论文标题
Sturm的定理带有端点
Sturm's Theorem with Endpoints
论文作者
论文摘要
Sturm的定理是19世纪的基本结果，将多项式$ f $的真实根数与符号交替的数量在类似多项式分裂的计算中与符号交替的数量有关。我们提供了Sturm定理的简短证明，包括数字上的烦恼案例（在许多已发布的帐户中忽略），其中间隔端点是$ f $的根。
Sturm's Theorem is a fundamental 19th century result relating the number of real roots of a polynomial $f$ in an interval to the number of sign alternations in a sequence of polynomial division-like calculations. We provide a short direct proof of Sturm's Theorem, including the numerically vexing case (ignored in many published accounts) where an interval endpoint is a root of $f$.
