(maxima.info)Lisp and Maxima

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37.1 Lisp and Maxima
====================

Maxima is written in Lisp, and it is easy to access Lisp functions and
variables from Maxima and vice versa.  Lisp and Maxima symbols are
distinguished by a naming convention.  A Lisp symbol which begins with a
dollar sign '$' corresponds to a Maxima symbol without the dollar sign.

   A Maxima symbol which begins with a question mark '?' corresponds to
a Lisp symbol without the question mark.  For example, the Maxima symbol
'foo' corresponds to the Lisp symbol '$FOO', while the Maxima symbol
'?foo' corresponds to the Lisp symbol 'FOO'.  Note that '?foo' is
written without a space between '?' and 'foo'; otherwise it might be
mistaken for 'describe ("foo")'.

   Hyphen '-', asterisk '*', or other special characters in Lisp symbols
must be escaped by backslash '\' where they appear in Maxima code.  For
example, the Lisp identifier '*foo-bar*' is written '?\*foo\-bar\*' in
Maxima.

   Lisp code may be executed from within a Maxima session.  A single
line of Lisp (containing one or more forms) may be executed by the
special command ':lisp'.  For example,

     (%i1) :lisp (foo $x $y)

calls the Lisp function 'foo' with Maxima variables 'x' and 'y' as
arguments.  The ':lisp' construct can appear at the interactive prompt
or in a file processed by 'batch' or 'demo', but not in a file processed
by 'load', 'batchload', 'translate_file', or 'compile_file'.

   The function 'to_lisp' opens an interactive Lisp session.  Entering
'(to-maxima)' closes the Lisp session and returns to Maxima.

   Lisp functions and variables which are to be visible in Maxima as
functions and variables with ordinary names (no special punctuation)
must have Lisp names beginning with the dollar sign '$'.

   Maxima is case-sensitive, distinguishing between lowercase and
uppercase letters in identifiers.  There are some rules governing the
translation of names between Lisp and Maxima.

  1. A Lisp identifier not enclosed in vertical bars corresponds to a
     Maxima identifier in lowercase.  Whether the Lisp identifier is
     uppercase, lowercase, or mixed case, is ignored.  E.g., Lisp
     '$foo', '$FOO', and '$Foo' all correspond to Maxima 'foo'.  But
     this is because '$foo', '$FOO' and '$Foo' are converted by the Lisp
     reader by default to the Lisp symbol '$FOO'.
  2. A Lisp identifier which is all uppercase or all lowercase and
     enclosed in vertical bars corresponds to a Maxima identifier with
     case reversed.  That is, uppercase is changed to lowercase and
     lowercase to uppercase.  E.g., Lisp '|$FOO|' and '|$foo|'
     correspond to Maxima 'foo' and 'FOO', respectively.
  3. A Lisp identifier which is mixed uppercase and lowercase and
     enclosed in vertical bars corresponds to a Maxima identifier with
     the same case.  E.g., Lisp '|$Foo|' corresponds to Maxima 'Foo'.

   The '#$' Lisp macro allows the use of Maxima expressions in Lisp
code.  '#$<expr>$' expands to a Lisp expression equivalent to the Maxima
expression <expr>.

     (msetq $foo #$[x, y]$)

This has the same effect as entering

     (%i1) foo: [x, y];

The Lisp function 'displa' prints an expression in Maxima format.

     (%i1) :lisp #$[x, y, z]$
     ((MLIST SIMP) $X $Y $Z)
     (%i1) :lisp (displa '((MLIST SIMP) $X $Y $Z))
     [x, y, z]
     NIL

   Functions defined in Maxima are not ordinary Lisp functions.  The
Lisp function 'mfuncall' calls a Maxima function.  For example:

     (%i1) foo(x,y) := x*y$
     (%i2) :lisp (mfuncall '$foo 'a 'b)
     ((MTIMES SIMP) A B)

   Some Lisp functions are shadowed in the Maxima package, namely the
following.

   complement     continue      //
   float          functionp     array
   exp            listen        signum
   atan           asin          acos
   asinh          acosh         atanh
   tanh           cosh          sinh
   tan            break         gcd