I have a particular combinatorics problem where I would like to generate lists that look like this:
These sorts of combinations come from taking derivatives with respect to different variables of a product of two functions. Using subscripts $1,2,3$ to denote differentiation with respect to the variables $z_1,z_2,z_3$, respectively, I'm looking at computations of the form:
Is there a quick way to generate such a list in Sage? I'm not actually looking to perform these symbolic derivatives. I just used the differentiation to demonstrate where these combinations come from. (And check with you whether or not I'm computing them correctly.)
I solved my own problem. The solution uses the function
For the case when $n=3$ I get what I want as well:
At the risk of sounding full of myself I'm going to answer my own question. Thanks to everyone who thought about it, though.
Asked: Dec 07 '10
Seen: 148 times
Last updated: Dec 07 '10
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