solvable

English dictionary entry

Meanings

adj
  1. Capable of being solved.
  2. various senses relating to terminating sequences or computability:
  3. Having terminating derived series; see Solvable group on Wikipedia.Wikipedia
  4. Having a Galois group which is solvable.
  5. Having terminating derived series (this is a distinct notion from the derived series of a group); see Solvable Lie algebra on Wikipedia.Wikipedia
  6. Such that the set of inputs for which the answer is yes is recursively enumerable.
  7. Capable of being dissolved or liquefied.
  8. Able to pay one's debts.
  9. Capable of being paid and discharged.

Pronunciation

/ˈsɒlvəbəl/ /ˈsɑlvəbəl/ LL-Q1860 (eng)-Vealhurl-solvable.wav

Word forms

solvable 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.

Translations

Armenian: լուծելի Czech: řešitelný Esperanto: solvebla Finnish: ratkeava French: résoluble German: lösbar Hebrew: פתיר Hungarian: megoldható Hungarian: megfejthető Japanese: 解決できる Japanese: 解ける Japanese: 割り切れる Portuguese: solúvel Romanian: plătibil Romanian: solvabil Russian: решаемый Spanish: soluble Spanish: solucionable Swedish: lösbar
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