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quotient sth
quotient 作动词时，宾语通常是数学对象，如集合、群或空间。
The algorithm quotients the set of all possible states.
该算法对所有可能状态的集合取商。
取商；作商
quotienting — present participle of quotient
先理解核心含义，再看它在真实句子里的用法。
取商；作商
To identify elements within a mathematical structure so as to create a quotient.
The algorithm quotients the set of all possible states.
该算法对所有可能状态的集合取商。
数学术语，常见于商群、商空间等。
To identify elements within a mathematical structure so as to create a quotient.
quotient
Base
原形
quotients
3rd person
第三人称单数
quotienting
-ing
现在分词
quotiented
Past
过去式
quotiented
Past participle
过去分词
We quotient the set by an equivalence relation.
我们用等价关系对集合求商。
The algorithm is quotienting the group step by step.
该算法正在逐步对群取商。
The team quotiented the ring to simplify the proof.
研究团队对环取商以简化证明。
规则动词，数学中表示按等价关系或子结构取商。
We quotient the set by an equivalence relation to simplify its structure.
我们通过等价关系对该集合作商来简化其结构。
She quotiented the group by its center to study the automorphisms.
她对该群以其中心作商来研究自同构。
Quotienting a topological space by a group action can create interesting new shapes.
按群作用对拓扑空间作商可以创造出有趣的新形状。
quotient 作动词时，宾语通常是数学对象，如集合、群或空间。
The algorithm quotients the set of all possible states.
该算法对所有可能状态的集合取商。
这里 by 引出用于识别的等价关系或子结构；被动式 be quotiented by 也很常见。
We quotient the group by its normal subgroup.
我们把这个群模其正规子群取商。
Not this
We quotient the group with the normal subgroup.
Use this
We quotient the group by the normal subgroup.
动词 quotient 表示“作商”时，须用介词 by 引出作商所用的子结构，不能用 with。
Not this
We made the quotient of the group by the normal subgroup.
Use this
We quotiented the group by the normal subgroup.
quotient 在此是动词，不应借助 make 加名词的结构；直接用动词（过去式 quotiented）表示“作商”。
Not this
We quotiented by the normal subgroup.
Use this
We quotiented the group by the normal subgroup.
quotient 是及物动词，须明确说出对哪个数学结构作商，不能省略宾语。
Focus on the distinctions below. Other candidates are kept compact until a reliable usage note is available.
按……作商；通过取商消去
We quotient out by the ideal to obtain the quotient ring.
我们按该理想作商，得到商环。
对……取商；关于……作商
Quotient the group by its center to get a simpler group.
把该群对它的中心取商，得到一个更简单的群。
对群按……取商
We quotient a group by any normal subgroup.
我们用任意正规子群对一个群取商。
对空间按……取商
We quotient a space by a group action to obtain an orbit space.
我们用群作用对一个空间取商，得到轨道空间。
被……取商；按……作商
The module is quotiented by a submodule to form a new algebraic structure.
该模按一个子模取商，以形成新的代数结构。
Use quotienting naturally, then get feedback on meaning, tone, grammar, and phrasing.
Revisit a common error or keep this word in your review list.
联想：quotient 以 quot- 开头，像“quote（引用）”，把一堆元素按规则归并成一份“商”，动词就是“作商”。
语域：formal 常见场景：mathematics、abstract algebra、academic writing quotient 作动词时是数学或抽象代数领域的专业术语，多用于学术或技术语境，比较常见于被动结构（如 be quotiented），日常口语中很少使用。
这些词都以 /ʃənt/ 结尾，与 quotient 的末尾音相同，但重音位置不同，所以不构成严格押韵。patient 的末尾拼写 tient 与 quotient 完全相同；其余词拼作 cient，也发 /ʃənt/。注意 quotient 中的 'ti' 读 /ʃ/，不是 /t/；不要按拼写把 'tient' 读成 /tɪənt/。
Dictionary facts from ECDICT, WIKTIONARY.