solvable
Meanings
adj
- Capable of being solved.
- various senses relating to terminating sequences or computability:
- Having terminating derived series; see Solvable group on Wikipedia.Wikipedia
- Having a Galois group which is solvable.
- Having terminating derived series (this is a distinct notion from the derived series of a group); see Solvable Lie algebra on Wikipedia.Wikipedia
- Such that the set of inputs for which the answer is yes is recursively enumerable.
- Capable of being dissolved or liquefied.
- Able to pay one's debts.
- Capable of being paid and discharged.
Pronunciation
Word forms
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.
Synonyms
Antonyms
Related words
Derived words
Translations
This entry uses open data from Wiktionary (CC BY-SA/GFDL). Word forms are used for search and are not indexed as separate pages.