solvable
Language: English
Part of speech: adj
Pronunciation: ipa: /ˈsɒlvəbəl/
ipa: /ˈsɑlvəbəl/
Forms: form: solvible
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.
Senses: examples: text: a solvable problem
text: 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:
text: Questions of this Nature may be easily solvable in the simple Cases.
ref: 1732, Henry Home, Lord Kames, “Beneficium cedendarum actionum”, in Essays upon Several Subjects in Law, Edinburgh, page 19:
text: 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.
text: 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.
ref: 1886, Thomas Hardy, chapter 17, in The Mayor of Casterbridge, volume 1, London: Smith, Elder, page 211:
text: This is a mystery that is solvable with a phone call.
ref: 2010, Howard Jacobson, The Finkler Question, New York: Bloomsbury, Part 1, Chapter 4, p. 97:
synonyms: soluble
antonyms: unsolvable
insolvable
insoluble
glosses: Capable of being solved.
topics: group-theory
mathematics
sciences
synonyms: soluble
antonyms: unsolvable
insolvable
insoluble
glosses: Capable of being solved.
various senses relating to terminating sequences or computability:
Having terminating derived series; see Solvable group on Wikipedia.Wikipedia
raw_tags: of a group
topics: mathematics
sciences
synonyms: soluble
antonyms: unsolvable
insolvable
insoluble
glosses: Capable of being solved.
various senses relating to terminating sequences or computability:
Having a Galois group which is solvable.
qualifier: Galois theory
raw_tags: of a Galois extension
topics: mathematics
sciences
synonyms: soluble
antonyms: unsolvable
insolvable
insoluble
glosses: 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
qualifier: Lie theory
raw_tags: of a Lie algebra
topics: computer
computing
engineering
mathematics
natural-sciences
physical-sciences
science
sciences
synonyms: soluble
antonyms: unsolvable
insolvable
insoluble
glosses: Capable of being solved.
Such that the set of inputs for which the answer is yes is recursively enumerable.
coordinate_terms: computable
decidable
raw_tags: of a decision problem
examples: 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:
synonyms: soluble
antonyms: unsolvable
insolvable
insoluble
glosses: Capable of being dissolved or liquefied.
examples: text: […] although imprisonment was imposed by law on persons not solvable, yet officers were unwilling to cast them into goale,
ref: 1655, Thomas Fuller, “Section 4”, in The Church-history of Britain; […], London: […] Iohn Williams […], →OCLC, (please specify |book=I to XI), page 131:
text: The Government is solvable in case of Loss, whereas private Men often fail;
ref: 1703, John Dennis, A Proposal for Putting a Speedy End to the War, London: Daniel Brown and Andrew Bell, page 19:
synonyms: solvent
glosses: Able to pay one's debts.
examples: solvable obligations
glosses: Capable of being paid and discharged.
Derived terms: solvable group
solvableness
insolvable
unsolvable
Related terms: solvability