Use of Lisp

Maxima is written in Lisp, a really unique programming language that was developed by John McCarthy at MIT. The earliest publication about Lisp is possibly:

McCarthy, John:
Recursive Functions of Symbolic Expressions and Their Computation, Part I
Communications of the ACM, Vol. 3, April 1960, pp. 184-195

To enter a piece of Lisp, you write:

:lisp (list 'a 'b 'c)
:q(a b c)

To enter the Lisp mode, you write :lisp, to quite the Lisp mode and return to Maxima, you write :q into a new line. The Lisp text itself must not contain a line break.

Alternatively, you can enter

to_lisp();

(%i1) to_lisp();
Type (to-maxima) to restart

MAXIMA> (cons 'a 'b)
(A . B)
MAXIMA> (append '(a b c) '(d e f))
(A B C D E F)
MAXIMA> (reverse '(a b c))
(C B A)
MAXIMA> (mapcar '(lambda(x) (list x)) '(a b c))
((A) (B) (C))
MAXIMA> (run)
Maxima restarted.

These are indeed very simple Lisp expressions. They should bring your Lisp knowledge back to live and give you a few hints about the dialect that is used for Maxima.

The internal respresentation of expressions

In Lisp mode, you can access the internal representation of expressions stored in result cells. To obtain a result, you enter the label of the result cell written between vertical slashes and with a prefixed dollar sign:

(%i1) (sin(x) + cos(x) + sin(x)/sec(x));
			   sin(x)
(%o1) 			   ------ + sin(x) + cos(x)
			   sec(x)
(%i2) to_lisp();
Type (to-maxima) to restart

MAXIMA> $%o1
((MPLUS SIMP) ((%COS SIMP) $X) ((%SIN SIMP) $X)
         ((MTIMES SIMP) ((MEXPT SIMP) ((%SEC SIMP) $X) -1)
          ((%SIN SIMP) $X)))
MAXIMA> (to-maxima)

$%o1 answers the internal representation of the expression in value cell %o1. For better readability, it is given here in formatted form:

((MPLUS SIMP) 
      ((%COS SIMP) $X)
      ((%SIN SIMP) $X)
      ((MTIMES SIMP)
           ((MEXPT SIMP) 
                ((%SEC SIMP) $X)
                  -1
           )
           ((%SIN SIMP) $X)
)     )

(%i1) 'integrate(sin(x)*exp(x), x);
				/
				[   x
(%o1) 			        I %e  sin(x) dx
				]
				/
(%i2) to_lisp();
Type (to-maxima) to restart

MAXIMA> $%o1
((%INTEGRATE SIMP)
         ((MTIMES SIMP) ((MEXPT SIMP) $%E $X) ((%SIN SIMP) $X))
         $X)

The second top-level element (cadr $%o1) is the integrand, the third top-level element (caddr $%o1) is the integration variable. With this knowledge we can carry out the integration in Lisp:

MAXIMA> ($INTEGRATE (cadr $%o1) (caddr $%o1))
((MTIMES SIMP) ((RAT SIMP) 1 2) ((MEXPT SIMP) $%E $X)
         ((MPLUS SIMP) ((MTIMES SIMP) -1 ((%COS SIMP) $X))
          ((%SIN SIMP) $X))) 
MAXIMA> (to-maxima)