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Symbolic vector handling
*To*: mathgroup at smc.vnet.net
*Subject*: [mg83353] Symbolic vector handling
*From*: "Dr. Wolfgang Hintze" <weh at snafu.de>
*Date*: Sun, 18 Nov 2007 04:46:03 -0500 (EST)
Hello group,
this is most probably a very simple question but still ...
Consider a set of vectors vA, vB, vC, ... and scalars a, b, c, ...
What I want to do is a symbolic handling of expressions like vA.(b vB +
vC)
which should be expanded to
(1) expr = vA.(b vB + vC) -> b vA.vB + vA.vC
i.e. I want Mathematica to apply the distributive law and the
extraction of scalars.
I don't want to use any coordinate representation.
The first thing that comes into mind would be to define a type "vector"
and another type "scalar" and then define the usual rules.
I'd like to execute a comand like
FunctionExpand[ expr , Assumptions->{{vA, vB, vC} "elem" vectors,
{a,b,c} "elem" scalars}]
Here's an example of a simple problem in which my question arises:
Let the vectors vR1 and vR2 be defined in terms of four other vectors
vA1, vA2, vN1, vN2 and two scalars a and b as follows:
vR1 = vA1 + a vN1
vR2 = vA2 + b vN2
and consider the function
U = (vR1 - vR2).(vR1 - vR2)
The task is to find the minimum of U in terms of a combination of
scalar product of the vectors vA1, vA2, vN1, vN2 and of the optimizing
parameters a and b.
Any help is greatly appreciated.
Regards,
Wolfgang
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