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# 3. Help

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## 3.1 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`, and `gcd`.

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@ref{Category: Programming}

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## 3.2 Garbage Collection

Symbolic computation tends to create a good deal of garbage (temporary or intermediate results that are eventually not used), and effective handling of this can be crucial to successful completion of some programs.

Under GCL, on UNIX systems where the mprotect system call is available (including SUN OS 4.0 and some variants of BSD) a stratified garbage collection is available. This limits the collection to pages which have been recently written to. See the GCL documentation under ALLOCATE and GBC. At the Lisp level doing (setq si::*notify-gbc* t) will help you determine which areas might need more space.

For other Lisps that run Maxima, we refer the reader to the documentation for that Lisp on how to control GC.

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## 3.3 Documentation

The Maxima on-line user's manual can be viewed in different forms. From the Maxima interactive prompt, the user's manual is viewed as plain text by the `?` command (i.e., the `describe` function). The user's manual is viewed as `info` hypertext by the `info` viewer program and as a web page by any ordinary web browser.

`example` displays examples for many Maxima functions. For example,

    (%i1) example (integrate);

yields

    (%i2) test(f):=block([u],u:integrate(f,x),ratsimp(f-diff(u,x)))
    (%o2) test(f) := block([u], u : integrate(f, x),

                                             ratsimp(f - diff(u, x)))
    (%i3) test(sin(x))
    (%o3)                           0
    (%i4) test(1/(x+1))
    (%o4)                           0
    (%i5) test(1/(x^2+1))
    (%o5)                           0

and additional output.

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@ref{Category: Console interaction}

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## 3.4 Functions and Variables for Help

Function: apropos (string)

  Searches for Maxima names which have string appearing anywhere within them. Thus, `apropos (exp)` returns a list of all the flags and functions which have `exp` as part of their names, such as `expand`, `exp`, and `exponentialize`. Thus if you can only remember part of the name of something you can use this command to find the rest of the name. Similarly, you could say `apropos (tr_)` to find a list of many of the switches relating to the translator, most of which begin with `tr_`.

  `apropos("")` returns a list with all Maxima names.

  `apropos` returns the empty list `[]`, if no name is found.

  Example:

  Show all Maxima symbols wich have `"gamma"` in the name:

      (%i1) apropos("gamma");
      (%o1) [%gamma, %gammagreek, gamma, gammagreek, gammalim, gamma_expand,
      gamma_imag, gamma_incomplete, gamma_incomplete_generalized,
      gamma_incomplete_regularized, gamma_radius, Gamma, log_gamma, makegamma,
      gamma_incomplete_generalized_regularized]

  ·

  @ref{Category: Help}

Function: demo (filename)

  Evaluates Maxima expressions in filename and displays the results. `demo` pauses after evaluating each expression and continues after the user enters a carriage return. (If running in Xmaxima, `demo` may need to see a semicolon `;` followed by a carriage return.)

  `demo` searches the list of directories `file_search_demo` to find `filename`. If the file has the suffix `dem`, the suffix may be omitted. See also `file_search`.

  `demo` evaluates its argument. `demo` returns the name of the demonstration file.

  Example:

      (%i1) demo ("disol");

      batching /home/wfs/maxima/share/simplification/disol.dem
       At the _ prompt, type ';' followed by enter to get next demo
      (%i2)                      load(disol)

      _
      (%i3)           exp1 : a (e (g + f) + b (d + c))
      (%o3)               a (e (g + f) + b (d + c))

      _
      (%i4)                disolate(exp1, a, b, e)
      (%t4)                         d + c

      (%t5)                         g + f

      (%o5)                   a (%t5 e + %t4 b)

      _
      (%i5) demo ("rncomb");

      batching /home/wfs/maxima/share/simplification/rncomb.dem
       At the _ prompt, type ';' followed by enter to get next demo
      (%i6)                     load(rncomb)

      _
                                   z         x
      (%i7)               exp1 : ----- + ---------
                                 y + x   2 (y + x)
                                z         x
      (%o7)                   ----- + ---------
                              y + x   2 (y + x)

      _
      (%i8)                     combine(exp1)
                                z         x
      (%o8)                   ----- + ---------
                              y + x   2 (y + x)

      _
      (%i9)                     rncombine(%)
                                   2 z + x
      (%o9)                       ---------
                                  2 (y + x)

      _
                                   d   c   b   a
      (%i10)                exp2 : - + - + - + -
                                   3   3   2   2
                                d   c   b   a
      (%o10)                    - + - + - + -
                                3   3   2   2

      _
      (%i11)                    combine(exp2)
                            2 d + 2 c + 3 (b + a)
      (%o11)                ---------------------
                                      6

      _
      (%i12)                   rncombine(exp2)
                            2 d + 2 c + 3 b + 3 a
      (%o12)                ---------------------
                                      6

      _
      (%i13)

  ·

  @ref{Category: Help} · @ref{Category: Console interaction} · @ref{Category: File input}

Function: describe (string)
Function: describe (string, exact)
Function: describe (string, inexact)

  `describe(string)` is equivalent to `describe(string, exact)`.

