Dictionary

solvable en · ADJ

Pronunciation

/ˈsɑlvəbəl/ (General-American)
(Southern-England) audio
/ˈsɒlvəbəl/ (Received-Pronunciation)

Etymology

From solve + -able. Piecewise doublet of soluble. More information 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.

Meanings

Capable of being solved.
- Questions of this Nature may be easily solvable in the simple Cases. 1732, Henry Home, Lord Kames, “Beneficium cedendarum actionum”, in Essays upon Several Subjects in Law, Edinburgh, page 19:
- 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. 1886, Thomas Hardy, chapter 17, in The Mayor of Casterbridge, volume 1, London: Smith, Elder, page 211:
- a solvable problem
- 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.
- 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:
- This is a mystery that is solvable with a phone call. 2010, Howard Jacobson, The Finkler Question, New York: Bloomsbury, Part 1, Chapter 4, p. 97:
(of a group) Capable of being solved. ▸ various senses relating to terminating sequences or computability: ▸ Having terminating derived series; see Solvable group on Wikipedia.Wikipedia
(of a Galois extension, qualifier:Galois theory) Capable of being solved. ▸ various senses relating to terminating sequences or computability: ▸ Having a Galois group which is solvable.
(of a Lie algebra, qualifier:Lie theory) Capable of being solved. ▸ various senses relating to terminating sequences or computability: ▸ Having terminating derived series (this is a distinct notion from the derived series of a group); see Solvable Lie algebra on Wikipedia.Wikipedia
(of a decision problem) Capable of being solved. ▸ Such that the set of inputs for which the answer is yes is recursively enumerable.
(obsolete) Capable of being dissolved or liquefied.
- 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.
- The Government is solvable in case of Loss, whereas private Men often fail; 1703, John Dennis, A Proposal for Putting a Speedy End to the War, London: Daniel Brown and Andrew Bell, page 19:
- […] although imprisonment was imposed by law on persons not solvable, yet officers were unwilling to cast them into goale, 1655, Thomas Fuller, “Section 4”, in The Church-history of Britain; […], London: […] Iohn Williams […], →OCLC, (please specify |book=I to XI), page 131:
(obsolete, rare) Capable of being paid and discharged.
- solvable obligations

Forms

Spelling	Features	Labels	Source
solvible		alternative, obsolete	lexicographic

Translations (30)

de löslich (''(obsolete in English)'' capable of being dissolved) · ru решаемый (capable of being solved) · pt solúvel (capable of being solved) · fr résoluble (capable of being solved) · pl rozwiązalny (capable of being solved) · fr soluble (''(obsolete in English)'' capable of being dissolved) · hy լուծելի (capable of being solved) · ja 割り切れる (capable of being solved) · ja 解決できる (capable of being solved) · fi liukeneva (''(obsolete in English)'' capable of being dissolved) · es soluble (capable of being solved) · cs řešitelný (capable of being solved) · ro plătibil (capable of being solved) · es soluble (''(obsolete in English)'' capable of being dissolved) · ja 解ける (capable of being solved) · ro solvabil (capable of being solved) · ja 溶かせる (''(obsolete in English)'' capable of being dissolved) · hu megfejthető (capable of being solved) · pl rozpuszczalny (''(obsolete in English)'' capable of being dissolved) · hu megoldható (capable of being solved) · ro dizolvabil (''(obsolete in English)'' capable of being dissolved) · sv löslig (''(obsolete in English)'' capable of being dissolved) · he פתיר (capable of being solved) · eo solvebla (capable of being solved) · sv lösbar (capable of being solved) · de lösbar (capable of being solved) · ro solubil (''(obsolete in English)'' capable of being dissolved) · es solucionable (capable of being solved) · fi ratkeava (capable of being solved) · pl rozwiązywalny (capable of being solved)

wikipedia: Solution in radicals · wikipedia: Évariste Galois · wikipedia: Galois theory

solvable en · ADJ

Pronunciation

Etymology

Meanings

Forms

Antonyms

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Synonyms

Translations (30)