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Roots

Usage

Roots[lhsEqualrhs, var] 产生一个表示多项式根的分离的方程。


Notes

Roots 在试图求根时使用FactorDecompose
• 可以通过应用N求根的数值解。
Roots 可以取下面的选项:
"\!\(\*StyleBox[\"\\\"Cubics\\\"\", \"MR\"]\) ""\!\(\*StyleBox[\"\\\"True\\\"\", \"MR\"]\) """是否对立方体产生确定的解
"\!\(\*StyleBox[\"\\\"EquatedTo\\\"\", \"MR\"]\) ""\!\(\*StyleBox[\"\\\"Null\\\"\", \"MR\"]\) """所求解的变量是地位相同的表达式
"\!\(\*StyleBox[\"\\\"Modulus\\\"\", \"MR\"]\) ""\!\(\*StyleBox[\"\\\"Infinity\\\"\", \"MR\"]\) """整数模
"\!\(\*StyleBox[\"\\\"Multiplicity\\\"\", \"MR\"]\) ""\!\(\*StyleBox[\"\\\"1\\\"\", \"MR\"]\) """在最后的解列表中解的个数
"\!\(\*StyleBox[\"\\\"Quartics\\\"\", \"MR\"]\) ""\!\(\*StyleBox[\"\\\"True\\\"\", \"MR\"]\) """是否对四次方程产生显式解
"\!\(\*StyleBox[\"\\\"Using\\\"\", \"MR\"]\) ""\!\(\*StyleBox[\"\\\"True\\\"\", \"MR\"]\) """求解的辅助方程
• 当Solve和相关函数不能产生确定的解时,产生Roots 。经常在这样的情况下给出选项。
• 当出现多于一个根时,Roots 给出几个等式方程。
• 参见Mathematica 全书: 1.5.7 and 节 3.4.1.
• 相关包: Algebra`RootIsolation`.
Further Examples
Further Examples

The roots of some cubic and quartic polynomials can be expressed in terms of radicals using Cardano's formulas. The results, while explicit, are often very complicated.

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You can use algebraic numbers instead.

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If any one of the coefficients of the polynomial is inexact, Roots finds approximate roots.

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You can find the roots of univariate polynomials for any finite modulus. When the modulus is not prime there may be more roots than the degree of the polynomial. This is in contrast to the fundamental theorem of algebra. It states that over the complexes there are as many roots (counting multiplicity) as the degree.

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