Word · Frequency #25046
quotienting
取商；作商
quotienting is the present participle of quotient.
To identify elements within a mathematical structure so as to create a quotient.
数学术语，常见于商群、商空间等。
- 1.
To identify elements within a mathematical structure so as to create a quotient.
商；份额
In use
We quotient the set by an equivalence relation to simplify its structure.
She quotiented the group by its center to study the automorphisms.
Quotienting a topological space by a group action can create interesting new shapes.
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。
quotient sth by sth
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。
Verb forms
base quotient · third person quotients · -ing quotienting · past quotiented · past participle quotiented
规则动词，数学中表示按等价关系或子结构取商。
Common mistakes
We quotient the group with the normal subgroup.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。
We made the quotient of the group by the normal subgroup.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”。
We quotiented by the normal subgroup.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。
Connections
Collocations
- quotient out by
- 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。
- quotient by
- 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。
- quotient a group by
- 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。
- quotient a space by
- 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。
- quotiented by
- 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。
Learner notes
Memory Tip
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”。
Context & Register
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。
Pronunciation & Spelling
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/。
Learn the forms together
页面下方列出了常见词形变化。学习时注意它们在句子中的语法位置。
Dictionary facts from ECDICT, WIKTIONARY.