[英]Exponential to trigonometric conversion in SymPy while simplifying - a stubborn expression
I have been trying to simplify我一直在努力简化
exp(2*I*N) - 1)**2/((exp(2*I*N) - 1)**2 - 4*exp(2*I*N)*cos(N)**2)
Where the answer should be (sin N)^2, but the output is same as input.答案应该是 (sin N)^2,但输出与输入相同。
I have tried .rewrite(cos)
and then simplify, trigsimp, expand and pretty much all I could discover quickly from help sources.我尝试过.rewrite(cos)
然后简化、trigsimp、扩展以及几乎所有我可以从帮助来源中快速发现的内容。
Rewriting in terms of exp
instead of cos
is more helpful:用exp
而不是cos
重写更有帮助:
expr.rewrite(exp).simplify()
returns -cos(2*N)/2 + 1/2
which is visibly equivalent to sin(N)**2
.返回-cos(2*N)/2 + 1/2
,这显然等同于sin(N)**2
。 Clean it up with用它清理
expr.rewrite(exp).simplify().trigsimp()
getting sin(N)**2
得到sin(N)**2
Old answer, might still be of value: You probably meant N
to be real, so let's declare it as such.旧答案,可能仍然有价值:您可能意味着N
是真实的,所以让我们这样声明。
Given a mix of complex exponentials and trigonometric functions, it will probably help to separate the real and imaginary parts with as_real_imag()
.考虑到复杂的指数和三角函数的混合,使用as_real_imag()
分离实部和虚部可能会有所帮助。 A direct application does not do much beyond putting re(...) and im(...), so rewriting in exponentials and expanding the squares/products is advisable first:除了放置 re(...) 和 im(...) 之外,直接应用程序并没有做太多事情,因此建议首先以指数形式重写并扩展平方/乘积:
N = symbols('N', real=True)
expr = (exp(2*I*N) - 1)**2/((exp(2*I*N) - 1)**2 - 4*exp(2*I*N)*cos(N)**2)
result = [a.trigsimp() for a in expr.rewrite(cos).expand().as_real_imag()]
Result: [sin(N)**2, 0]
, meaning the real and imaginary parts of the expression.结果: [sin(N)**2, 0]
,表示表达式的实部和虚部。 It can be recombined into a single expression with result[0] + I*result[1]
.它可以用result[0] + I*result[1]
重新组合成单个表达式。
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