Error while working with: Affine, quaternions and cos/sin
Subject: Error while working with: Affine, quaternions and cos/sin
From: Marcel Tünnissen
Date: Sat, 16 Apr 2005 07:38:13 +0000
I try to make some calculations with quarternions. As suggested in
http://www.math.utexas.edu/pipermail/maxima/2003/004142.html I use
Schelter's `affine' package with the suggested setup:
packagemp:false;
dotscrules:true;
matrix_element_mult:".";
current_variables:[i,j,k];
declare_weights(i,0,j,0,k,0);
set_up_dot_simplifications([i.i+1,j.j+1,i.j-k,j.i+k]);
Now I get an error when using a cos or sin:
(%i8) dotsimp(expand((cos*i+2*j).(4-6*j)));
Maxima encountered a Lisp error:
FUNCALL: undefined function FERROR
Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.
When I use variables like cos_alpha and sin_alpha, the simplifier doesn't
work as I would expect.
Take e.g. the following example:
(%i10) ya: ((SQRT(5) + 3)*k) / (SQRT(3)*SQRT(5) + SQRT(3)) + (2*i) /
(SQRT(3)*SQRT(5) + SQRT(3));
(SQRT(5) + 3) k 2 i
(%o10) ------------------------- + -------------------------
SQRT(3) SQRT(5) + SQRT(3) SQRT(3) SQRT(5) + SQRT(3)
(%i11) Sa: ((SQRT(2)*SQRT(5) + 3*SQRT(2))*k) / (SQRT(3)*SQRT(5) + SQRT(3)) -
j + (2*SQRT(2)*i) / (SQRT(3)*SQRT(5) + SQRT(3));
(SQRT(2) SQRT(5) + 3 SQRT(2)) k 2 SQRT(2) i
(%o11) ------------------------------- - j + -------------------------
SQRT(3) SQRT(5) + SQRT(3) SQRT(3) SQRT(5) + SQRT(3)
(%i12) dotsimp(expand(Sa . (cos_alpha - ya * sin_alpha)));
Beginning to simplify:
2
- ((3 SQRT(5) + 10 SQRT(5) + 7) SQRT(3) SQRT(2) (k . k sin_alpha)
2
+ (SQRT(5) + 4 SQRT(5) + 3) SQRT(3) SQRT(2) (k . i sin_alpha)
... etc
2
+ (- SQRT(5) - 4 SQRT(5) - 3) SQRT(3) SQRT(2) i) (i . j . sin_alpha)
... etc
(%o12)/R/ ((3 SQRT(5) + 18 SQRT(5) + 27) (j . k sin_alpha)
2
+ (6 SQRT(5) + 18) (j . i sin_alpha) + (- 3 SQRT(5) - 12 SQRT(5) - 9)
SQRT(3)
2
(j . cos_alpha) + (- SQRT(5) - 4 SQRT(5) - 3) SQRT(3) SQRT(2)
(i . k sin_alpha) + (- 2 SQRT(5) - 2) SQRT(3) SQRT(2) (i . i sin_alpha)
2
+ ((- 3 SQRT(5) - 10 SQRT(5) - 7) SQRT(3) SQRT(2) (i . j)
2
+ (- SQRT(5) - 4 SQRT(5) - 3) SQRT(3) SQRT(2) i) (i . j . sin_alpha)
2
+ (3 SQRT(5) + 18 SQRT(5) + 27) SQRT(2) (i . j . cos_alpha)
+ (6 SQRT(5) + 18) SQRT(2) (i . cos_alpha))
2
/((3 SQRT(5) + 12 SQRT(5) + 9) SQRT(3))
How can I make Maxima work with cos and sin as well?
Or
Why doesn't Maxima write j.k sin_alpha as i sin_alpha and how can I make
it to rewrite it like that?
I am new with Maxima.
I have:
Maxima 5.9.1 http://maxima.sourceforge.net
Using Lisp CLISP 2.33.2 (2004-06-02)
and OS: Linux, distrib Fedora Core 3.
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