<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %A  mloop.msk                  GAP documentation             Martin Schönert -->
<!-- %% -->
<!-- %A @(#)<M>Id: mloop.msk,v 1.34 2006/09/12 14:51:14 jjm Exp </M> -->
<!-- %% -->
<!-- %Y Copyright 1990-1992, Lehrstuhl D für Mathematik, RWTH Aachen, Germany -->
<!-- %% -->
<Chapter Label="Main Loop and Break Loop">
<Heading>Main Loop and Break Loop</Heading>

This chapter is a first of a series of chapters that describe the
interactive environment in which you use &GAP;.


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Main Loop">
<Heading>Main Loop</Heading>

<Index>read eval print loop</Index>
<Index Subkey="read eval print">loop</Index>
<Index>prompt</Index>
<Index Subkey="partial">prompt</Index>
<Index>syntax errors</Index>
<Index Subkey="syntax">errors</Index>
<Index Subkey="suppressing">output</Index>
<Index Key="last"><C>last</C></Index>
<Index Key="last2"><C>last2</C></Index>
<Index Key="last3"><C>last3</C></Index>
<Index>previous result</Index>
The normal interaction with &GAP; happens in the so-called
<E>read-eval-print</E> loop.
This means that you type an input, &GAP; first reads it,
evaluates it, and then shows the result.
Note that the term <E>print</E> may be confusing since there is a &GAP;
function called <Ref Func="Print"/> (see&nbsp;<Ref Sect="View and Print"/>)
which is in fact <E>not</E> used in the read-eval-print loop,
but traditions are hard to break.
In the following, whenever we want to express that &GAP; places some
characters on the standard output, we will say that &GAP; <E>shows</E>
something.
<P/>
The exact sequence in the read-eval-print loop is as follows.
<P/>
To signal that it is ready to accept your input,
&GAP; shows the <E>prompt</E> <C>gap></C>.
When you see this, you know that &GAP; is waiting for your input.
<P/>
Note that every statement must be terminated by a semicolon. You must
also enter <B>Return</B> (i.e., strike the <B>Return</B> key)
before &GAP; starts to read and evaluate your input.
(The <B>Return</B> key may actually be marked with the word <B>Enter</B>
and a returning arrow on your terminal.)
Because &GAP; does not do anything until you enter <B>Return</B>, you can
edit your input to fix typos and only when everything is correct enter
<B>Return</B> and have &GAP; take a look at it
(see&nbsp;<Ref Sect="Line Editing"/>). It is
also possible to enter several statements as input on a single line. Of
course each statement must be terminated by a semicolon.
<P/>
It is absolutely acceptable to enter a single statement on several lines.
When you have entered the beginning of a statement, but the statement is
not yet complete, and you enter <B>Return</B>,
&GAP; will show the <E>partial prompt</E> <C>></C>.
When you see this, you know that &GAP; is waiting for the rest
of the statement. This happens also when you forget
the semicolon <C>;</C> that terminates every &GAP; statement.
Note that when <B>Return</B> has been entered and the current statement is not
yet complete, &GAP; will already evaluate those parts of the input that 
are complete, for example function calls that appear as arguments in
another function call which needs several input lines.
So it may happen that one has to wait some time for the partial prompt.
<!-- % And side-effects caused by the first lines are executed although -->
<!-- % a syntax error in a later input line may invalidate the whole statement. -->
<P/>
When you enter <B>Return</B>, &GAP; first checks your input to see if it is
syntactically correct
(see Chapter&nbsp;<Ref Chap="The Programming Language"/> for the
definition of syntactically correct). If it is not, &GAP; prints an
error message of the following form
<P/>
<Log><![CDATA[
gap> 1 * ;
Syntax error: expression expected
1 * ;
    ^
]]></Log>
<P/>
The first line tells you what is wrong about the input, in this case the
<C>*</C> operator takes two expressions as operands, so obviously the right
one is missing.
If the input came from a file (see&nbsp;<Ref Func="Read"/>), this line
will also contain the filename and the line number. The second line is a
copy of the input. And the third line contains a caret pointing to the
place in the previous line where &GAP; realized that something is wrong.
This need not be the exact place where the error is, but it is usually
quite close.
<P/>
Sometimes, you will also see a partial prompt after you have entered an
input that is syntactically incorrect. This is because &GAP; is so
confused by your input, that it thinks that there is still something to
follow.
In this case you should enter <C>;</C><B>Return</B> repeatedly,
ignoring
further error messages, until you see the full prompt again. When you
see the full prompt, you know that &GAP; forgave you and is now ready to
accept your next &ndash;hopefully correct&ndash; input.
<P/>
If your input is syntactically correct, &GAP; evaluates or executes it,
i.e., performs the required computations
(see Chapter&nbsp;<Ref Chap="The Programming Language"/>
for the definition of the evaluation).
<P/>
If you do not see a prompt, you know that &GAP; is still working on your
last input. Of course, you can <E>type ahead</E>, i.e., already start
entering new input, but it will not be accepted by &GAP; until &GAP;
has completed the ongoing computation.
<P/>
When &GAP; is ready it will usually show the result of the computation,
i.e., the value computed. Note that not all statements produce a value,
for example, if you enter a <K>for</K> loop, nothing will be printed,
because the <K>for</K> loop does not produce a value that could be shown.
<P/>
Also sometimes you do not want to see the result. For example if you
have computed a value and now want to assign the result to a variable,
you probably do not want to see the value again. You can terminate
statements by <E>two semicolons</E> to suppress showing the result.
<P/>
If you have entered several statements on a single line &GAP; will first
read, evaluate, and show the first one, then read, evaluate, and show
the second one, and so on. This means that the second statement will not
even be checked for syntactical correctness until &GAP; has completed
the first computation.
<P/>
After the result has been shown &GAP; will display another prompt, and
wait for your next input.
And the whole process starts all over again.
Note that if you have entered several statements on a single line,
a new prompt will only be printed after &GAP; has read, evaluated,
and shown the last statement.
<P/>
In each statement that you enter, the result of the previous statement
that produced a value is available in the variable <C>last</C>.
The next to previous result is available in <C>last2</C>
and the result produced before that is available in <C>last3</C>.
<P/>
<Example><![CDATA[
gap> 1;2;3;
1
2
3
gap> last3 + last2 * last;
7
]]></Example>
<P/>
Also in each statement the time spent by the last statement, whether it
produced a value or not, is available in the variable <Ref Var="time"/>.
This is an integer that holds the number of milliseconds.

