solvable

Capable of being solved.

Adjective

  1. Capable of being solved.
    • 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,...
    • 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:

    Synonyms: soluble

    Antonyms: unsolvable insolvable insoluble

    1. (mathematics) various senses relating to terminating sequences or computability:

      (group theory, of a group) Having terminating derived series; see Solvable group on Wikipedia.Wikipedia

      Synonyms: soluble

      Antonyms: unsolvable insolvable insoluble

    2. (mathematics) various senses relating to terminating sequences or computability:

      (Galois theory, of a Galois extension) Having a Galois group which is solvable.

      Synonyms: soluble

      Antonyms: unsolvable insolvable insoluble

    3. (mathematics) various senses relating to terminating sequences or computability:

      (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

      Synonyms: soluble

      Antonyms: unsolvable insolvable insoluble

    4. (computer science, of a decision problem) Such that the set of inputs for which the answer is yes is recursively enumerable.

      Synonyms: soluble

      Antonyms: unsolvable insolvable insoluble

      Coordinate Terms: computable decidable

  2. 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...

    Synonyms: soluble

    Antonyms: unsolvable insolvable insoluble

  3. Able to pay one's debts.
    • […] 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...
    • 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:

    Synonyms: solvent

  4. Capable of being paid and discharged.
    • solvable obligations

Origin

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.

Forms

solvible

Wikipedia

Galois theory

Related

solvability

Derived

insolvable nonsolvable solvable group solvableness solvmanifold supersolvable unsolvable