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,^[2]
  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^[3], 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,^[4]
  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^[5], 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^[6], 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,^[7]
  […] 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^[8], 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