Thanks Aaron for pointing out the simplification section of the tutorial.

 Actually, collect(expr1, [x11, x12, x13]) does almost what I wanted. I 
still need to factor a -1 from x12( -x21x33 + x23x31). How would you do it 
using replace() like what I did? I also tried putting (x12*a).factor() as 
the value for replace but that didn't work. I had to use Mul() with 
evaluate = False to get it to do what I wanted.

On Wednesday, 4 November 2015 06:19:34 UTC+8, Aaron Meurer wrote:
>
> A good start would be the simplification section of the tutorial 
> http://docs.sympy.org/latest/tutorial/index.html. 
>
> In this case, collect(expr1, [x11, x12, x13]) does what you want. 
> factor() only does complete factorizations (into products of terms). 
> This is explained in more depth in the tutorial. 
>
> Aaron Meurer 
>
> On Tue, Nov 3, 2015 at 2:47 PM, Hugh <[email protected] <javascript:>> 
> wrote: 
> > import sympy 
> > sympy.init_session() 
> > 
> > 
> > x11, x12, x13, x21, x22, x23, x31, x32, x33 = symbols('x_1:4(1:4)') 
> > 
> > A = Matrix(3,3,symbols('x_1:4(1:4)')) 
> > expr1 = A.det() 
> > 
> > expr2 = x11*(x22*x33 - x23*x32) - x12*(x21*x33 -x23*x31) + x13*(x21*x32 
> - 
> > x22*x31) 
> > 
> > # How to get expr2 from expr1? 
> > 
> > I would like to use sympy to rewrite expressions just like how people 
> would 
> > commonly do when writing proofs or doing homework. What are the 
> > documentation that I must read so that I can be proficient at this? 
> > 
> > I've read the tutorial and some of the modules in the module reference 
> but 
> > feel that I have just barely touched the surface of sympy's 
> capabilities. 
> > For example, in the above code snippet, I don't know how to manipulate 
> expr1 
> > to get expr2. I thought expr1.factor() would work but it didn't. 
> > 
> > Please advise. 
> > 
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