solvable

English

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

1. 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.

2. (mathematics, group theory, of a group) Having terminating derived series; see Solvable group on Wikipedia.Wikipedia
3. (mathematics, Galois theory, of a Galois extension) Having a Galois group which is solvable.
4. (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
5. (computer science, of a decision problem) Such that the set of inputs for which the answer is yes is recursively enumerable.
6. (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:

7. (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;

8. (obsolete, rare) Capable of being paid and discharged.

   solvable obligations

Derived terms

• solvable group
• solvableness
• insolvable
• unsolvable

Related terms

• solvability

Translations

capable of being solved

• Armenian: լուծելի (hy) (luceli)
• Czech: řešitelný (cs) m
• Esperanto: solvebla
• Finnish: ratkeava (fi)
• French: résoluble (fr)
• German: lösbar (de)
• Hebrew: פתיר m (Pathir)
• Hungarian: megoldható (hu), megfejthető (hu)
• Japanese: 解決できる (ja) (kaiketsu dekiru), 解ける (ja) (tokeru), 割り切れる (warikireru)
• Portuguese: solúvel (pt)
• Romanian: plătibil (ro) m or n, solvabil (ro) m or n, solvabilă f
• Spanish: soluble (es), solucionable
• Swedish: lösbar (sv)

(obsolete in English) capable of being dissolved — see also soluble

• Finnish: liukeneva (fi)
• French: soluble (fr)
• German: löslich (de)
• Japanese: 溶かせる (ja) (tokaseru)
• Romanian: solubil (ro) m or n (chim.), dizolvabil m or n, dizolvabilă f
• Spanish: soluble (es)
• Swedish: löslig (sv)

French

Etymology

From Latin solvere +‎ -able.

Pronunciation

• IPA^(key): /sɔl.vabl/

• Audio:

  (file)

Adjective

solvable (plural solvables)

1. solvent

   Antonym: insolvable

Related terms

• soluble

Further reading

• “solvable”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.