solvable
形容词 adj.
英 /ˈsɒlvəbəl/
美 /ˈsɑlvəbəl/
英文释义
形容词 adj.
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Capable of being solved.
— a solvable problem
- Capable of being solved.; various senses relating to terminating sequences or computability:; Having terminating derived series; see Solvable group on Wikipedia.Wikipedia
- Capable of being solved.; various senses relating to terminating sequences or computability:; Having a Galois group which is solvable.
- 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
- Capable of being solved.; Such that the set of inputs for which the answer is yes is recursively enumerable.
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Capable of being dissolved or liquefied.
— 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:
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Able to pay one's debts.
— […] although imprisonment was imposed by law on persons not solvable, yet officers were unwilling to cast them into goale,
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Capable of being paid and discharged.
— solvable obligations
词形变化
词汇关系
词源
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.
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.
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