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Root

Usage

Root[f, k] 表示多项式方程f[x] Equal 0 的第k个根.


Notes

f 必须是一个诸如(#^5 - 2 # + 1)& Function对象.
Root[f, k] 自动进行化简以使得 f 具有可能的最小次数和最小整系数.
Root 把实根放在复根之前,而把一对复共轭根放在相邻位置.
• 多项式f[x]的系数可以包含符号参数.
• 对线性的和二次多项式 f[x],Root[f, k]自动化简为显式有理形式或根形式.
N 给出Root对象的近似数值.
• 诸如 Abs, Re, RoundLess的运算可以使用到Root对象上.
• 如果 f 不包含符号参数, 则Root[f, k]被视作一个数值量.
• 缺省情形下,Root使用近似数值方法对多项式的根进行分离. 该方法何种情况下失败还不知道,然而 SetOptions[Root, ExactRootIsolation->True]将使用慢得多的但完全严格的方法产生 Root.
• 参见Mathematica 全书: 1.5.7节 和 3.4.2节.
• 相关包: Algebra`RootIsolation`.
Further Examples

The polynomial that appears in Root is automatically reduced to a minimal polynomial in the form of a pure function.

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It can be cast into the form of a polynomial in one variable.

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In the quadratic case the Root object is automatically expressed in terms of radicals.

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For degree three or higher, Root objects are not automatically expressed in terms of radicals.

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ToRadicals attempts to express all Root objects in terms of radicals.

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To get a Root object from performing algebraic operations on algebraic numbers, use RootReduce.

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Here is a more complicated expression involving algebraic numbers.

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Sometimes RootReduce gives a simple result. This is the product of the roots of the polynomial.

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