论文标题
一种用于求解自由基任意程度的可解多项式方程的算法
An Algorithm for Solving Solvable Polynomial Equations of Arbitrary Degree by Radicals
论文作者
论文摘要
这项工作提供了一种方法（一种算法），用于求解任意程度的可解决的单一代数方程$ f（x）= 0 $（$ f（x）\ in \ mathbb {q} [x] $），并获得精确的自由基。此方法要求我们知道Galois组是$ f（x）$的根部的排列组，并以足够的精度为基础。当然，近似根不是必需的，但可以帮助减少计算数量。算法复杂性与$ f（x）$的Galois组大小的第四功率大致成正比。整个算法无需处理巨大的多项式或减少对称多项式。
This work provides a method(an algorithm) for solving the solvable unary algebraic equation $f(x)=0$ ($f(x)\in\mathbb{Q}[x]$) of arbitrary degree and obtaining the exact radical roots. This method requires that we know the Galois group as the permutation group of the roots of $f(x)$ and the approximate roots with sufficient precision beforehand. Of course, the approximate roots are not necessary but can help reduce the quantity of computation. The algorithm complexity is approximately proportional to the 4th power of the size of the Galois group of $f(x)$. The whole algorithm doesn't need to deal with tremendous polynomials or reduce symmetric polynomials.
