> For the complete documentation index, see [llms.txt](https://johannesliu.gitbook.io/learning-advanced-mathematics-with-python/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://johannesliu.gitbook.io/learning-advanced-mathematics-with-python/3.0-sympy_foundation/3.1-basic_manipulator.md).

# 3.1 基本操作

## 3.1.1 替换

使用数学表达式最常见的一种方法是替换。替换将表达式中某物的所有实例替换为另一物。这是使用symbols对象的subs方法完成的。

### 普通替换

例：替换$$cos(x)+sin(pi/2)$$中的$$x$$为 $$\frac{\pi}{2}$$

```python
[]:expr=cos(x)+sin(pi/2)

expr.subs(x, pi/2)
```

\[]: ![](/files/toso8FTlgWmlm1WJCkdZ)

### 循环替换

例：对表达式$$1/(1+x)$$，执行5次将$$x$$替换为$$\frac{1}{1+x}$$的循环替换

```python
[]:expr=1/(1+x)

for i in range(5): expr=expr.subs(x, 1/(1+x))

expr
```

\[]: ![](/files/hj9I09Bfl8liOZzMelBs)

## 3.1.2 字符串转为SymPy表达式

使用simpify函数，可以将字符串类型的表达式转为SymPy表达式 例：将字符串类型表达式"x\*\*2+2\*x+1"转为SymPy表达式：

```python
[]:str_expr=’x\*\*2+2\*x+1’

expr=sympify(str_expr)

expr
```

\[]: ![](/files/Df5TrpdifFuE7reC9A6l)

## 3.1.3 表达式求值

使用exalf(precision)可以对数值表达式求值，precision为小数保留位数，precision默认为15。

例：对表达式$$\sqrt{13}$$求值：

```python
[]:expr=sqrt(13)

expr.evalf(13)
```

\[]: ![](/files/HoTETK1uVkFb9EWm8Tzb)

## 3.1.4 使用NumPy和SciPy计算

尽管subs和evalf可以很好的帮助我们进行计算，但是如果我们希望同时代入大量参数到一个公式进行计算，那么这时候你可能就忍受不了SymPy的运行效率了。

另外SymPy在计算精度上不如NumPy和SciPy，如果对机器精度有较高的要求的话，应该使用NumPy或SciPy这样的库。

将一个SymPy符号表达式转换成一个数值计算表达式最简单的方法是使用lambdify函数。lambdify的作用类似于lambda函数，只不过它将SymPy名称转换为特定数值库的名称，通常是NumPy。（？）

lambdify()函数用于转换表达式进行数值计算时需要指定三个参数，分别是变量，表达式和数值库。

例 将符号表达$$\sin x + cos x$$转为函数，并分别将0\~9十个整数代入计算。

```python
[]:import numpy

arr=numpy.arange(10)

expr=sin(x)+cos(x)

f=lambdify(x, expr, 'numpy')

type(f)

[]:function

[]:f(arr)

[]:array([ 1. , 1.38177329, 0.49315059, -0.84887249, -1.41044612, -0.67526209, 0.68075479, 1.41088885, 0.84385821, -0.49901178])
```


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