You can also use refine() to select specific parts from a Piecewise.
>>> refine(expr, Ne(w, 0))
6*sin(w/2)/w**3 - 2*sin(3*w/2)/w**3
Aaron Meurer
On Wed, Sep 7, 2022 at 9:36 AM Oscar <oscar.j.benja...@gmail.com> wrote:
>
>
>
> On Wednesday, 7 September 2022 at 15:38:44 UTC+1 brombo wrote:
>>
>> I calculated an integral g when printed grives:
>>
>> Piecewise((sin(w/2)/w - 2*cos(w/2)/w**2 + 4*sin(w/2)/w**3, Ne(w, 0)), (2/3,
>> True)) + 2*Piecewise((-sin(w/2)/(2*w) + cos(w/2)/w**2 + sin(w/2)/w**3 -
>> sin(3*w/2)/w**3, Ne(w, 0)), (1/6, True))
>
>
> So this is what we have:
>
> In [13]: w = symbols('w')
>
> In [14]: result = Piecewise((sin(w/2)/w - 2*cos(w/2)/w**2 + 4*sin(w/2)/w**3,
> Ne(w, 0)), (2/3, True))
> ...: + 2*Piecewise((-sin(w/2)/(2*w) + cos(w/2)/w**2 + sin(w/2)/w**3 -
> sin(3*w/2)/w**3, Ne(w, 0)),
> ...: (1/6, True))
>
> In [15]: result = nsimplify(result)
>
> In [16]: result
> Out[16]:
> ⎛⎧ ⎛w⎞ ⎛w⎞ ⎛w⎞ ⎞ ⎛⎧ ⎛w⎞ ⎛w⎞ ⎛w⎞
> ⎛3⋅w⎞ ⎞
> ⎜⎪sin⎜─⎟ 2⋅cos⎜─⎟ 4⋅sin⎜─⎟ ⎟ ⎜⎪ sin⎜─⎟ cos⎜─⎟ sin⎜─⎟
> sin⎜───⎟ ⎟
> ⎜⎪ ⎝2⎠ ⎝2⎠ ⎝2⎠ ⎟ ⎜⎪ ⎝2⎠ ⎝2⎠ ⎝2⎠
> ⎝ 2 ⎠ ⎟
> ⎜⎪────── - ──────── + ──────── for w ≠ 0⎟ ⎜⎪- ────── + ────── + ────── -
> ──────── for w ≠ 0⎟
> ⎜⎨ w 2 3 ⎟ + 2⋅⎜⎨ 2⋅w 2 3
> 3 ⎟
> ⎜⎪ w w ⎟ ⎜⎪ w w
> w ⎟
> ⎜⎪ ⎟ ⎜⎪
> ⎟
> ⎜⎪ 2/3 otherwise⎟ ⎜⎪ 1/6
> otherwise⎟
> ⎝⎩ ⎠ ⎝⎩
> ⎠
>
>>
>>
>> First, how can I extract from g (without cutting and pasting the output)
>> what I really want which is:
>>
>> (sin(w/2)/w - 2*cos(w/2)/w**2 + 4*sin(w/2)/w**3)+2*(-sin(w/2)/(2*w) +
>> cos(w/2)/w**2 + sin(w/2)/w**3 - sin(3*w/2)/w**3)
>
>
> In [23]: piecewise_fold(result)
> Out[23]:
> ⎧ ⎛w⎞ ⎛3⋅w⎞
> ⎪6⋅sin⎜─⎟ 2⋅sin⎜───⎟
> ⎪ ⎝2⎠ ⎝ 2 ⎠
> ⎪──────── - ────────── for w ≠ 0
> ⎨ 3 3
> ⎪ w w
> ⎪
> ⎪ 1 otherwise
> ⎩
>
> In [24]: piecewise_fold(result).args[0][0]
> Out[24]:
> ⎛w⎞ ⎛3⋅w⎞
> 6⋅sin⎜─⎟ 2⋅sin⎜───⎟
> ⎝2⎠ ⎝ 2 ⎠
> ──────── - ──────────
> 3 3
> w w
>
>>
>>
>> Secondly, I can substitute y = w/2. In the resulting expression force
>> expansion of sin(3*y). trigsimp doesn't do that. I know the answer is
>> supposed to be of the form (sin(y)/y)**3.
>
>
>
> In [26]: _.subs(w, 2*y)
> Out[26]:
> 3⋅sin(y) sin(3⋅y)
> ──────── - ────────
> 3 3
> 4⋅y 4⋅y
>
> In [27]: _.expand(trig=True)
> Out[27]:
> 3
> sin (y)
> ───────
> 3
> y
>
> --
> Oscar
>
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