/*************** -*- Mode: MACSYMA; Package: MAXIMA -*-  ******************/
/***************************************************************************
***                                                                    *****
***     Copyright (c) 1984 by William Schelter,University of Texas     *****
***     All rights reserved                                            *****
***************************************************************************/


KILL(FUNCTIONS,ARRAYS,VALUES);
DONE$
use_fast_arrays:false;
false;
A[N]:=N*A[N-1];
A[N]:=N*A[N-1]$
A[0]:1;
1$
A[5];
120$
A[N]:=N;
A[N]:=N$
A[6];
6$
A[4];
24$
(use_fast_arrays:true,kill(a));
done;
LAMBDA([X,Y,Z],X^2+Y^2+Z^2);
LAMBDA([X,Y,Z],X^2+Y^2+Z^2)$
%(1,2,A);
A^2+5$
1+2+A;
A+3$
EXP:[X^2,Y/3,-2];
[X^2,Y/3,-2]$
%[1]*X;
X^3$
[A,EXP,%];
[A,[X^2,Y/3,-2],X^3]$
M:MATRIX([A,0],[B,1]);
MATRIX([A,0],[B,1])$
M^2;
MATRIX([A^2,0],[B^2,1])$
EXP:M . M;
MATRIX([A^2,0],[A*B+B,1])$
M[1,1]*M;
MATRIX([A^2,0],[A*B,A])$
%-EXP+1;
MATRIX([1,1],[1-B,A])$
M^^(-1);
MATRIX([1/A,0],[-B/A,1])$
[X,Y] . M;
MATRIX([B*Y+A*X,Y])$
MATRIX([A,B,C],[D,E,F],[G,H,I]);
MATRIX([A,B,C],[D,E,F],[G,H,I])$
%^^2;
MATRIX([C*G+B*D+A^2,C*H+B*E+A*B,C*I+B*F+A*C],
       [F*G+D*E+A*D,F*H+E^2+B*D,F*I+E*F+C*D],
       [G*I+D*H+A*G,H*I+E*H+B*G,I^2+F*H+C*G])$
EXP:X+1 = Y^2;
X+1 = Y^2$
X-1 = 2*Y+1;
X-1 = 2*Y+1$
EXP+%;
2*X = Y^2+2*Y+1$
EXP/Y;
(X+1)/Y = Y$
1/%;
Y/(X+1) = 1/Y$
FIB[N]:=IF N = 1 OR N = 2 THEN 1 ELSE FIB[N-1]+FIB[N-2];
FIB[N]:=IF N = 1 OR N = 2 THEN 1 ELSE FIB[N-1]+FIB[N-2]$
FIB[1]+FIB[2];
2$
FIB[3];
2$
FIB[5];
5$
ETA(MU,NU):=IF MU = NU THEN MU ELSE (IF MU > NU THEN MU-NU ELSE MU+NU);
ETA(MU,NU):=IF MU = NU THEN MU ELSE (IF MU > NU THEN MU-NU ELSE MU+NU)$
ETA(5,6);
11$
ETA(ETA(7,7),ETA(1,2));
4$
IF NOT 5 >= 2 AND 6 <= 5 OR 4+1 > 3 THEN A ELSE B;
A$
KILL(F);
DONE$
HESSIAN(F):=BLOCK([DFXX,DFXY,DFXZ,DFYY,DFYZ,DFZZ],DFXX:DIFF(F,X,2),
	DFXY:DIFF(F,X,1,Y,1),DFXZ:DIFF(F,X,1,Z,1),DFYY:DIFF(F,Y,2),
	DFYZ:DIFF(F,Y,1,Z,1),DFZZ:DIFF(F,Z,2),
	DETERMINANT(MATRIX([DFXX,DFXY,DFXZ],[DFXY,DFYY,DFYZ],
			   [DFXZ,DFYZ,DFZZ])));
HESSIAN(F):=BLOCK([DFXX,DFXY,DFXZ,DFYY,DFYZ,DFZZ],DFXX:DIFF(F,X,2),
	DFXY:DIFF(F,X,1,Y,1),DFXZ:DIFF(F,X,1,Z,1),DFYY:DIFF(F,Y,2),
	DFYZ:DIFF(F,Y,1,Z,1),DFZZ:DIFF(F,Z,2),
	DETERMINANT(MATRIX([DFXX,DFXY,DFXZ],[DFXY,DFYY,DFYZ],
			   [DFXZ,DFYZ,DFZZ])))$
KILL(X,Y,Z);
DONE$
HESSIAN(X^3-3*A*X*Y*Z+Y^3);
-3*A*Y*(9*A^2*X*Z+18*A*Y^2)-27*A^3*X*Y*Z-54*A^2*X^3$
SUBST(1,Z,QUOTIENT(%,-54*A^2));
Y^3+A*X*Y+X^3$
F(X):=BLOCK([a,Y],LOCAL(A),Y:4,A[Y]:X,DISPLAY(A[Y]));
F(X):=BLOCK([a,Y],LOCAL(A),Y:4,A[Y]:X,DISPLAY(A[Y]))$
Y:2;
2$
A[Y+2]:0;
0$
F(9);
DONE$
A[Y+2];
0$