超越次數

Chinese

		to exceed; to surpass; to transcend to exceed; to surpass; to transcend; to surmount; to overstep the bounds; to go beyond one's role	frequency; order of a monomial or polynomial
trad. (超越次數)		超越	次數
simp. (超越次数)		超越	次数

Pronunciation

• Mandarin

  (Pinyin): chāoyuè cìshù

  (Zhuyin): ㄔㄠ ㄩㄝˋ ㄘˋ ㄕㄨˋ

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• Mandarin
  • (Standard Chinese)⁺
    • Hanyu Pinyin: chāoyuè cìshù
    • Zhuyin: ㄔㄠ ㄩㄝˋ ㄘˋ ㄕㄨˋ
    • Tongyong Pinyin: chaoyuè cìhshù
    • Wade–Giles: chʻao¹-yüeh⁴ tzʻŭ⁴-shu⁴
    • Yale: chāu-ywè tsz̀-shù
    • Gwoyeu Romatzyh: chauyueh tsyhshuh
    • Palladius: чаоюэ цышу (čaojue cyšu)
    • Sinological IPA ^(key): /ʈ͡ʂʰɑʊ̯⁵⁵ ɥɛ⁵¹⁻⁵³ t͡sʰz̩⁵¹⁻⁵³ ʂu⁵¹/

Noun

超越次數

1. (algebra, field theory, of a field extension) transcendence degree

   • 特別，K的擴域是代數的，當且僅當它在K上的超越次數為零。 [MSC, trad.]
     特别，K的扩域是代数的，当且仅当它在K上的超越次数为零。 [MSC, simp.]

     From: 2003, 朱尧辰 (Zhu Yaochen), 徐广善 (Xu Guangshan), 《超越数引论》 [Introduction to Transcendental Number]

     Tèbié, K de kuòyù shì dàishù de, dāngqiějǐndāng tā zài K shàng de chāoyuè cìshù wèi líng. [Pinyin]

     Particularly, the extension field of K is algebraic if and only if its transcendence degree on K is zero.