Solvable
adj ·Uncommon ·Advanced level
Definitions
- 1 Capable of being solved.
"a solvable problem"
- 2 Capable of being solved.; various senses relating to terminating sequences or computability:; Having terminating derived series; see Solvable group on Wikipedia.Wikipedia
- 3 Capable of being solved.; various senses relating to terminating sequences or computability:; Having a Galois group which is solvable.
- 4 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
- 5 Capable of being solved.; Such that the set of inputs for which the answer is yes is recursively enumerable.
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- 6 Capable of being dissolved or liquefied. obsolete
"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:"
- 7 Able to pay one's debts. obsolete
"[…] although imprisonment was imposed by law on persons not solvable, yet officers were unwilling to cast them into goale,"
- 8 Capable of being paid and discharged. obsolete, rare
"solvable obligations"
- 1 capable of being solved wordnet
Example
More examples"These problems are all solvable."
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.