  `describe(string, exact)` finds an item with title equal (case-insensitive) to string, if there is any such item.

  `describe(string, inexact)` finds all documented items which contain string in their titles. If there is more than one such item, Maxima asks the user to select an item or items to display.

  At the interactive prompt, `? foo` (with a space between `?` and `foo`) is equivalent to `describe("foo", exact)`, and `?? foo` is equivalent to `describe("foo", inexact)`.

  `describe("", inexact)` yields a list of all topics documented in the on-line manual.

  `describe` quotes its argument. `describe` returns `true` if some documentation is found, otherwise `false`.

  See also @ref{Documentation}.

  Example:

      (%i1) ?? integ
       0: Functions and Variables for Elliptic Integrals
       1: Functions and Variables for Integration
       2: Introduction to Elliptic Functions and Integrals
       3: Introduction to Integration
       4: askinteger  (Functions and Variables for Simplification)
       5: integerp  (Functions and Variables for Miscellaneous Options)
       6: integer_partitions  (Functions and Variables for Sets)
       7: integrate  (Functions and Variables for Integration)
       8: integrate_use_rootsof  (Functions and Variables for
          Integration)
       9: integration_constant_counter  (Functions and Variables for
          Integration)
       10: nonnegintegerp  (Functions and Variables for linearalgebra)
      Enter space-separated numbers, `all' or `none': 7 8

       -- Function: integrate (<expr>, <x>)
       -- Function: integrate (<expr>, <x>, <a>, <b>)
           Attempts to symbolically compute the integral of <expr> with
           respect to <x>.  `integrate (<expr>, <x>)' is an indefinite
           integral, while `integrate (<expr>, <x>, <a>, <b>)' is a
           definite integral, [...]

       -- Option variable: integrate_use_rootsof
           Default value: `false'

           When `integrate_use_rootsof' is `true' and the denominator of
           a rational function cannot be factored, `integrate' returns
           the integral in a form which is a sum over the roots (not yet
           known) of the denominator.
           [...]

  In this example, items 7 and 8 were selected (output is shortened as indicated by `[...]`. All or none of the items could have been selected by entering `all` or `none`, which can be abbreviated `a` or `n`, respectively.

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  @ref{Category: Help} · @ref{Category: Console interaction}

Function: example (topic)
Function: example ()

  `example (topic)` displays some examples of topic, which is a symbol or a string. To get examples for operators like `if`, `do`, or `lambda` the argument must be a string, e.g. `example ("do")`. `example` is not case sensitive. Most topics are function names.

  `example ()` returns the list of all recognized topics.

  The name of the file containing the examples is given by the global option variable `manual_demo`, which defaults to `"manual.demo"`.

  `example` quotes its argument. `example` returns `done` unless no examples are found or there is no argument, in which case `example` returns the list of all recognized topics.

  Examples:

      (%i1) example(append);
      (%i2) append([x+y,0,-3.2],[2.5E+20,x])
      (%o2)                    [y + x, 0, - 3.2, 2.5E+20, x]
      (%o2)                                done
      (%i3) example("lambda");
      (%i4) lambda([x,y,z],z^2+y^2+x^2)
                                                 2    2    2
      (%o4)                   lambda([x, y, z], z  + y  + x )
      (%i5) %(1,2,a)
                                           2
      (%o5)                               a  + 5
      (%i6) a+2+1
      (%o6)                                a + 3
      (%o6)                                done
      (%i7) example("allROOTS");
      (%i8) (1+2*x)^3 = 13.5*(1+x^5)
                                         3          5
      (%o8)                     (2 x + 1)  = 13.5 (x  + 1)
      (%i9) allroots(%)
      (%o9) [x = .8296749902129361, x = - 1.015755543828121,
      x = .9659625152196369 %i - .4069597231924075,
      x = - .9659625152196369 %i - .4069597231924075, x = 1.0]
      (%o9)                                done

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  @ref{Category: Help} · @ref{Category: Console interaction}

Option variable: manual_demo

  Default value: `"manual.demo"`

  `manual_demo` specifies the name of the file containing the examples for the function `example`. See `example`.

  ·

  @ref{Category: Help} · @ref{Category: Global variables}

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