dear Rene,
| 2) Is genmatrix the right way to go, like in
| gradient(expr,var) := genmatrix(lambda([i,j],diff(expr,var[j])),1,n)
| where n is the length of var?
your defintion is reflected in the following definition (from Barton Willis
AFAIK) which is directly usable at the maxima prompt:
hessian (e, vars) :=
block([n:length(vars)],
genmatrix (lambda([i,j], diff(e[i],vars[i],1,vars[j],1) n,
n) );
jacobian(e, vars) :=
block( [m:length(e),n:length(vars)],
genmatrix(lambda([i,j],diff(e[i],vars[j])), m, n) );
So I like to define in my courses:
grad(f,X) := jacobian([f],X);
at( grad(x*y,[x,y]), [x=1,y=1]);
jacobian ([x*y], [x,y]);
at(%, [x=1,y=1]);
hessian (x^2-x*y+2*y, [x, y] );
determinant(hessian (x^2-x*y+2*y, [x, y] ));
It is also possible to use package 'vect':
load ("vect")$
grad (x^2 + y^2 + z^2);
express (%);
ev (%, diff);
.. or something like this (depending on what the students are knowing):
grad2(f,X):=[diff(f,X[1]),diff(f,X[2])];
grad3(f,X):=[diff(f,X[1]),diff(f,X[2]), diff(f,X[3])];
Let us know what's your opinion.
sincerely
Wolfgang
-----Urspr?ngliche Nachricht-----
Von: Rene Grothmann <2008 at rene-grothmann.de>
An: maxima at math.utexas.edu <maxima at math.utexas.edu>
Datum: Donnerstag, 18. Dezember 2008 15:16
Betreff: [Maxima] Problem with Matrix
I am trying to make some student functions for differentiation, such as
gradient, Jordan matrix, Hesse matrix. However, I have troubles handling
matrices.
1) Is there a way to ask the dimensions of a matrix?
2) Is genmatrix the right way to go, like in
gradient(expr,var) := genmatrix(lambda([i,j],diff(expr,var[j])),1,n)
where n is the length of var?
3) Is there any difference between a vector [x,y] and a 1x2-matrix?
Thanks for any responses.
Ren??
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