FullForm , Echo , PrettyForm , EvalFormula , TeXForm , CForm , Write , WriteString , Space , NewLine , FromFile , FromString , ToFile , ToString , Read , LispRead , ReadToken , Load , Use , DefLoad , FindFile , PatchLoad , Nl , V, Verbose , Plot2D .

# Input/output and plotting

This chapter contains commands to use for input and output and plotting. All output commands write to the same destination stream, called the "current output". This is initially the screen, but may be redirected by some commands. Similarly, most input commands read from the "current input" stream, which can also be redirected. The exception to this rule are the commands for reading script files, which simply read a specified file.

FullForm | print an expression in LISP-format
Echo | high-level printing routine
PrettyForm | print an expression nicely with ASCII art
EvalFormula | print an evaluation nicely with ASCII art
TeXForm | export expressions to LaTeX
CForm | export expression to C code
Write | low-level printing routine
WriteString | low-level printing routine for strings
Space | print one or more spaces
NewLine | print one or more newline characters
FromFile | connect current input to a file
FromString | connect current input to a string
ToFile | connect current output to a file
ToString | connect current output to a string
Read | read an expression from current input
LispRead | read an expression in LISP-syntax
ReadToken | read an token from current input
Load | evaluate all expressions in a file
Use | load a file, but not twice
DefLoad | load a `.def` file
FindFile | find a file in the current path
PatchLoad | execute commands between `<?` and `?>` in file
Nl | the newline character
V, Verbose | set verbose output mode
Plot2D | adaptive two-dimensional plotting

###

FullForm -- print an expression in LISP-format

##### Internal function

##### Calling format:

    FullForm(expr)

##### Parameters:

expr - expression to be printed in LISP-format

##### Description:

Evaluates "expr", and prints it in LISP-format on the current output. It is followed by a newline. The evaluated expression is also returned.

This can be useful if you want to study the internal representation of a certain expression.

##### Examples:

    In> FullForm(a+b+c);
    (+ (+ a b )c )
    Out> a+b+c;
    In> FullForm(2*I*b^2);
    (* (Complex 0 2 )(^ b 2 ))
    Out> Complex(0,2)*b^2;

The first example shows how the expression `a+b+c` is internally represented. In the second example, `2*I` is first evaluated to `Complex(0,2)` before the expression is printed.

##### See also:

LispRead , Listify , Unlist .

###

Echo -- high-level printing routine

##### Standard library

##### Calling format:

    Echo(item)
    Echo(list)
    Echo(item,item,item,...)

##### Parameters:

`item` -- the item to be printed

`list` -- a list of items to be printed

##### Description:

If passed a single item, `Echo` will evaluate it and print it to the current output, followed by a newline. If `item` is a string, it is printed without quotation marks.

If there is one argument, and it is a list, `Echo` will print all the entries in the list subsequently to the current output, followed by a newline. Any strings in the list are printed without quotation marks. All other entries are followed by a space.

`Echo` can be called with a variable number of arguments, they will all be printed, followed by a newline.

`Echo` always returns `True`.

##### Examples:

    In> Echo(5+3);
     8
    Out> True;
    In> Echo({"The square of two is ", 2*2});
    The square of two is 4
    Out> True;
    In> Echo("The square of two is ", 2*2);
    The square of two is 4
    Out> True;

Note that one must use the second calling format if one wishes to print a list:

    In> Echo({a,b,c});
    a b c
    Out> True;
    In> Echo({{a,b,c}});
    {a,b,c}
    Out> True;

##### See also:

PrettyForm , Write , WriteString , RuleBaseListed .

###

PrettyForm -- print an expression nicely with ASCII art

##### Standard library

##### Calling format:

    PrettyForm(expr)

##### Parameters:

expr - an expression

##### Description:

PrettyForm renders an expression in a nicer way, using ascii art. This is generally useful when the result of a calculation is more complex than a simple number.

##### Examples:

    In> Taylor(x,0,9)Sin(x)
    Out> x-x^3/6+x^5/120-x^7/5040+x^9/362880;
    In> PrettyForm(%)

         3    5      7       9
        x    x      x       x
    x - -- + --- - ---- + ------
        6    120   5040   362880

    Out> True;

##### See also:

EvalFormula , PrettyPrinter .

