Is there a package for physics vector notation?

Richard Hennessy <rich.hennessy at verizon.net> writes:

> "Knowing this, we can write rules for the simplifier to do what you want:"
>
> I can't get this to work for some reason.  I tried copying your code into 
> Maxima, but for the dot product, I get wrong results.
>
> v1:6*%I+4*%K;
> v2:4.4*%I-3.7*%J+8.9*%K;
>
> (%i23) xp(v1,v2);  // OK
> (%o23) -22.2*%K-35.8*%J+14.8*%I
> (%i24) dotp(v1,v2);
>
> (%o24) 'realpart((4*%K+6*%I) . (-8.9*%K+3.7*%J-4.4*%I))
> (%i25) ev(%);
>
> (%o25) 'realpart((4*%K+6*%I) . (-8.9*%K+3.7*%J-4.4*%I))
> (%i26) ev(%,nouns);
>
> (%o26) 'realpart((4*%K+6*%I) . (-8.9*%K+3.7*%J-4.4*%I))
> (%i27) 6*4.4+4*8.9;
>
> (%o27) 62.0
> (%i28) expand(dotp(v1,v2));
>
> (%o28) 'realpart(22.2*%K+35.8*%J-14.8*%I+62.0)
>

Try
dotdistrib:true;

> This does not simplify to 62.0.  BTW it is a fascinating and curious thing 
> that this way works at all.  I suppose if I understood the article you 
> mentioned better I would know why. I did take a look, but I found it 
> contained too much terminology that I don't know.

The article is interesting for the historical bits, if nothing else. 

>
> Rich
>
>
> -----Original Message----- 
> From: Leo Butler
> Sent: Saturday, March 10, 2012 1:41 PM
> To: Richard Hennessy
> Cc: maxima at math.utexas.edu
> Subject: Re: [Maxima] Is there a package for physics vector notation?
>
> Richard Hennessy <rich.hennessy at verizon.net> writes:
>
>> Hi,
>>
>> I want to use Maxima to use i, j, k notation for vectors and have a dot
>> product and cross product operation for two vectors inputted this way.  I
>> have quickly tried the dirty method below but if there is something 
>> already
>> written then maybe I can avoid reinventing the wheel.
>
> Rich, you may not know this, but this notation is actually a legacy of
> the quaternions. Baez spins a nice yarn here
> http://math.ucr.edu/home/baez/octonions/octonions.html
>
> In particular, R^3 is the subspace of purely imaginary quaternions, the
> cross product is the imaginary part of x . y, and the dot product is the
> real part of x . conjuage(y).
>
> Knowing this, we can write rules for the simplifier to do what you want:
>
> kill(all);
> qbasis:{%I,%J,%K};
> declare([%I,%J,%K],imaginary);
> dotscrules:true $
> tellsimp(%I . %I, -1);
> tellsimp(%J . %J, -1);
> tellsimp(%K . %K, -1);
> tellsimp(%I . %J, %K);
> tellsimp(%J . %I, -%K);
> tellsimp(%J . %K, %I);
> tellsimp(%K . %J, -%I);
> tellsimp(%K . %I, %J);
> tellsimp(%I . %K, -%J);
>
>
> /* cross product */
> xp(a,b) := block([x:expand(a . b)], x-realpart(x))$
> x : 3*%I $
> y : 4*%J $
> xp(x,y);
> declare([r,s],scalar);
> xp(r*%I + 4*%K, r*%J);
>
> /* dot product */
> dotp(x,y) := realpart(x . conjugate(y));
> dotp(x,y);
>
> You may prefer infix notation for these operators, but the ascii
> character set is so small that I prefer not to do this.
>
> Leo
>
>>
>> (%i9) reset();
>> (%o1)
>> (%i2) kill(rules);
>> (%o2)
>> (%i3) kill(all);
>> (%o0)
>> (%i1) display2d:false;
>>
>> (%o1) false
>> (%i2) tellsimp(i*i,1);
>>
>> (%o2) [?\^rule7,?simpexpt]
>> (%i3) tellsimp(j*j,1);
>>
>> (%o3) [?\^rule8,?\^rule7,?simpexpt]
>> (%i4) tellsimp(k*k,1);
>>
>> (%o4) [?\^rule9,?\^rule8,?\^rule7,?simpexpt]
>> (%i5) v1=.7*i-3.4*j-.6*k;
>>
>> (%o5) v1 = -0.6*k-3.4*j+0.7*i
>> (%i6) v2=1.4*i+6.9*j-9.78*k;
>>
>> (%o6) v2 = -9.779999999999999*k+6.9*j+1.4*i
>> (%i7) v1*v2,%o5,%o6;
>>
>> (%o7) (-9.779999999999999*k+6.9*j+1.4*i)*(-0.6*k-3.4*j+0.7*i)
>> (%i8) expand(%);
>>
>> (%o8) 29.112*j*k-7.685999999999999*i*k+0.07*i*j-16.612
>>
>> I can pick off the answer as the last item in the last sum (-16.612).  Is
>> there another way?  As far as the cross product is concerned, I know there
>> already is a way using matrices, but I want to avoid that too.
>>
>> Rich
>>
>> _______________________________________________
>> Maxima mailing list
>> Maxima at math.utexas.edu
>> http://www.math.utexas.edu/mailman/listinfo/maxima
>>

-- 
Leo Butler                <l_butler at users.sourceforge.net>
SDF Public Access UNIX System -   http://sdf.lonestar.org