设F是任意域；以0，1分别表示它的零元和乘法单位元。若-1不能表作F中的平方和，就称F为实域（或者形式实域）。常见的有理数域Q和实数域R，都是这个意义下的实域；但复数域C以及有限域，都不是实域。
实域中两个真理之间的最短路程是通过复域。
Jacques Hadamard the shortest path between two truths in the real domain passes through the complex domain.
通过运用吴消元法求解电力系统潮流方程，求得了全部实域精确解，同时避免了因以数值迭代方法求解出现雅可比矩阵奇异的现象。
By using Wu s method, all the precise solutions of power flow equations are worked out without encountering the numerical difficulty of ill-condition.
证明了任一环有代数封闭的扩张环，且实封闭域上的四元数体是代数封闭的，给出了代数封闭环的若干性质。
The two theorems are proved that any ring can be extended into an algebraically closed ring and that the quaternionic skew field over a real closed field is algebraically closed.
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