###

EvalFormula -- print an evaluation nicely with ASCII art

##### Standard library

##### Calling format:

    EvalFormula(expr)

##### Parameters:

expr - an expression

##### Description:

Show an evaluation in a nice way, using PrettyPrinter to show 'input = output'.

##### Examples:

    In> EvalFormula(Taylor(x,0,7)Sin(x))

                                          3    5
                                         x    x
    Taylor( x , 0 , 5 , Sin( x ) ) = x - -- + ---
                                         6    120

    Out> True

##### See also:

PrettyForm .

###

TeXForm -- export expressions to LaTeX

##### Standard library

##### Calling format:

    TeXForm(expr)

##### Parameters:

`expr` -- an expression to be exported

##### Description:

`TeXForm` returns a string containing a LaTeX representation of the Yacas expression `expr`. Currently the exporter handles most expression types but not all.

##### Example:

    In> TeXForm(Sin(a1)+2*Cos(b1))
    Out> "$\sin a_{1} + 2 \cos b_{1}$";

##### See also:

PrettyForm , CForm , ShowPS .

###

CForm -- export expression to C code

##### Standard library

##### Calling format:

    CForm(expr)

##### Parameters:

`expr` -- expression to be exported

##### Description:

`CForm` returns a string containing a C/C++ code implementing the Yacas expression `expr`. Currently the exporter handles most expression types but not all.

##### Example:

    In> CForm(Sin(a1)+2*Cos(b1));
    Out> "sin(a1) + 2 * cos(b1)";

##### See also:

PrettyForm , TeXForm .

###

Write -- low-level printing routine

##### Internal function

##### Calling format:

    Write(expr, ...)

##### Parameters:

`expr` -- expression to be printed

##### Description:

The expression "expr" is evaluated and written to the current output. Note that Write accept an arbitrary number of arguments, all of which are written to the current output (see second example). `Write` always returns `True`.

##### Examples:

    In> Write(1);
    1Out> True;
    In> Write(1,2);
     1 2Out> True;

Write does not write a newline, so the `Out>` prompt immediately follows the output of `Write`.

##### See also:

Echo , WriteString .

###

WriteString -- low-level printing routine for strings

##### Internal function

##### Calling format:

    WriteString(string)

##### Parameters:

`string` -- the string to be printed

##### Description:

The expression "string" is evaluated and written to the current output without quotation marks. The argument should be a string. WriteString always returns True.

##### Examples:

    In> Write("Hello, world!");
    "Hello, world!"Out> True;
    In> WriteString("Hello, world!");
    Hello, world!Out> True;

This example clearly shows the difference between Write and WriteString. Note that Write and WriteString do not write a newline, so the `Out>` prompt immediately follows the output.

##### See also:

Echo , Write .

###

Space -- print one or more spaces

##### Standard library

##### Calling format:

    Space()
    Space(nr)

##### Parameters:

`nr` -- the number of spaces to print

##### Description:

The command `Space()` prints one space on the current output. The second form prints `nr` spaces on the current output. The result is always True.

##### Examples:

    In> Space(5);
         Out> True;

##### See also:

Echo , Write , NewLine .

###

NewLine -- print one or more newline characters

##### Standard library

##### Calling format:

    NewLine()
    NewLine(nr)

##### Parameters:

`nr` -- the number of newline characters to print

##### Description:

The command `NewLine()` prints one newline character on the current output. The second form prints "nr" newlines on the current output. The result is always True.

##### Examples:

    In> NewLine();

    Out> True;

##### See also:

Echo , Write , Space .

###

FromFile -- connect current input to a file

##### Internal function

##### Calling format:

    FromFile(name) body

##### Parameters:

`name` - string, the name of the file to read

`body` - expression to be evaluated

##### Description:

The current input is connected to the file "name". Then the expression "body" is evaluated. If some functions in "body" try to read from current input, they will now read from the file "name". Finally, the file is closed and the result of evaluating "body" is returned.

##### Examples:

Suppose that the file `foo` contains

    2 + 5;

Then we can have the following dialogue:

    In> FromFile("foo") res := Read();
    Out> 2+5;
    In> FromFile("foo") res := ReadToken();
    Out> 2;

##### See also:

ToFile , FromString , Read , ReadToken .

