Is there a package for physics vector notation?

>-----Original Message----- 
>From: Leo Butler
>Sent: Saturday, March 10, 2012 5:56 PM
>To: Richard Hennessy
>Cc: l_butler at users.sourceforge.net ; maxima at math.utexas.edu
>Subject: Re: [Maxima] 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.

It is more accessible than I first thought, I have been reading more of it. 
It is interesting.  I was a turned off by the Fano plane diagram on the 
first page, but then after reading the explanation of what it is for and how 
to use it, it is quite easy.

Thank you,

Rich

>
> 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