On Sun, Apr 20, 2014 at 7:33 PM, Peter Eastman <[email protected]> wrote:
> I'm just learning Sympy, so I apologize if this is a beginner question.  I'm
> trying to figure out how to use intermediate variables when simplifying
> expressions.
>
> Here's a simple example of the sort of thing I'm trying to do.  Suppose I
> have a vector v=(v1,v2,v3).  Next I define u to be a unit vector parallel to
> v: u=(u1,u2,u3)=v/|v|.  And then I want to compute the derivative du1/dv1.
> I can do it like this:
>
>>>> v = Matrix([symbols('v1 v2 v3')])
>>>> u = v/sqrt(v.dot(v))
>>>> u[0].diff(v[0])
>
> which produces the output
>
> -v1**2/(v1**2 + v2**2 + v3**2)**(3/2) + 1/sqrt(v1**2 + v2**2 + v3**2)
>
> That's a very complicated way of writing it, because it's fully expanded out
> in terms of the individual components of v.  It could be written much more
> simply as (1-u1**2)/|v|.  But how do I get Sympy to figure that out?  How do
> I create intermediate variables like u and v, tell it how they're defined in
> terms of v1, v2, etc., and then tell it to perform whatever transformations
> among them leads to the simplest expression?

Another option might be to use a substitution sqrt(v1**2 + v2**2 +
v3**2) -> |v|.

-- 
You received this message because you are subscribed to the Google Groups 
"sympy" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sympy.
To view this discussion on the web visit 
https://groups.google.com/d/msgid/sympy/CADDwiVCN%3DmNVsQv7LJjk%3DrjnvzqYL%3D6vvqMPC%2BpzZDWBeHHoxA%40mail.gmail.com.
For more options, visit https://groups.google.com/d/optout.

Reply via email to