###

FromString -- connect current input to a string

##### Internal function

##### Calling format:

    FromString(str) body;

##### Parameters:

str - a string containing the text to parse

body - expression to be evaluated

##### Description:

The commands in "body" are executed, but everything that is read from the current input is now read from the string "str". The result of "body" is returned.

##### Examples:

    In> FromString("2+5; this is never read") \
      res := Read();
    Out> 2+5;
    In> FromString("2+5; this is never read") \
      res := Eval(Read());
    Out> 7;

##### See also:

ToString , FromFile , Read , ReadToken .

###

ToFile -- connect current output to a file

##### Internal function

##### Calling format:

    ToFile(name) body

##### Parameters:

name - string, the name of the file to write the result to

body - expression to be evaluated

##### Description:

The current output is connected to the file "name". Then the expression "body" is evaluated. Everything that the commands in "body" print to the current output, ends up in the file "name". Finally, the file is closed and the result of evaluating "body" is returned.

##### Examples:

Here is how one can create a file with C code to evaluate an expression:

    In> ToFile("expr1.c") WriteString(
      CForm(Sqrt(x-y)*Sin(x)) );
    Out> True;

The file `expr1.c` was created in the current working directory and it contains

    sqrt(x-y)*sin(x)

As another example, take a look at the following command:

    In> [ Echo("Result:");  \
      PrettyForm(Taylor(x,0,9) Sin(x)); ];
    Result:

         3    5      7       9
        x    x      x       x
    x - -- + --- - ---- + ------
        6    120   5040   362880

    Out> True;

Now suppose one wants to send the output of this command to a file. This can be achieved as follows:

    In> ToFile("out") [ Echo("Result:");  \
      PrettyForm(Taylor(x,0,9) Sin(x)); ];
    Out> True;

After this command the file `out` contains:

    Result:

         3    5      7       9
        x    x      x       x
    x - -- + --- - ---- + ------
        6    120   5040   362880

##### See also:

FromFile , ToString , Echo , Write , WriteString , PrettyForm , Taylor .

###

ToString -- connect current output to a string

##### Internal function

##### Calling format:

    ToString() body

##### Parameters:

body - expression to be evaluated

##### Description:

The commands in "body" are executed. Everything that is printed on the current output, by `Echo` for instance, is collected in a string and this string is returned.

##### Examples:

    In> str := ToString() [ WriteString(  \
      "The square of 8 is "); Write(8^2); ];
    Out> "The square of 8 is  64";

##### See also:

FromFile , ToString , Echo , Write , WriteString .

###

Read -- read an expression from current input

##### Internal function

##### Calling format:

    Read()

##### Description:

Read an expression from the current input, and return it unevaluated. When the end of an input file is encountered, the token atom `EndOfFile` is returned.

##### Examples:

    In> FromString("2+5;") Read();
    Out> 2+5;
    In> FromString("") Read();
    Out> EndOfFile;

##### See also:

FromFile , FromString , LispRead , ReadToken , Write .

###

LispRead -- read an expression in LISP-syntax

##### Internal function

##### Calling format:

    LispRead()

##### Description:

Read an expression in LISP syntax from the current input, and return it unevaluated. When the end of an input file is encountered, the token atom `EndOfFile` is returned.

The expression `a+b` is written in LISP syntax as `(+ a b)`. The advantage of this syntax is that it is less ambiguous than the infix operator grammar that Yacas uses by default.

##### Examples:

    In> FromString("(+ a b)") LispRead();
    Out> a+b;
    In> FromString("(List (Sin x) (- (Cos x)))") \
      LispRead();
    Out> {Sin(x),-Cos(x)};

##### See also:

FromFile , FromString , Read , ReadToken , FullForm .

###

ReadToken -- read an token from current input

##### Internal function

##### Calling format:

    ReadToken()

##### Description:

Read a token from the current input, and return it unevaluated. When the end of an input file is encountered, the token atom `EndOfFile` is returned.

A token is for computer languages what a word is for human languages: it is the smallest unit in which a command can be divided, so that the semantics (that is the meaning) of the command is in some sense a combination of the semantics of the tokens. Hence `a := foo` consists of three tokens, namely `a`, `:=`, and `foo`.

##### Examples:

    In> FromString("a := Sin(x)") While \
      ((tok := ReadToken()) != EndOfFile) \
      Echo(tok);
    a
    :=
    Sin
    (
    x
    )
    Out> True;

##### See also:

FromFile , FromString , Read , LispRead .

