python - Sympy - 比较表达式

Question

有没有办法检查两个表达式在数学上是否相等？我期望tg(x)cos(x) == sin(x) 输出True，但它输出False。有没有办法与 sympy 进行这样的比较？另一个例子是(a+b)**2 == a**2 + 2*a*b + b**2 出人意料地也输出 False。

我发现了一些类似的问题，但没有一个涵盖这个确切的问题。

Answer 1

来自 the SymPy documentation

== represents exact structural equality testing. “Exact” here means that two expressions will compare equal with == only if they are exactly equal structurally. Here, (x+1)^2 and x^2+2x+1 are not the same symbolically. One is the power of an addition of two terms, and the other is the addition of three terms.

It turns out that when using SymPy as a library, having == test for exact symbolic equality is far more useful than having it represent symbolic equality, or having it test for mathematical equality. However, as a new user, you will probably care more about the latter two. We have already seen an alternative to representing equalities symbolically, Eq. To test if two things are equal, it is best to recall the basic fact that if a=b, then a−b=0. Thus, the best way to check if a=b is to take a−b and simplify it, and see if it goes to 0. We will learn later that the function to do this is called simplify. This method is not infallible—in fact, it can be theoretically proven that it is impossible to determine if two symbolic expressions are identically equal in general—but for most common expressions, it works quite well.

作为您特定问题的演示，我们可以使用等价表达式的减法并像这样与 0 进行比较

>>> from sympy import simplify
>>> from sympy.abc import x,y
>>> vers1 = (x+y)**2
>>> vers2 = x**2 + 2*x*y + y**2
>>> simplify(vers1-vers2) == 0
True
>>> simplify(vers1+vers2) == 0
False