solvable

English

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solvable

Wikipedia

Alternative forms

solvible (obsolete)

Etymology

From solve +‎ -able. Piecewise doublet of soluble.

The mathematical senses derive from Galois theory: Galois discovered that one could determine whether a given polynomial could be solved by radicals by studying the properties of a particular group attached to a particular field extension deriving from the polynomial in question; if the group satisfies some conditions then polynomial can be solved by radicals. Any group meeting these conditions — whether or not it arises from this process — is thus called solvable, as is any field extension giving rise to such a group. The Lie-theoretic sense is by analogy, the study of Lie algebras deriving much of its terminology from group theory. In regular use by the late 19th century.

Pronunciation

Audio (Southern England): (file)

Adjective

solvable

Capable of being solved.
Synonym: soluble

Antonyms: unsolvable, insolvable, insoluble

a solvable problem
- 1677, Matthew Hale, The Primitive Origination of Mankind, London: William Shrowsbery, “De homine,” Chapter 2, p. 56,
  Intellective Memory, which I call an act of the intellective faculty because it is wrought by it, though I do not inquire how or where, because it is not solvible:
- 1732, Henry Home, Lord Kames, “Beneficium cedendarum actionum”, in Essays upon Several Subjects in Law‎, Edinburgh, page 19:
  Questions of this Nature may be easily solvable in the simple Cases.
- 1856, Abraham Lincoln, Speech delivered before the first Republican State Convention of Illinois, Bloomington, 29 May, 1856, in Arthur Brooks Lapsley (ed.), The Writings of Abraham Lincoln, New York: The Lamb Publishing Company, Volume 2, p. 271,
  It is a very strange thing, and not solvable by any moral law that I know of, that if a man loses his horse, the whole country will turn out to help hang the thief; but if a man but a shade or two darker than I am is himself stolen, the same crowd will hang one who aids in restoring him to liberty.
- 1886, Thomas Hardy, chapter 17, in The Mayor of Casterbridge‎, volume 1, London: Smith, Elder, page 211:
  Would Mr. Farfrae stay in Casterbridge despite his words and her father’s dismissal? His occult breathings to her might be solvable by his course in that respect.
- 2010, Howard Jacobson, The Finkler Question‎, New York: Bloomsbury, Part 1, Chapter 4, p. 97:
  This is a mystery that is solvable with a phone call.
(mathematics, group theory, of a group) Having terminating derived series; see Solvable group on Wikipedia.Wikipedia
(mathematics, Galois theory, of a Galois extension) Having a Galois group which is solvable.
(mathematics, Lie theory, of a Lie algebra) Having terminating derived series (this is a distinct notion from the derived series of a group); see Solvable Lie algebra on Wikipedia.Wikipedia
(computer science, of a decision problem) Such that the set of inputs for which the answer is yes is recursively enumerable.
(obsolete) Capable of being dissolved or liquefied.
Synonym: soluble

Antonyms: unsolvable, insolvable, insoluble
- 1664, John Chandler (translator), Van Helmont’s Works, London: Lodowick Lloyd, A Treatise of Fevers, Chapter 8, p. 971,
  they administer Pearles, and Corrals being beaten to dust or dissolved in distilled vinegar, or the juice of limons, and again dryed, and solvable in any potable liquour:
(obsolete) Able to pay one's debts.
Synonym: solvent
- 1655, Thomas Fuller, “Section 4”, in The Church-history of Britain; , London: Iohn Williams , →OCLC, (please specify |book=I to XI), page 131:
  […] although imprisonment was imposed by law on persons not solvable, yet officers were unwilling to cast them into goale,
- 1703, John Dennis, A Proposal for Putting a Speedy End to the War‎, London: Daniel Brown and Andrew Bell, page 19:
  The Government is solvable in case of Loss, whereas private Men often fail;
(obsolete, rare) Capable of being paid and discharged.^[1]
solvable obligations