###

Load -- evaluate all expressions in a file

##### Internal function

##### Calling format:

    Load(name)

##### Parameters:

name - string, name of the file to load

##### Description:

The file "name" is opened. All expressions in the file are read and evaluated. `Load` always returns `true`.

##### See also:

Use , DefLoad , DefaultDirectory , FindFile .

###

Use -- load a file, but not twice

##### Internal function

##### Calling format:

    Use(name)

##### Parameters:

name - string, name of the file to load

##### Description:

If the file "name" has been loaded before, either by an earlier call to `Use` or via the `DefLoad` mechanism, nothing happens. Otherwise all expressions in the file are read and evaluated. `Use` always returns `true`.

The purpose of this function is to make sure that the file will at least have been loaded, but is not loaded twice.

##### See also:

Load , DefLoad , DefaultDirectory .

###

DefLoad -- load a `.def` file

##### Internal function

##### Calling format:

    DefLoad(name)

##### Parameters:

name - string, name of the file (without `.def` suffix)

##### Description:

The suffix `.def` is appended to "name" and the file with this name is loaded. It should contain a list of functions, terminated by a closing brace \} (the end-of-list delimiter). This tells the system to load the file "name" as soon as the user calls one of the functions named in the file (if not done so already). This allows for faster startup times, since not all of the rules databases need to be loaded, just the descriptions on which files to load for which functions.

##### See also:

Load , Use , DefaultDirectory .

###

FindFile -- find a file in the current path

##### Internal function

##### Calling format:

    FindFile(name)

##### Parameters:

name - string, name of the file or directory to find

##### Description:

The result of this command is the full path to the file that would be opened when the command `Load(name)` would be invoked. This means that the input directories are subsequently searched for a file called "name". If such a file is not found, `FindFile` returns an empty string.

`FindFile("")` returns the name of the default directory (the first one on the search path).

##### See also:

Load , DefaultDirectory .

###

PatchLoad -- execute commands between `<?` and `?>` in file

##### Internal function

##### Calling format:

    PatchLoad(name)

##### Parameters:

name - string, name of the file to "patch"

##### Description:

`PatchLoad` loads in a file and outputs the contents to the current output. The file can contain blocks delimited by `<?` and `?>` (meaning "Yacas Begin" and "Yacas End"). The piece of text between such delimiters is treated as a separate file with Yacas instructions, which is then loaded and executed. All output of write statements in that block will be written to the same current output.

This is similar to the way PHP works. You can have a static text file with dynamic content generated by Yacas.

##### See also:

PatchString , Load .

###

Nl -- the newline character

##### Standard library

##### Calling format:

    Nl()

##### Description:

This function returns a string with one element in it, namely a newline character. This may be useful for building strings to send to some output in the end.

Note that the second letter in the name of this command is a lower case `L` (from "line").

##### Examples:

    In> WriteString("First line" : Nl() : "Second line" : Nl());
    First line
    Second line
    Out> True;

##### See also:

NewLine .

###

V, Verbose -- set verbose output mode

##### Standard library

##### Calling format:

    V(expression)

##### Parameters:

`expression` -- expression to be evaluated in verbose mode

##### Description:

The function `V(expression)` will evaluate the expression in verbose mode. Various parts of Yacas can show extra information about the work done while doing a calculation when using `V`.

The function is currently implemented using a global variable `Verbose` which can be set to `True` or `False`.

##### Examples:

    In> Solve({x+2==0},{x})
    Out> {{-2}};
    In> V(Solve({x+2==0},{x}))
    Entering Solve
    From  x+2==0  it follows that  x  = -2
       x+2==0  simplifies to  True
    Leaving Solve
    Out> {{-2}};

##### See also:

Echo , N , Solve .

###

Plot2D -- adaptive two-dimensional plotting

##### Standard library

##### Calling format:

    Plot2D(f(x))
    Plot2D(f(x), a:b)
    Plot2D(f(x), a:b, option=value)
    Plot2D(f(x), a:b, option=value, ...)
    Plot2D(list, ...)

