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/*************** -*- 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$
kill(x,y,z);
done$
determinant(hessian(x^3-3*a*x*y*z+y^3,[x,y,z]));
-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$
(use_fast_arrays : false, kill(a), 0);
0$
/* ensure that matrix construction works as advertised */
(L : makelist ([i], i, 1, 100), apply (matrix, L), [op (%%), args (%%)]);
[matrix, ''(makelist ([i], i, 1, 100))];
(L : makelist ([i], i, 1, 100), apply (matrix, L), transpose (%%));
''(matrix (tree_reduce (append, L))); /* call tree_reduce instead of append because GCL barfs ... */
(matrix (), [op (%%), args (%%)]);
[matrix, []];
/* construct a matrix of modest size */
(apply (matrix, makelist ([i], i, 1, 1000)), 0);
0;
/* construct a matrix of modest size */
(apply (matrix, makelist ([i], i, 1, 10000)), 0);
0;
/* verify that arguments are evaluated exactly once */
block ([a : b, b : c, c: d, d : 1], matrix ([a, b], [c, d]), [op (%%), args (%%)]);
[matrix, '[[b, c], [d, 1]]];
/* verify that arguments are evaluated exactly once */
block ([a : b, b : c, c: d, d : 1, L1 : '[a, b], L2 : '[c, d]], matrix (L1, L2), [op (%%), args (%%)]);
[matrix, '[[a, b], [c, d]]];
/* should trigger an error */
errcatch (matrix ([1], [1, 2]));
[];
/* should trigger an error */
errcatch (matrix ([1], '(a + b)));
[];
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