[sympy] Re: Combine logs in a large expression

[Boris Kheyfets]

Images were working when I posted. Any way the latex code shown instead of 
images is correct. Here I attach a MathML html file with the original post 
anyway.

On Wednesday, August 14, 2013 4:40:29 PM UTC+4, Boris Kheyfets wrote:
>
> Hello SymPy users and devs,
>
> I have a large expressions with
>
>    - [image: $\log^2(\frac{R}{R_1})$] split into [image: $\log^2(R) - 2 
>    \log(R) \log(R_1) + \log^2 (R_1)$], and
>    - [image: $\log^3(\frac{R}{R_1})$] split into [image: $\left [ \log(R) 
>    - \log(R_1)\right ]^3 = \ldots$] 
>
> I want to combine logs (so to make it more readable).
>
> I think I need to factor the thing first, but factor fails and powsimpmakes 
> it even worse.
>
> Here's an image of the of the expression:
>  [image: $$\Gamma_{R}^{2} R^{4} R_{1}^{2} + 4 \Gamma_{R}^{2} R^{2} 
> R_{1}^{4} \log^{3}{\left (R \right )} - 12 \Gamma_{R}^{2} R^{2} R_{1}^{4} 
> \log^{2}{\left (R \right )} \log{\left (R_{1} \right )} - 8 \Gamma_{R}^{2} 
> R^{2} R_{1}^{4} \log^{2}{\left (R \right )} + 12 \Gamma_{R}^{2} R^{2} 
> R_{1}^{4} \log{\left (R \right )} \log^{2}{\left (R_{1} \right )} + 16 
> \Gamma_{R}^{2} R^{2} R_{1}^{4} \log{\left (R \right )} \log{\left (R_{1} 
> \right )} + 2 \Gamma_{R}^{2} R^{2} R_{1}^{4} \log{\left (R \right )} - 4 
> \Gamma_{R}^{2} R^{2} R_{1}^{4} \log^{3}{\left (R_{1} \right )} - 8 
> \Gamma_{R}^{2} R^{2} R_{1}^{4} \log^{2}{\left (R_{1} \right )} - 2 
> \Gamma_{R}^{2} R^{2} R_{1}^{4} \log{\left (R_{1} \right )} - \Gamma_{R}^{2} 
> R^{2} R_{1}^{4} - 2 \Gamma_{R}^{2} R_{1}^{6} \log^{2}{\left (R \right )} + 
> 4 \Gamma_{R}^{2} R_{1}^{6} \log{\left (R \right )} \log{\left (R_{1} \right 
> )} - 2 \Gamma_{R}^{2} R_{1}^{6} \log^{2}{\left (R_{1} \right )} + 4 
> \Gamma_{R} P R^{4} R_{1}^{2} \log{\left (R \right )} - 4 \Gamma_{R} P R^{4} 
> R_{1}^{2} \log{\left (R_{1} \right )} + 2 \Gamma_{R} P R^{4} R_{1}^{2} - 8 
> \Gamma_{R} P R^{2} R_{1}^{4} \log^{3}{\left (R \right )} + 24 \Gamma_{R} P 
> R^{2} R_{1}^{4} \log^{2}{\left (R \right )} \log{\left (R_{1} \right )} - 8 
> \Gamma_{R} P R^{2} R_{1}^{4} \log^{2}{\left (R \right )} - 24 \Gamma_{R} P 
> R^{2} R_{1}^{4} \log{\left (R \right )} \log^{2}{\left (R_{1} \right )} + 
> 16 \Gamma_{R} P R^{2} R_{1}^{4} \log{\left (R \right )} \log{\left (R_{1} 
> \right )} + 8 \Gamma_{R} P R^{2} R_{1}^{4} \log^{3}{\left (R_{1} \right )} 
> - 8 \Gamma_{R} P R^{2} R_{1}^{4} \log^{2}{\left (R_{1} \right )} - 2 
> \Gamma_{R} P R^{2} R_{1}^{4} + 4 \Gamma_{R} P R^{2} R_{1}^{2} 
> \log^{2}{\left (R \right )} - 8 \Gamma_{R} P R^{2} R_{1}^{2} \log{\left (R 
> \right )} \log{\left (R_{1} \right )} - 4 \Gamma_{R} P R^{2} R_{1}^{2} 
> \log{\left (R \right )} + 4 \Gamma_{R} P R^{2} R_{1}^{2} \log^{2}{\left 
> (R_{1} \right )} + 4 \Gamma_{R} P R^{2} R_{1}^{2} \log{\left (R_{1} \right 
> )} - 4 \Gamma_{R} P R_{1}^{4} \log{\left (R \right )} + 4 \Gamma_{R} P 
> R_{1}^{4} \log{\left (R_{1} \right )} + 8 P^{2} R^{4} R_{1}^{2} 
> \log^{2}{\left (R \right )} - 16 P^{2} R^{4} R_{1}^{2} \log{\left (R \right 
> )} \log{\left (R_{1} \right )} + 8 P^{2} R^{4} R_{1}^{2} \log^{2}{\left 
> (R_{1} \right )} + 2 P^{2} R^{4} R_{1}^{2} - 2 P^{2} R^{2} R_{1}^{4} - 8 
> P^{2} R^{2} R_{1}^{2} \log^{2}{\left (R \right )} + 16 P^{2} R^{2} 
> R_{1}^{2} \log{\left (R \right )} \log{\left (R_{1} \right )} - 8 P^{2} 
> R^{2} R_{1}^{2} \log{\left (R \right )} - 8 P^{2} R^{2} R_{1}^{2} 
> \log^{2}{\left (R_{1} \right )} + 8 P^{2} R^{2} R_{1}^{2} \log{\left (R_{1} 
> \right )} + 2 P^{2} R^{2} - 2 P^{2} R_{1}^{2}$$]
>
> My question: is there a way to combine logs in this case?
>

