nontrivial
nontrivial — 形容詞
- nontrivialpositive
- more nontrivialcomparative
- most nontrivialsuperlative
1. important, difficult, or serious enough to deserve time, effort, or attention —
重大；困難
重要或困難到值得關注
important, difficult, or serious enough to deserve time, effort, or attention — the opposite of simple or minor.
The engineering team faced a nontrivial challenge when designing the bridge for the earthquake zone.
工程團隊在為地震帶設計橋樑時，面臨了一項重大的挑戰。
nontrivial + challenge (difficult task context)
Learning Japanese as a native English speaker is a nontrivial task requiring years of dedication.
對於以英語為母語的人來說，學習日語是一項困難的任務，需要多年的努力。
The company invested a nontrivial amount of money in developing the new medical device.
該公司在開發新型醫療設備上投入了一筆可觀的金額。
Mira realised that fixing the software bug was a nontrivial problem requiring weeks of work.
Mira 意識到修復那個軟體錯誤是一項複雜的問題，需要數週的工作。
The committee spent hours discussing the nontrivial implications of the new privacy law.
委員會花了數小時討論新隱私法帶來的重大影響。
- significant
focuses on importance rather than difficulty
- substantial
emphasises size or amount rather than complexity
- challenging
highlights difficulty and is common in everyday use
- trivial
direct opposite; unimportant, simple, or minor
- insignificant
opposite on the importance dimension
文法句型
nontrivial + noun
be + nontrivial
用法筆記
Common in academic, technical, and professional writing. In everyday conversation, speakers usually prefer simpler words such as 'difficult', 'big', or 'serious'.
常見錯誤
2. referring to a mathematical result in which not every component is equal to zero
非零的
至少一個變數或項不為零
referring to a mathematical result in which not every component is equal to zero — the opposite of a trivial solution where all quantities are zero.
The equation has a nontrivial solution when x is greater than zero.
當 x 大於零時，這個方程式有一個非零解。
nontrivial + solution (mathematics collocation)
In linear algebra, students distinguish between trivial and nontrivial solutions of a system of equations.
在線性代數中，學生區分方程組的零解與非零解。
The algorithm searches for nontrivial factors of large composite numbers.
該演算法會搜尋大型合數的非零因數。
Yara's research paper proved the existence of nontrivial symmetries in the data set.
Yara 的研究論文證明了該資料集中存在非零對稱性。
- non-zero
more general term; not limited to technical contexts
- non-vanishing
specific to mathematics, means not becoming zero
- trivial
in mathematics, a 'trivial' solution is one where all variables equal zero
文法句型
nontrivial + noun
用法筆記
Primarily used in mathematics, physics, and computer science. The term contrasts with 'trivial', where a solution is obvious or all values are zero.