solvable
UK /ˈsɒlvəbəl/ · US /ˈsɑlvəbəl/ adjective
Forms solvible
- adjective Capable of being solved. “a solvable problem”
- adjective (group theory, of a group) Having terminating derived series; see Solvable group on Wikipedia.Wikipedia
- adjective (Galois theory, of a Galois extension) Having a Galois group which is solvable.
- adjective (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
- adjective (computer science, of a decision problem) Such that the set of inputs for which the answer is yes is recursively enumerable.
- adjective (obsolete) Capable of being dissolved or liquefied.
- adjective (obsolete) Able to pay one's debts.
- adjective (obsolete, rare) Capable of being paid and discharged. “solvable obligations”
Synonyms
Antonyms
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.
Webster’s 1913
- adjective Susceptible of being solved, resolved, or explained; admitting of solution.
- adjective Capable of being paid and discharged; as, solvable obligations.
Etymology [F. solvable. See Solve, and cf. Soluble, Solvible.]
Sources: Wiktionary · WordNet 3.0 · Webster’s 1913 — from the Wiktionary entry “solvable”, CC BY-SA 4.0. Details