##### Parameters:

`f(x)` -- unevaluated expression containing one variable (function to be plotted)

`list` -- list of functions to plot

`a`, `b` -- numbers, plotting range

`option` -- atom, option name

`value` -- atom, number or string (value of option)

##### Description:

The routine `Plot2D` performs adaptive plotting of one or several functions of one variable in the specified range. Several functions are specified by giving a list of expressions. Various plotting options can be specified. Output can be directed to a plotting program (the default is to use `gnuplot`), to a data file, or to a list of values.

The function parameter `f(x)` must be an unevaluated expression containing a variable (not necessarily called `x`). Several functions may be specified as a list and they do not have to depend on the same variable, for example, `{f(x), g(y)}`.

Data files are created in a temporary directory `/tmp/plot.tmp/`. File names and other information is printed if the `Verbose` option is switched on using `V()`.

The current algorithm uses Newton-Cotes quadratures and some heuristics for error estimation (see the essay chapter on adaptive plotting). The initial grid of `points+1` points is refined between any grid points a, b where the integral Integrate(x,a,b)f(x) is not approximated within given precision by the existing grid.

Default plotting range is `-5:5`. Range can also be specified by `x=-5:5`; currently the variable name `x` is ignored.

Options are of the form `option=value`. Currently supported option names are: "points", "precision", "depth", "output", "filename". Option values are either numbers or special unevaluated atoms such as `data`. If names of these atoms are needed in the program, strings can be used (e.g. `output="gnuplot"`). Several option/value pairs may be specified (the function `Plot2D` has a variable number of arguments).

- `points`: initial number of points (default 23) -- at least that many points will be plotted. The initial grid of this many points will be adaptively refined.
- `precision`: graphing precision (default 10^(-6)). This is interpreted as the relative precision of computing the integral of f(x)-Min(f(x)) using the grid points. For a smooth, non-oscillating function this value should be roughly 1/(number of screen pixels in the plot).
- `depth`: max. refinement depth, logarithmic (default 5) -- means there will be at most 2^depth extra points per initial grid point.
- `output`: symbolic name of the plotting backend. Supported values: `gnuplot` (default), `plotutils`, `datafile`, `data`. The `gnuplot` value will display the plot on the screen (requires the `gnuplot` program). The `plotutils` value requires the GNU `plotutils` suite and the `graph` program (under X Window).The `datafile` value will write the data to a text file with specified name. The `data` value will return the data as a list of pairs such as `{{x1,y1}, {x2,y2}, ...}`
- `filename`: specify name of the output file (currently used only by the `datafile` output option). For example: `filename="data1.txt"`. Default is the name `"output.data"`.

Other options may be supported in the future. Note that currently the support for `gnuplot` and GNU `plotutils` is Unix-specific.

A frequently encountered problem: the parameter `f(x)` must evaluate to an expression that contains a variable (or to a constant). Test your function for this! If you have defined some `f(x)` which accepts a number but does not accept an undefined variable, `Plot2D` will fail to plot it. Use `NFunction` to overcome this difficulty.

The current implementation can deal with a singularity at endpoints or at any grid point only if the function `f(x)` returns `Infinity`, `-Infinity` or `Undefined`. If the function `f(x)` generates a numerical error and fails at a singularity, `Plot2D` will fail too, if one of the grid points falls on the singularity. (All grid points are generated by bisection so in principle the endpoints and the `points` parameter could be chosen to avoid numerical singularities.)

##### Examples:

    In> Plot2D({(2+x)/(2-x),Exp(y)},-1.8:1.5)
    Out> True;
    In> V(Plot2D(Sin(1/x),0:1, depth=4, \
    In>   precision=0.001, output=plotutils))
    Plot2D: using 65 points for function Sin(1/x)
    Plot2D'datafile: created file '/tmp/plot.tmp/data1'
    Out> True;

If a function takes a long time to evaluate, one can use `MakeFunctionPlugin` (a Unix-specific tool) to compile the function and plot it faster:

    In> f(x) := Cos( (Abs(Pi/x))^1.5 )
    Out> True;
    In> Time( Plot2D(f(x),0:1) )
    94.93 seconds taken
    Out> True;
    In> MakeFunctionPlugin("f1", f(x))
    Function f1(x) loaded from plugins.tmp/
      libf1_plugin_cc.so
    Out> True;
    In> Time( Plot2D(f1(x),0:1) )
    6.97 seconds taken
    Out> True;

##### See also:

V , NFunction , MakeFunctionPlugin .