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