vector and matrix valued functions
- To: mathgroup at smc.vnet.net
- Subject: [mg105771] vector and matrix valued functions
- From: Daniel <dalist0 at gmail.com>
- Date: Fri, 18 Dec 2009 06:22:50 -0500 (EST)
Hello,
I am working with functions that have vector and matrix valued
arguments. I'd like to postpone going to a component representation as
late as possible, but that is not easy because some vectors are
already in the component form and this gives me error messages from
cross and times.
One example: I have several vector valued quantities x,y,z (let's say
100 dimensional).
I'd like to write all expressions in the form
f[x_,y_]:=x.y
instead of
f[x1_,x2_,...,_x100,y1_,...]:=...
The problem is, that in the first case the system does not know it is
dealing with 100 dimensional vectors.
g[x_] :=5 x
Cross[g[a] , {1, 0, 0}]
should give me something like g[a] x {1,0,0}, e.g. stay unevaluated
or alternatively be evaluated in component form {0, 5 a3, - 5 a2}.
Instead I get an error message:
Cross::nonn1: The arguments are expected to be vectors of equal
length, and the number of arguments is expected to be 1 less than
their length
In addition, I'd like to write the gradient of a function with one or
several vector arguments, i.e. something like
gradient_y f,
which should be a vector with the components df/dy_i, i.e. D[f[x,y],
{{y1,y2,y3,...y100}}]. This does not work either, because the system
does not now that y is in reality {y1,..,y100}
How can I deal naturally with vectors, e.g. have vector valued
variables as function arguments and return values, use the usual
vector functions (cross, dot, grad, div, rot), and diff with respect
to a vector.
Many thanks
Dan