text: # 域中分數場
  
  ## 等價設定
  
  ${\displaystyle {\textbf {D}}}$ 係一個域。將${\displaystyle P={\textbf {D}}\backslash ({\textbf {D}}^{\times }\cup \{0\})=\{(a,b):a,b\in {\textbf {D}},b\neq 0\}}$
  
  • 自反性${\displaystyle (a,b)\equiv (a,b)\iff ab=ab}$
  • 對稱性${\displaystyle (a,b)\equiv (c,d)\iff ad=cb\iff (c,d)\equiv (a,b)}$
  • 傳遞性${\displaystyle (a,b)\equiv (c,d)\iff ad=cb}$ 同時${\displaystyle (c,d)\equiv (e,f)\iff cf=de}$ ${\displaystyle af=be\iff (a,b)\equiv (e,f)}$
  
  ${\displaystyle P/\equiv }$ 叫做${\displaystyle Q({\textbf {D}})}$ ，而${\displaystyle Q({\textbf {D}})}$ 就係分數場（Field of Fractions）
  
  ## 加法同乘法
  
  ${\displaystyle Q({\textbf {D}})}$ 入面，都會有加法同乘法，而佢哋都係普通嘅加同乘。
  
  ${\displaystyle {\frac {a}{b}}={\frac {a'}{b'}}}$ ${\displaystyle {\frac {c}{d}}={\frac {c'}{d'}}}$
  
  ${\displaystyle ab'=a'b}$ ${\displaystyle cd'=c'd}$
  
  ${\displaystyle (ad+bc)b'd'=ab'd'+bb'cd'=a'bdd'+bb'c'd=(a'd'+b'c')bd}$
  
  ${\displaystyle {\frac {a}{b}}\cdot {\frac {c}{d}}={\frac {a'}{b'}}\cdot {\frac {c'}{d'}}}$