all functions of x. {Algebraic function}, a quantity whose connection with the variable is expressed by an equation that involves only the algebraic operations of addition, subtraction, multiplication, division, raising to a given power, and extracting a given root; -- opposed to transcendental function. {Arbitrary function}. See under {Arbitrary}. {Calculus of functions}. See under {Calculus}. {Carnot's function} (Thermo-dynamics), a relation between the amount of heat given off by a source of heat, and the work which can be done by it. It is approximately equal to the mechanical equivalent of the thermal unit divided by the number expressing the temperature in degrees of the air thermometer, reckoned from its zero of expansion. {Circular functions}. See {Inverse trigonometrical functions} (below). -- Continuous function, a quantity that has no interruption in the continuity of its real values, as the variable changes between any specified limits. {Discontinuous function}. See under {Discontinuous}. {Elliptic functions}, a large and important class of functions, so called because one of the forms expresses the relation of the arc of an ellipse to the straight lines connected therewith. {Explicit function}, a quantity directly expressed in terms of the independently varying quantity; thus, in the equations y = 6x^{2}, y = 10 -x^{3}, the quantity y is an explicit function of x. {Implicit function}, a quantity whose relation to the variable is expressed indirectly by an equation; thus, y in the equation x^{2} + y^{2} = 100 is an implicit function of x. {Inverse trigonometrical functions}, [or] {Circular function}, the lengths of arcs relative to the sines, tangents, etc. Thus, AB is the arc whose sine is BD, and (if the length of BD is x) is written sin ^{-1}x, and so of the other lines. See {Trigonometrical function} (below). Other transcendental functions are the exponential functions, the elliptic functions, the gamma functions, the theta functions, etc. {One-valued function}, a quantity that has one, and only one, value for each value of the variable. -- {Transcendental functions}, a quantity whose connection with the variable cannot be expressed by algebraic operations; thus, y in the equation y = 10^{x} is a transcendental function of x. See {Algebraic function} (above). -- {Trigonometrical function}, a quantity whose relation to the variable is the same as that of a certain straight line drawn in a circle whose radius is unity, to the length of a corresponding are of the circle. Let AB be an arc in a circle, whose radius OA is unity let AC be a quadrant, and let OC, DB, and AF be drawnpependicular to OA, and EB and CG parallel to OA, and let OB be produced to G and F. E Then BD is the sine of the arc AB; OD or EB is the cosine, AF is the tangent, CG is the cotangent, OF is the secant OG is the cosecant, AD is the versed sine, and CE is the coversed sine of the are AB. If the length of AB be represented by x (OA being unity) then the lengths of Functions. these lines (OA being unity) are the trigonometrical functions of x, and are written sin x, cos x, tan x (or tang x), cot x, sec x, cosec x, versin x, coversin x. These quantities are also considered as functions of the angle BOA. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Sum \Sum\, n. [OE. summe, somme, OF. sume, some, F. somme, L. summa, fr. summus highest, a superlative from sub under. See {Sub-}, and cf. {Supreme}.] 1. The aggregate of two or more numbers, magnitudes, quantities, or particulars; the amount or whole of any number of individuals or particulars added together; as, the sum of 5 and 7 is 12. Take ye the sum of all the congregation. --Num. i. 2. Note: Sum is now commonly applied to an aggregate of numbers, and number to an aggregate of persons or things. 2. A quantity of money or currency; any amount, indefinitely; as, a sum of money; a small sum, or a large sum. [bd]The sum of forty pound.[b8] --Chaucer. With a great sum obtained I this freedom. --Acts xxii. 28. 3. The principal points or thoughts when viewed together; the amount; the substance; compendium; as, this is the sum of all the evidence in the case; this is the sum and substance of his objections. 4. Height; completion; utmost degree. Thus have I told thee all my state, and brought My story to the sum of earthly bliss. --Milton. 5. (Arith.) A problem to be solved, or an example to be wrought out. --Macaulay. A sum in arithmetic wherein a flaw discovered at a particular point is ipso facto fatal to the whole. --Gladstone. A large sheet of paper . . . covered with long sums. --Dickens. {Algebraic sum}, as distinguished from arithmetical sum, the aggregate of two or more numbers or quantities taken with regard to their signs, as + or -, according to the rules of addition in algebra; thus, the algebraic sum of -2, 8, and -1 is 5. {In sum}, in short; in brief. [Obs.] [bd]In sum, the gospel . . . prescribes every virtue to our conduct, and forbids every sin.[b8] --Rogers. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Algebraic \Al`ge*bra"ic\, Algebraical \Al`ge*bra"ic*al\, a. Of or pertaining to algebra; containing an operation of algebra, or deduced from such operation; as, algebraic characters; algebraical writings. {Algebraic curve}, a curve such that the equation which expresses the relation between the co[94]rdinates of its points involves only the ordinary operations of algebra; -- opposed to a transcendental curve. