Symbolic vectors and differentiation
- To: mathgroup at smc.vnet.net
- Subject: [mg24700] Symbolic vectors and differentiation
- From: Ralph Benzinger <ralph at ptolemy.arc.nasa.gov>
- Date: Fri, 4 Aug 2000 01:19:25 -0400 (EDT)
- Organization: The Final Frontier
- Sender: owner-wri-mathgroup at wolfram.com
Hello world,
Does anybody know how to define or simulate "symbolic vectors",
i.e. something like
v = Table[i, {i, 1, n}]
but where n is a symbolic constant? All regular vector and matrix
operations like Dot and Cross should still work, e.g. given above
definition,
v.v
should yield something like
Sum[i^2, {i, 1, n}] or n/6 (n+1)(2n+1).
A related problem I'm currently facing: Is there a way to make
Mathematica differentiate with respect to indexed variables? For
example,
D[Sum[x[i]^2, {i, 1, n}], x[j]]
should yield
2 x[j]
rather than the actual output 0.
Any comments are highly appreciated.
Ralph