Euler

Euler是一个数学计算工具，提供了数值计算、符号计算、数学绘图、数学文档等多种功能。

安装

Euler支持Windows、Linux和Mac OS X操作系统。访问Euler官网下载对应的安装包并安装即可。

数值计算

Euler提供了多种数值计算方法，如牛顿迭代法、龙格库塔法、辛普森法等。以下是用牛顿迭代法求方程x^2-2=0的解的示例：

from euler.math.num_method import newton_method

def f(x):
    return x ** 2 - 2

def fprime(x):
    return 2 * x

x0 = 1
tol = 1e-6

x, num_iter = newton_method(f, fprime, x0, tol)

print('x:', x)
print('num_iter:', num_iter)

输出：

x: 1.4142135623746899
num_iter: 4

符号计算

Euler支持符号计算，可以方便地进行代数运算和微积分运算。以下是计算(x^2+3x+2)/(x+2)的值的示例：

from euler.math.symbolic import *

x = Symbol('x')
f = (x ** 2 + 3 * x + 2) / (x + 2)

print(f)
print(f.simplify())

输出：

(x^2+3*x+2)/(x+2)
x+1

数学绘图

Euler提供了多种绘图功能，如2D绘图、3D绘图、参数方程绘图等。以下是绘制正弦曲线的示例：

from euler.math.plot import Plot

plot = Plot()

plot.add_func(lambda x: math.sin(x), 'sin(x)')

plot.show()

绘制效果如下图所示：

数学文档

Euler提供了方便的文档编辑功能，可以用LaTeX语法编写数学公式和文档。以下是一个使用Euler编写的LaTeX文档的示例：

\documentclass{article}

\begin{document}

\section{Introduction}
Euler is a powerful mathematical tool that provides numerical computation, symbolic computation, mathematical plotting and document editing capabilities.

\section{Symbolic Computation}
Euler supports symbolic computation, which makes it easy to perform algebraic and calculus operations. Here is an example of computing the value of $(x^2+3x+2)/(x+2)$ using the simplify function:
$$
\frac{x^2+3x+2}{x+2}=\frac{(x+1)(x+2)}{x+2}=x+1
$$

\section{Numerical Computation}
Euler provides several numerical computation methods, such as Newton's method, Runge-Kutta method, Simpson's rule, and so on. Here is an example of using Newton's method to find the solution of $x^2-2=0$:
$$
f(x)=x^2-2,\ f'(x)=2x\\
x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}
$$
Starting from $x_0=1$, we get $x=1.4142135623746899$ after 4 iterations.

\section{Mathematical Plotting}
Euler provides powerful plotting capabilities that can generate 2D plots, 3D plots, parametric plots, and so on. Here is an example of plotting the sine function:
$$
y=\sin(x)
$$
![sin(x)](https://github.com/OSsez/Euler/blob/master/doc/images/sin.png)

\section{Conclusion}
Euler is a comprehensive mathematical tool that can handle various mathematical tasks with ease and flexibility.

\end{document}

编译后的文档效果如下图所示：

总结

Euler是一款功能强大的数学计算工具，具有多种数值计算、符号计算、数学绘图和数学文档编辑功能。无论您是在学术研究、工程计算还是数学教育上，都能用它高效地完成各种数学任务。