ratmx + matrix_element_mult + ...

Thanks. Also, dotscrules needs to be true (nondefault value):

 (%i14) declare([a, b,c,d], scalar)$
 (%i15) matrix_element_mult : "."$

 (%i16) dotscrules : true$

 (%i17) s.s;
 (%o17) matrix([b*c+a^2+7,b*d+a*b+10],[c*d+a*c+15,d^2+b*c+22])

The ratmx : true case is still trouble:

 (%i18) ratmx : true$

 (%i19) s.s;
 (%o19) matrix([1,2],[3,4])^2+matrix([a,b],[c,d])^2

 (%i20) expand(%);
 (%o20) matrix([a^2+1,b^2+4],[c^2+9,d^2+16])

Barton

macrakis at gmail.com wrote on 11/04/2009 07:34:55 AM:

> [image removed] 
> 
> Re: [Maxima] ratmx + matrix_element_mult + ...
> 
> Stavros Macrakis 
> 
> to:
> 
> Barton Willis, maxima
> 
> 11/04/2009 07:34 AM
> 
> Sent by:
> 
> macrakis at gmail.com
> 
> Barton,
> 
> If you declare the matrix elements scalar, the non-commutative ops
> will simplify to commutative.
> 
>           -s
> 
> On 11/4/09, Barton Willis <willisb at unk.edu> wrote:
> >
> > Consider a list of matrices
> >
> >  (%i2)  s : [matrix([1,2],[3,4]), matrix([a,b],[c,d])]$
> >
> > OK
> >
> >  (%i3)  first(s).first(s) + second(s).second(s);
> >  (%o3) matrix([b*c+a^2+7,b*d+a*b+10],[c*d+a*c+15,d^2+b*c+22])
> >
> > Can we do this with s.s? No, to get the dot product to work, we need
> > to set matrix_element_mult to noncummuative multiplication, but then
> > the matrix products are done with noncommuative multiplication too.
> >
> >  (%i4)  matrix_element_mult : "."$
> >
> >  (%i5) s.s;
> >  (%o5) matrix([b . c+a^^2+7,b . d+a . b+10],[d . c+c . a+15,d^^2+c . 
b+22])
> >
> > When ratmx is true (often a good choice), it's worse
> >
> >  (%i6) ratmx : true$
> >  (%i7) s.s;
> >
> > Unsimplified:
> >
> >  (%o7) matrix([1,2],[3,4])^2+matrix([a,b],[c,d])^2
> >  (%i8) expand(%,0,0);
> >  (%o8) matrix([a^2+1,b^2+4],[c^2+9,d^2+16])
> >
> > Barton
> >
> > Barton
> >
> > _______________________________________________
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> > Maxima at math.utexas.edu
> > http://www.math.utexas.edu/mailman/listinfo/maxima
> >