What is "solvable"

Solvable \Solv"a*ble\, a. [F. solvable. See Solve, and cf. Soluble, Solvible.]

1. Susceptible of being solved, resolved, or explained; admitting of solution.

2. Capable of being paid and discharged; as, solvable obligations.
   --Tooke.

3. Able to pay one's debts; solvent. [Obs.]
   --Fuller.

1640s, from solve + -able.

a. 1 Capable of being solved. 2 (context archaic English) Capable of being dissolved or liquefy. 3 (context obsolete English) Capable of being paid and discharged. 4 (context obsolete English) Able to pay one's debts; solvent.

adj. possible to solve; "such problems are perfectly solvable" [syn: resolvable]

In mathematics, solvable may refer to:

• Solvable group, a group that can be constructed by compositions of abelian groups, or equivalently a group whose derived series reaches the trivial group in finitely many steps
• Solvable extension, a field extension whose Galois group is a solvable group
• Solvable equation, a polynomial equation whose Galois group is solvable, or equivalently, one whose solutions may be expressed by nested radicals
• Solvable Lie algebra, a Lie algebra whose derived series reaches the zero algebra in finitely many steps
• Solvable problem, a computational problem that can be solved by a Turing machine
• Exactly solvable model in statistical mechanics, a system whose solution can be expressed in closed form, or alternatively, another name for completely integrable systems