SymPy:我可以安全地区分 atan2() 吗? [英] SymPy: Can I safely differentiate atan2()?

问题描述

我想获得一个符号表达式，它是 atan2(y,x) 的导数，其中 y 和 x 是一些带有变量 z 的表达式.我可以安全地假设 diff(atan2(y,x),z) 给了我我想要的吗?

I would like to obtain a symbolic expression which is the derivative of atan2(y,x), where y and x are some expressions with a variable z. Can I safely assume that diff(atan2(y,x),z) gives me what I want?

在 math.stackexchange.com 中有证据表明atan2 在 (-pi,pi) 中是连续可微的，但在 SymPy 中是吗?

In math.stackexchange.com there is a proof that atan2 is continuously differentialable in (-pi,pi), but is it in SymPy?

推荐答案

atan2(y, x) 关于 x 和 y 的偏导数 由 SymPy 计算为

The partial derivatives of atan2(y, x) with respect to x and y are computed by SymPy as

-y/(x**2 + y**2) 
 x/(x**2 + y**2)

并且这些表达式是连续的，只要 x, y 不立即变成零.(当然，假设是实参 x、y - 我认为没有人会在 atan2 中放入复数).

and these expressions are continuous as long as x, y do not turn into zero at once. (Assuming real arguments x, y, of course - I don't think anyone puts complex numbers in atan2).

以上公式是硬编码的herea>，所以我们可以非常确定 SymPy 会返回它们.

The above formulas are hardcoded here, so we can be very sure that SymPy will return them.

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