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Title: 2013-Aug-15, 16:03:10

Hello SymPy users and devs,

I have a large expressions with

• ${\displaystyle {\log }^2\left(\frac{R}{R_1}\right)}$ split into ${\displaystyle {\log }^2(R)-2\log (R)\log (R_1)+{\log }^2(R_1)}$, and
• ${\displaystyle {\log }^3\left(\frac{R}{R_1}\right)}$ split into ${\displaystyle {\left[\log (R)-\log (R_1)\right]}^3=\dots }$

I want to combine logs (so to make it more readable).

I think I need to factor the thing first, but factor fails and powsimp makes it even worse.

Here's an image of the of the _expression_:

${\displaystyle {\mathrm{\Gamma }}_R^2{R}^4{R}_1^2+4{\mathrm{\Gamma }}_R^2{R}^2{R}_1^4{\log }^3\left(R\right)-12{\mathrm{\Gamma }}_R^2{R}^2{R}_1^4{\log }^2\left(R\right)\log \left(R_1\right)-8{\mathrm{\Gamma }}_R^2{R}^2{R}_1^4{\log }^2\left(R\right)+12{\mathrm{\Gamma }}_R^2{R}^2{R}_1^4\log \left(R\right){\log }^2\left(R_1\right)+16{\mathrm{\Gamma }}_R^2{R}^2{R}_1^4\log \left(R\right)\log \left(R_1\right)+2{\mathrm{\Gamma }}_R^2{R}^2{R}_1^4\log \left(R\right)-4{\mathrm{\Gamma }}_R^2{R}^2{R}_1^4{\log }^3\left(R_1\right)-8{\mathrm{\Gamma }}_R^2{R}^2{R}_1^4{\log }^2\left(R_1\right)-2{\mathrm{\Gamma }}_R^2{R}^2{R}_1^4\log \left(R_1\right)-{\mathrm{\Gamma }}_R^2{R}^2{R}_1^4-2{\mathrm{\Gamma }}_R^2{R}_1^6{\log }^2\left(R\right)+4{\mathrm{\Gamma }}_R^2{R}_1^6\log \left(R\right)\log \left(R_1\right)-2{\mathrm{\Gamma }}_R^2{R}_1^6{\log }^2\left(R_1\right)+4{\mathrm{\Gamma }}_{R}P{R}^4{R}_1^2\log \left(R\right)-4{\mathrm{\Gamma }}_{R}P{R}^4{R}_1^2\log \left(R_1\right)+2{\mathrm{\Gamma }}_{R}P{R}^4{R}_1^2-8{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^4{\log }^3\left(R\right)+24{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^4{\log }^2\left(R\right)\log \left(R_1\right)-8{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^4{\log }^2\left(R\right)-24{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^4\log \left(R\right){\log }^2\left(R_1\right)+16{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^4\log \left(R\right)\log \left(R_1\right)+8{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^4{\log }^3\left(R_1\right)-8{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^4{\log }^2\left(R_1\right)-2{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^4+4{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^2{\log }^2\left(R\right)-8{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^2\log \left(R\right)\log \left(R_1\right)-4{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^2\log \left(R\right)+4{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^2{\log }^2\left(R_1\right)+4{\mathrm{\Gamma }}_{R}P{R}^2{R}_1^2\log \left(R_1\right)-4{\mathrm{\Gamma }}_{R}P{R}_1^4\log \left(R\right)+4{\mathrm{\Gamma }}_{R}P{R}_1^4\log \left(R_1\right)+8P^2{R}^4{R}_1^2{\log }^2\left(R\right)-16P^2{R}^4{R}_1^2\log \left(R\right)\log \left(R_1\right)+8P^2{R}^4{R}_1^2{\log }^2\left(R_1\right)+2P^2{R}^4{R}_1^2-2P^2{R}^2{R}_1^4-8P^2{R}^2{R}_1^2{\log }^2\left(R\right)+16P^2{R}^2{R}_1^2\log \left(R\right)\log \left(R_1\right)-8P^2{R}^2{R}_1^2\log \left(R\right)-8P^2{R}^2{R}_1^2{\log }^2\left(R_1\right)+8P^2{R}^2{R}_1^2\log \left(R_1\right)+2P^2{R}^2-2P^2{R}_1^2}$

My question: is there a way to combine logs in this case?