在符号中运行表达式的 AST

Question

我正在使用sympy来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，例如先遍历节点深度。我该怎么做？

Answer 1

一个简单的深度优先旅行是这样的：

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)

使用其他参数，可以达到更复杂的目标，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：

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