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Algebraically \Al`ge*bra"ic*al*ly\, adv. By algebraic process. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Algebraist \Al"ge*bra`ist\, n. One versed in algebra. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Algebraize \Al"ge*bra*ize\, v. t. To perform by algebra; to reduce to algebraic form. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Algific \Al*gif"ic\, a. [L. algificus, fr. algus cold + facere to make.] Producing cold. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Aliseptal \Al`i*sep"tal\, a. [L. ala wing + E. septal.] (Anat.) Relating to expansions of the nasal septum. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Alisphenoid \Al`i*sphe"noid\, Alisphenoidal \Al`i*sphe*noid"al\, a. [L. ala wing + E. sphenoid.] (Anat.) Pertaining to or forming the wing of the sphenoid; relating to a bone in the base of the skull, which in the adult is often consolidated with the sphenoid; as, alisphenoid bone; alisphenoid canal. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Alisphenoid \Al`i*sphe"noid\, n. (Anat.) The alisphenoid bone. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Alisphenoid \Al`i*sphe"noid\, Alisphenoidal \Al`i*sphe*noid"al\, a. [L. ala wing + E. sphenoid.] (Anat.) Pertaining to or forming the wing of the sphenoid; relating to a bone in the base of the skull, which in the adult is often consolidated with the sphenoid; as, alisphenoid bone; alisphenoid canal. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Allegeable \Al*lege"a*ble\, a. Capable of being alleged or affirmed. The most authentic examples allegeable in the case. --South. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Allspice \All"spice`\, n. The berry of the pimento ({Eugenia pimenta}), a tree of the West Indies; a spice of a mildly pungent taste, and agreeably aromatic; Jamaica pepper; pimento. It has been supposed to combine the flavor of cinnamon, nutmegs, and cloves; and hence the name. The name is also given to other aromatic shrubs; as, the {Carolina allspice} ({Calycanthus floridus}); {wild allspice} ({Lindera benzoin}), called also {spicebush}, {spicewood}, and {feverbush}. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Allusive \Al*lu"sive\, a. 1. Figurative; symbolical. 2. Having reference to something not fully expressed; containing an allusion. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Allusively \Al*lu"sive*ly\, adv. Figuratively [Obs.]; by way of allusion; by implication, suggestion, or insinuation. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Allusiveness \Al*lu"sive*ness\, n. The quality of being allusive. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Porbeagle \Por"bea`gle\, n. (Zo[94]l.) A species of shark ({Lamna cornubica}), about eight feet long, having a pointed nose and a crescent-shaped tail; -- called also {mackerel shark}. [Written {also probeagle}.] | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Barn \Barn\, n. [OE. bern, AS. berern, bern; bere barley + ern, [91]rn, a close place. [?]92. See {Barley}.] A covered building used chiefly for storing grain, hay, and other productions of a farm. In the United States a part of the barn is often used for stables. {Barn owl} (Zo[94]l.), an owl of Europe and America ({Aluco flammeus}, or {Strix flammea}), which frequents barns and other buildings. {Barn swallow} (Zo[94]l.), the common American swallow ({Hirundo horreorum}), which attaches its nest of mud to the beams and rafters of barns. | |
From Webster's Revised Unabridged Dictionary (1913) [web1913]: | |
Awl-shaped \Awl"-shaped`\, a. 1. Shaped like an awl. 2. (Nat. Hist.) Subulate. See {Subulate}. --Gray. | |
From U.S. Gazetteer (1990) [gazetteer]: | |
Alcova, WY Zip code(s): 82620 | |
From U.S. Gazetteer (1990) [gazetteer]: | |
Alcove, NY Zip code(s): 12007 | |
From U.S. Gazetteer (1990) [gazetteer]: | |
Aliceville, AL (city, FIPS 1228) Location: 33.12508 N, 88.15800 W Population (1990): 3009 (1293 housing units) Area: 11.6 sq km (land), 0.0 sq km (water) Zip code(s): 35442 | |
From U.S. Gazetteer (1990) [gazetteer]: | |
Aliquippa, PA (city, FIPS 820) Location: 40.61740 N, 80.25504 W Population (1990): 13374 (6118 housing units) Area: 10.6 sq km (land), 1.0 sq km (water) | |
From U.S. Gazetteer (1990) [gazetteer]: | |
Aliso Viejo, CA (CDP, FIPS 947) Location: 33.56754 N, 117.72531 W Population (1990): 7612 (3884 housing units) Area: 25.4 sq km (land), 0.0 sq km (water) Zip code(s): 92656 | |
From U.S. Gazetteer (1990) [gazetteer]: | |
Alkabo, ND Zip code(s): 58845 | |
From U.S. Gazetteer (1990) [gazetteer]: | |
Alsip, IL (village, FIPS 1010) Location: 41.67035 N, 87.73578 W Population (1990): 18227 (7144 housing units) Area: 16.3 sq km (land), 0.4 sq km (water) Zip code(s): 60658 | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
