song hữu tỉ
Definition
- Adjective (Mathematics):
- Birationally equivalent: Describes two algebraic varieties (like curves or surfaces) that are connected by a birational transformation, meaning there exists a rational map between them that has a rational inverse. This indicates the varieties are essentially the same from a birational geometry perspective, sharing key properties.
- Related to birationality: Pertaining to the concept or property of being birational.
Usage Examples
- Adjective:
- Hai đường cong này là song hữu tỉ. (These two curves are birationally equivalent.)
- Phép biến đổi song hữu tỉ bảo toàn một số tính chất hình học. (A birational transformation preserves certain geometric properties.)
- Lý thuyết về các đa tạp song hữu tỉ rất quan trọng trong hình học đại số. (The theory of birationally equivalent varieties is very important in algebraic geometry.)
Advanced Usage
- In advanced mathematics, "song hữu tỉ" is a fundamental concept in algebraic geometry. Two varieties being "song hữu tỉ" means they have isomorphic function fields, which allows one to study one variety by studying the other.
Variants and Related Words
Ánh xạ song hữu tỉ (n): Birational map.
- Ánh xạ song hữu tỉ thiết lập mối quan hệ giữa hai đa tạp. (The birational map establishes a relationship between the two varieties.)
Tương đương song hữu tỉ (n): Birational equivalence.
- Tương đương song hữu tỉ là một quan hệ tương đương. (Birational equivalence is an equivalence relation.)
Synonyms
- Birationally equivalent
- Birational (in the context of "birational map" or "birational geometry")
Notes on Usage
- "Song hữu tỉ" is a specialized mathematical term. It is a compound word where "song" implies a mutual or two-way relationship and "hữu tỉ" means "rational." It is almost exclusively used in academic and technical contexts related to higher mathematics, particularly algebraic geometry.
- It is not used in everyday conversation.