I am trying to apply a lot of multivariate derivatives to a complex vector
and I'm attempting to break apart my answer into sub-expressions to reduce
the number of terms.
To support this in Sage 7.3, I need to identify subexpressions that can be
simplified back into my original set of variables.
In this toy example I have a radius variable r, the norm of the vector
(x,y,z) . A simple direct substitution for r works, but it fails when even
the simplest operations are performed on the variables.
An example follows:
var('x y z', domain='real')
var('r', domain='positive')
r2 = x^2 + y^2 + z^2
show(r2.subs(r2 == r^2))
q = (r2 - 3 * r^2)/ (r^3)
show(q)
qr = q.subs(r2 == r^2)
show(qr.simplify())
The result is:
r2
−3r2−x2−y2−z2r3
−3r2−x2−y2−z2r3
So the first substitution of x^2+y^2+z^2 directly for r^2 works fine, but
the second case, which involves a simple rational combination of terms
fails miserably.
Is there any way to make this work? Apparently subs is unable to identify
the simplest subexpressions.
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