Is there a package for physics vector notation?

On 03/10/2012 06:25 PM, Richard Hennessy wrote:
> Thanks, this is just what I have been looking for.  The only thing is, 
> I don't mind the answers coming back as lists except when you have to 
> use the answer as input in another computation, then you would have to 
> turn the list back into i,j,k notation.  Is that something you have 
> done? I may be able to figure out something, or not. 
You can do further calculations with the results, because the . and ? 
operators accept lists are their arguments:

(%i4) v1: .7*i - 3.4*j - .6*k;

(%o4) [0.7,-3.4,-0.6]
(%i5) v2: 1.4*i + 6.9*j - 9.78*k;

(%o5) [1.4,6.9,-9.78]
(%i6) v1?v2;

(%o6) [37.392,6.006,9.59]
(%i7) 3*% ? [2,0,-3];

(%o7) [-54.054,394.068,-36.036]

Only when I have to put the result back into a text file, for instance 
for the answers in a multiple-choice quiz
generated from Maxima, do I have to go back to the i, j, k notation. In 
those cases I use the following:

(%i8) print_vector (%);

(%o8) "-54.054*i-394.068*j-36.036*k"

Notice that the result is a string and cannot be used to make 
calculations. The function print_vector above has been defined as:

print_vector(x) := block ([res],
   if (first(x) # 0) then res: printf (false, "~a*i", first(x)),
   if (length (x) > 1) then
      (if (second(x) # 0) then
          (if (second(x) < 0)
              then res: concat (res, printf( false, "~a*j", second(x)))
              else res: concat (res, printf( false, "-~a*j", second(x))))),
   if (length (x) > 2) then
      (if (third (x) # 0) then
          (if (third(x) < 0)
              then res: concat (res, printf( false, "~a*k", third(x)))
              else res: concat (res, printf( false, "-~a*k", third(x))))),
   printf(false, "~a", res))$

There might be more clever ways to achieve that. print_vector only works 
for vectors with numerical components and not for vectors with 
expressions in their components.
Cheers,
Jaime