# [Maxima] simplification in matrices

Andrea Panizza andrea.panizza75 at libero.it
Fri Mar 7 03:53:20 CST 2008

```>*Hi,
*>*
*>*I have the antisymmetric matrix
*>*
*>*M:matrix([0,(u[1,2]-u[2,1])/2,(u[1,3]-u[3,1])/2],[(u[2,1]-u[1,2])/2,0,(u[2
*>*,3]-u[3,2])/2],[(u[3,1]-u[1,3])/2,(u[3,2]-u[2,3])/2,0])
*>*
*>*I would like Maxima to reckon that, since the vector (Omg_1, Omg_2, Omg_3)
*>*(how do I input a vector in Maxima?) has components
*>*
*>*
*>*Omg_1 = u[3,2]-u[2,3]
*>*Omg_2 = u[1,3]-u[3,1]
*>*Omg_3 = u[2,1]-u[1,2]
*>*
*>*then M has the expression
*>*
*>*M:matrix([0,-Omg[3]/2,Omg[2]/2],[-Omg[3]/2,0,-Omg[1]/2],[-Omg[2]/2,Omg[3]/
*>*2,0])
*>*
*>*Is this possible? Thanks,
*
Try something like this:

(%i10)
M:matrix([0,(u[1,2]-u[2,1])/2,(u[1,3]-u[3,1])/2],[(u[2,1]-u[1,2])/2,0,(u[2,3]-u[3,2])/2],[(u[3,1]

-u[1,3])/2,(u[3,2]-u[2,3])/2,0])\$

(%i11) M : ratsubst(Omg_1, u[3,2]-u[2,3], M)\$

(%i12) M : ratsubst(Omg_2, u[1,3]-u[3,1], M)\$

(%i13) M : ratsubst(Omg_3, u[2,1]-u[1,2], M);

(%o13)
matrix([0,-Omg_3/2,Omg_2/2],[Omg_3/2,0,-Omg_1/2],[-Omg_2/2,Omg_1/2,0])

To read the user documentation for ratsubst, enter "? ratsubst" on a
command
line.

There is no vector object in Maxima. Either you need to represent a vector
as
a list or as a Matrix. Examples:

(%i14) vec : matrix([1],[2],[3]);
(%o14) matrix([1],[2],[3])

(%i15) M . vec;
(%o15) matrix([(3*Omg_2)/2-Omg_3],[Omg_3/2-(3*Omg_1)/2],[Omg_1-Omg_2/2])

(%i16) u : [1,2,3];
(%o16) [1,2,3]

(%i17) u . M;
(%o17) matrix([Omg_3-(3*Omg_2)/2,(3*Omg_1)/2-Omg_3/2,Omg_2/2-Omg_1])

Maxima, but I don't know if anybody is working on it.

I hope this helps; let us know if you have additional questions
or if something I said isn't clear.

Barton

Hi,

thank you very much for your valuable help. It would be very useful for me if
Maxima had a vector object. Functions like finding the vector associated
to a skew-symmetric matrix are very useful in vector calculus. Also things
like decomposing a symmetric or skew-symmetric matrix in terms of its

Best regards,

Andrea

ps I don' understand how to reply directly to your post. Hope this shows in the