algebra structure}. 2. A {vector space} that is also a {ring}, where the vector space and the ring share the same addition operation and are related in certain other ways. An example algebra is the set of 2x2 {matrices} with {real numbers} as entries, with the usual operations of addition and matrix multiplication, and the usual {scalar} multiplication. Another example is the set of all {polynomials} with real coefficients, with the usual operations. In more detail, we have: (1) an underlying {set}, (2) a {field} of {scalars}, (3) an operation of scalar multiplication, whose input is a scalar and a member of the underlying set and whose output is a member of the underlying set, just as in a {vector space}, (4) an operation of addition of members of the underlying set, whose input is an {ordered pair} of such members and whose output is one such member, just as in a vector space or a ring, (5) an operation of multiplication of members of the underlying set, whose input is an ordered pair of such members and whose output is one such member, just as in a ring. This whole thing constitutes an `algebra' iff: (1) it is a vector space if you discard item (5) and (2) it is a ring if you discard (2) and (3) and (3) for any scalar r and any two members A, B of the underlying set we have r(AB) = (rA)B = A(rB). In other words it doesn't matter whether you multiply members of the algebra first and then multiply by the scalar, or multiply one of them by the scalar first and then multiply the two members of the algebra. Note that the A comes before the B because the multiplication is in some cases not commutative, e.g. the matrix example. Another example (an example of a {Banach algebra}) is the set of all {bounded} {linear operators} on a {Hilbert space}, with the usual {norm}. The multiplication is the operation of {composition} of operators, and the addition and scalar multiplication are just what you would expect. Two other examples are {tensor algebras} and {Clifford algebras}. [I. N. Herstein, "Topics_in_Algebra"]. (1999-07-14) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
Algebra of Communicating Processes Compare {CCS}. ["Algebra of Communicating Processes with Abstraction", J.A. Bergstra & J.W. Klop, Theor Comp Sci 37(1):77-121 1985]. [Summary?] (1994-11-08) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
algebraic 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) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
ALGEBRAIC [CACM 2(5):16 (May 1959)]. (1995-01-24) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
algebraic 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) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
ALGEBRAIC [CACM 2(5):16 (May 1959)]. (1995-01-24) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
algebraic data type programming}, new types can be defined, each of which has one or more {constructor}s. 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 Tree with constructors "Empty", "Leaf" and "Node". The constructors can be used much like functions in that they can be (partially) applied to arguments of the appropriate type. For example, the Leaf constructor has the functional type Int -> Tree. A constructor application cannot be reduced (evaluated) like a function application though since it is already in {normal form}. Functions which operate on algebraic data types can be defined using {pattern matching}: depth :: Tree -> Int depth Empty = 0 depth (Leaf n) = 1 depth (Node l r) = 1 + max (depth l) (depth r) The most common algebraic data type is the list which has constructors Nil and Cons, written in Haskell using the special syntax "[]" for Nil and infix ":" for Cons. Special cases of algebraic types are {product type}s (only one constructor) and {enumeration type}s (many constructors with no arguments). Algebraic types are one kind of {constructed type} (i.e. a type formed by combining other types). An algebraic data type may also be an {abstract data type} (ADT) if it is exported from a {module} without its constructors. Objects of such a type can only be manipulated using functions defined in the same {module} as the type itself. In {set theory} the equivalent of an algebraic data type is a {discriminated union} - a set whose elements consist of a tag (equivalent to a constructor) and an object of a type corresponding to the tag (equivalent to the constructor arguments). (1994-11-23) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
Algebraic Interpretive Dialogue ["AID (Algebraic Interpretive Dialogue)", DEC manual, 1968]. (1995-04-12) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
Algebraic Logic Functional language {functional programming} and {logic programming} techniques. ALF is based on {Horn clause} logic with equality which consists of {predicate}s and Horn clauses for {logic programming}, and functions and equations for {functional programming}. Any functional expression can be used in a {goal} literal and arbitrary predicates can occur in conditions of equations. ALF uses {narrowing} and {rewriting}. ALF includes a compiler to {Warren Abstract Machine} code and {run-time support}. {(ftp://ftp.germany.eu.net/pub/programming/languages/LogicFunctional)}. ["The Implementation of the Functional-Logic Language ALF", M. Hanus and A. Schwab]. (1992-10-08) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
Algebraic Manipulation Package written in {Modula-2}, seen on {CompuServe}. (1994-10-19) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
Algebraic Specification Language 1. ["Structured Algebraic Specifications: A Kernel Language", M. Wirsing, Theor Comput Sci 42, pp.123-249, Elsevier 1986]. 2. {abstract data types}. ["Algebraic Specification", J.A. Bergstra et al, A-W 1989]. (1995-12-13) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
algebraic structure set of objects and operations on those objects. Examples are {Boolean algebra}, numerical algebra, set algebra and matrix algebra. [Is this the most common name for this concept?] (1997-02-25) | |
From The Free On-line Dictionary of Computing (15Feb98) [foldoc]: | |
ALJABR {Fort Pond Research}. (1995-02-21) |