/************************************************************************************
this is a maxima batch file,
containinig an example of linear algebra

call this file in batch mode with the command 

$ maxima -b maxima_test.txt

or from inside maxima by

(%ix) batch("maxima_test.txt");

**********************************************************************************/
" some examples "$
" "$
A : matrix([1,2],[2,3]);
B : matrix([1,0],[0,1]);

Ainverse: invert(A);
Atransposed: transpose(A);
AtimesB : A.B;
eigenvectors(A);

rankA : rank(A);

e1 : x + z = y;
e2 : 2*a*x - y = 2*a^2;
e3 : y - 2*z = 2;

[globalsolve: false, programmode: false];
linsolve ([e1, e2, e3], [x, y, z]);
" "$

/**********  III / 6  *******************************/
" III / 6 "$
" "$
f: matrix([1, 0, 1], [0, -1, 1], [0, 1, 1]);
g: matrix([1, 0, 1], [0, -1, 1], [0, 1, -1]);

eigenvectors(f);
eigenvectors(g);

charpoly(f, x);
factor(%);

/**********  III / 7  *******************************/
" III / 7 "$
" "$
MatrixC: matrix([a, c, c, b], [c, a, b, c], [c, b, a, c], [b, c, c, a]);
rank(MatrixC);
det_MatrixC : determinant(MatrixC);
factor(%);
" "$

/********   III / 8   *******************************/
" III / 8 "$

S11: 2*x + 3*z = 7;
S12: 5*x + 4*z = 8;
linsolve([S11, S12], [x, y, z]);

S21: 2*x + y - z = 1;
S22: 3*x + 2*y + z = 4;
S23: x + y + 2*z = 2;
/*
linsolve([S21, S22, S23], [x, y, z]);  
*/

S41: 2*x - y - z = 1;
S42: 3*x - 2*y + z = 4;
S43: x - 3*z = -2;
linsolve([S41, S42, S43], [x, y, z]);  



/*******   III / 9   ****************************/

S1: x + (3*m + 7)*y = 1;
S2: (m+4)*x + (4*m + 10)*y = 2;
linsolve([S1, S2],[x,y]);

T1: x - y + z = 2 - m;
T2: -m*x - 2*y + 2*z = 3;
T3: 3*x - (m+1)* z = 1 - 2*m;

linsolve([T1, T2, T3], [x, y, z]);  

T: matrix([1, -1, 1], [-m, -2, 2], [3, 0, m+1]);
det_T = factor(determinant(T));

" "$
" "$

S11: x + a*y + z = 2;
S12: a*x + y + z = b;
linsolve([S11, S12], [x, y, z]);  

/*******************************************************************************************/
/* the following is an automatically created batch file
the creating program is called wxMaxima - a graphical user interface for Maxima

the example is taken from exercise sheet III, exo 3
*/

/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/

/* [wxMaxima: input   start ] */
A:matrix([3, 2, -1], [-2, -1, 0], [4, 3, -1]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
M:matrix([0, -1, -2], [0, 0, 2], [1, -1, -3]);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
MI:invert(M);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
B:MI.A.M;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
eigenvectors(A);
/* [wxMaxima: input   end   ] */

/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$