在sympy中运行表达式的AST

问题描述：

我正在使用sympy计算复杂函数表达式的一些高阶导数。我想遍历表达式的AST，例如首先通过节点深度。我该怎么做？

I'm using sympy to compute some higher order derivatives of a complicated function expression. I'd like to traverse the AST of the expression, e.g. go through the nodes depth first. How do I do that ?

答

简单的深度优先旅行是这样的：

A simple depth-first travel would be like this:

from sympy import pi, sin
from sympy.abc import a,x,y

def depth_first_traverse(expr):
    for arg in expr.args:
        depth_first_traverse(arg, depth+1, new_marks+'+---', parent_ind=ind)
    if len(expr.args) == 0:
        # we reached a leaf of the tree
        pass  # do something with leaf expr
    else:
        pass  # do something with compound expr
depth_first_traverse(sin(a*x*pi+1.5)/y)

带有附加参数，更多可以达到复杂的目标，例如以深度优先的顺序打印树，同时显示所有内容如何组合在一起：

With additional parameters, more complex goals can be reached, for example printing the tree in depth-first order while showing how everything fits together:

from sympy import srepr, pi, sin
from sympy.abc import a,x,y

def depth_first_traverse(expr, depth=0, marks='', parent_ind=None):
    for ind, arg in enumerate(expr.args):
        new_marks = marks.replace('+', '|').replace('-', ' ')
        if parent_ind == 0:
            new_marks = new_marks[:-4] + ' ' + new_marks[-3:]
        depth_first_traverse(arg, depth+1, new_marks+'+---', parent_ind=ind)
    if len(expr.args) == 0:
        print(marks, end="> ")
        print("symbol", srepr(expr))
    else:
        print(marks, end="+ ")
        print("function", expr.func, "had", len(expr.args), "arguments")

    print(marks.replace('+', '|').replace('-', ' '))

depth_first_traverse(sin(a*x*pi+1.5)/y)

输出：

    +---> symbol Symbol('y')
    |   
    +---> symbol Integer(-1)
    |   
+---+ function <class 'sympy.core.power.Pow'> had 2 arguments
|   
|       +---> symbol Float('1.5', precision=53)
|       |   
|       |   +---> symbol pi
|       |   |   
|       |   +---> symbol Symbol('a')
|       |   |   
|       |   +---> symbol Symbol('x')
|       |   |   
|       +---+ function <class 'sympy.core.mul.Mul'> had 3 arguments
|       |   
|   +---+ function <class 'sympy.core.add.Add'> had 2 arguments
|   |   
+---+ function sin had 1 arguments
|   
+ function <class 'sympy.core.mul.Mul'> had 2 arguments

在sympy中运行表达式的AST

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