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Simplify

Usage

Simplify[expr]expr上执行一组代数变换, 并返回它找到的最简单形式.
Simplify[expr, assum] 使用假定进行化简.


Notes

Simplify 尝试在表达式上进行展开,因式分解和其它变换,并返回所得到的最简单形式.
• 可以使用的可选项:
"\!\(\*StyleBox[\"\\\"ComplexityFunction\\\"\", \"MR\"]\) ""\!\(\*StyleBox[\"\\\"Automatic\\\"\", \"MR\"]\) """怎样估计所生成的每种形式的复杂度
"\!\(\*StyleBox[\"\\\"TimeConstraint\\\"\", \"MR\"]\) ""\!\(\*StyleBox[\"\\\"300\\\"\", \"MR\"]\) """尝试进行任何特殊变换的时间(以秒为单位)
"\!\(\*StyleBox[\"\\\"TransformationFunctions\\\"\", \"MR\"]\) ""\!\(\*StyleBox[\"\\\"Automatic\\\"\", \"MR\"]\) """对表达式进行变换的函数
"\!\(\*StyleBox[\"\\\"Trig\\\"\", \"MR\"]\) ""\!\(\*StyleBox[\"\\\"True\\\"\", \"MR\"]\) """是否进行同代数变换以及三角变换
• 假定可以由方程,不等式,诸如x  Integers的域声明,以及这些的逻辑组合组成.
• 例如: Simplify[Sqrt[x^2], x  Reals]LongRightArrow .
Simplify可被用到方程,不等式,以及域声明上.
• 例如: Simplify[x^2 > 3, x > 2]LongRightArrow .
• 指定满足不等式的对象总被假定为实数. • 例如: Simplify[x  Reals, x > 0]LongRightArrow .
FullSimplify 进行比Simplify 更深层次的化简.
• 参见Mathematica 全书: 1.4.4节, 1.4.6节 和 3.3.9节.
Further Examples

Simplify factors these polynomials.

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Simplify may not factor completely.

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Here Simplify does nothing at all. Simplicity is largely based on the expression's LeafCount.

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The leaf count is not the only consideration, however. Here, Log[256] is considered simpler than 4 Log[4], but Log[10000] is not simpler than 4 Log[10]. You can override this behavior; see the Further Examples for ComplexityFunction.

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This integral returns a sum of three terms.

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Differentiating the result gives an expression that is more complicated than the original integrand, but mathematically equivalent to it.

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Simplify gets back to the original form of the expression.

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Using Assumptions

Variables in an inequality are implicitly assumed to be real.

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The first assumption says that m and n are both integers.

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It is not true in general that  .

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If both exponents are integers,  simplifies to  .

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Here are some more examples using assumptions.

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See also the Further Examples for FullSimplify and for the option ComplexityFunction.