automorphism

automorphism的音标是["ɔːtəʊmɔːsɪfɪk]，意思是“自同态”。

速记技巧：可以将单词划分为音节，记住每个音节的首个字母，从而快速记忆。例如，可以将单词划分为“auto”和“morph”，其中“auto”可以联想到“自己”，“morph”可以联想到“形态”，从而联想到“自己改变形态”的意思，帮助记忆。

Automorphism这个词源于希腊语词根“auto”和“morph”组合而成，意为“自我形态”。它的变化形式包括名词形式automorphism和形容词形式automorphic。

相关单词：

automaton: 自动机械，机器人，机械人

self-morphing: 自变形，自我改变的

isomorphic: 同构的，相似的

homomorphism: 同态，相似性

metamorphic: 变形的，变化的

autonomy: 自立，自治

autogenic: 自源的，自主的

autotransformation: 自变换

self-transformation: 自我转变

self-similarity: 自我相似性

以上单词都与automorphism这个词有某种程度的关联，它们都表示自我改变、相似性或自立等含义。每个单词都有其独特的语境和用法，需要结合具体语境来理解和使用。

automorphism短语：

1. automorphism group

2. automorphism mapping

3. automorphic function

4. automorphic representation

5. automorphic field

6. automorphic form

7. automorphic automorphism

双语例句：

1. The automorphism group of a group is the set of all elements that leave the group invariant under an automorphism.

2. The automorphic function of a mathematical object is a function that transforms in a way that preserves its properties.

3. The automorphic field of a number field is a field extension that is invariant under the action of the Galois group.

4. The automorphism mapping of a surface preserves its topology and geometry.

5. The automorphism of a code is a transformation that leaves the code invariant.

6. The automorphic representation of a group is a representation that transforms in a way that preserves its properties under the action of the group.

7. The automorphism of a text can be used to generate new variations of it.

英文小作文：

Automorphisms are transformations that leave a mathematical object unchanged. They are an essential tool in many fields, including number theory, geometry, and mathematical physics. Automorphisms can be used to study the structure and properties of mathematical objects, and they can also be used to generate new variations of them. For example, automorphisms can be used to generate new fields from number fields, or they can be used to generate new representations from existing ones. Understanding automorphisms is crucial for understanding the structure and properties of mathematical objects, and it is also essential for developing new mathematical tools and methods.