I have a bevy of algebra/calculus to work through for my research. I
have been using Sage to check my derivation for specific instances,
but it would be great if Sage could help me *derive* the results in
the first place.
Here is a simplified example. (Hopefully the mixed math/LaTeX/Sage
syntax makes sense.) I have a multivariate generating function in x1,
x2, ..., xn and a list of exponents {di} where each di can be
considered a vector [di1, di2, ..., din]. Then I have a generating
function like the following.
F1(x) = prod_{di} (1 + ci * x^di)
where {ci} are constants associated with each exponent, and
x^d = x1^di1 * x2^di2 * ... * xn^din.
Now I want to find the functions
ai(x) = xi * F1.derivative(xi) / F1
Can I do this in Sage? I have a fixed but arbitrary (symbolic) number
of variables in my function. I want to create a function based on an
unspecified list of exponents. Then I want an equation for a new list
of functions based on the original function and its derivatives. Can
I do this all symbolically? Is there another CAS that can do it?
Thanks!
- Ryan
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