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Special Rules for Input Lines">
<Heading>Special Rules for Input Lines</Heading>

The input for some &GAP; objects may not fit on one line, in particular 
big integers, long strings or long identifiers. In these cases you can still
type or paste them in long single lines.
<!-- if most people use readline this becomes irrelevant:
but on screen you may only
see the last part (with a <C>$</C> character in front). -->
For nicer display you
can also specify  the input on several lines. This is achieved by ending a
line  by a backslash or by a backslash and a carriage return character, then
continue the input on the beginning of the next line. When reading this 
&GAP; will ignore such continuation backslashes, carriage return characters 
and newline characters. &GAP; also prints long strings and integers this way.
<P/>
<Example><![CDATA[
gap> n := 1234\
> 567890;
1234567890
gap> "This is a very long string that does not fit on a line \
> and is therefore continued on the next line.";
"This is a very long string that does not fit on a line and is therefo\
re continued on the next line."
gap> bla\
> bla := 5;; blabla;
5
]]></Example>
<P/>
There is a special rule about &GAP; prompts in input lines: In line editing 
mode (usual user input and &GAP; started without <C>-n</C>)  in lines starting 
with whitespace following <C>gap> </C>, <C>> </C> or <C>brk> </C> this 
beginning part is removed.
This rule is very convenient because it allows to cut and paste input
from other &GAP; sessions or manual examples easily into your current session.

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="View and Print">
<Heading>View and Print</Heading>

&GAP; has three different operations to display or print objects: 
<Ref Oper="Display"/>, <Ref Oper="ViewObj"/> and <Ref Oper="PrintObj"/>, 
and these three have different purposes as follows. The first, <Ref
    Oper="Display"/>, should print the object to the standard output
in a human-readable
relatively complete and verbose form. The second, <Ref
    Oper="ViewObj"/>, should print the object to the standard output
in a short and concise
form, it is used in the main read-eval-print loop to display the
resulting object of a computation. The third, <Ref Oper="PrintObj"/>,
should print the object to the standard output 
in a complete form which is &GAP;-readable if at all
possible, such that reading the output into &GAP; produces an object
which is equal to the original one.

<P/>
All three operations have corresponding operations which do not print
anything to standard output but return the output as a string. These
are <Ref Oper="DisplayString"/>, <Ref Oper="ViewString"/> and
<Ref Oper="PrintString"/> (corresponding to <Ref Oper="PrintObj"/>).
Additionally, there is <Ref Oper="String"/> which is very similar
to <Ref Oper="PrintString"/> but does not insert control characters
for line breaks.

<P/>
For implementation convenience it is allowed that some of these
operations have methods which delegate to some other of these
operations. However, the rules for this are that a method may only
delegate to another operation which appears further down in the
following table:

<P/>
<Table Align="|c|">
    <HorLine/>
    <Row> <Item><Ref Oper="Display"/></Item> </Row>
    <HorLine/>
    <Row> <Item><Ref Oper="ViewObj"/></Item> </Row>
    <HorLine/>
    <Row> <Item><Ref Oper="PrintObj"/></Item> </Row>
    <HorLine/>
    <Row> <Item><Ref Oper="DisplayString"/></Item> </Row>
    <HorLine/>
    <Row> <Item><Ref Oper="ViewString"/></Item> </Row>
    <HorLine/>
    <Row> <Item><Ref Oper="PrintString"/></Item> </Row>
    <HorLine/>
    <Row> <Item><Ref Oper="String"/></Item> </Row>
    <HorLine/>
</Table>

<P/>
This is to avoid circular delegations.

<P/>
Note in particular that none of the methods of the string producing operations 
may delegate to the corresponding printing operations. Note also that
the above mentioned purposes of the different operations suggest that
delegations between different operations will be sub-optimal in most
scenarios.

<Subsection>
    <Heading>Default delegations in the library</Heading>

The library contains the following low ranked default methods:

<List>
<Item>
    A method for 
<Ref Oper="DisplayString"/> which returns the constant value
of the global variable <Ref Var="DEFAULTDISPLAYSTRING"/>.
</Item>

<Item>
A method for 
<Ref Oper="ViewString"/> which returns the constant value
of the global variable <Ref Var="DEFAULTVIEWSTRING"/>.
</Item>

<Item>
A method for <Ref
    Oper="Display"/> which first calls <Ref Oper="DisplayString"/>
and prints the result, if it is a different object than <Ref
    Var="DEFAULTDISPLAYSTRING"/>. Otherwise the method delegates
to <Ref Oper="PrintObj"/>.
</Item>

<Item>
A method for <Ref
    Oper="ViewObj"/> which first calls <Ref Oper="ViewString"/>
and prints the result, if it is a different object than <Ref
    Var="DEFAULTVIEWSTRING"/>. Otherwise the method delegates
to <Ref Oper="PrintObj"/>.
</Item>

<Item>
A method for <Ref Oper="PrintObj"/> which prints the result of <Ref
    Oper="PrintString"/>.
</Item>

<Item>
    A method for <Ref Oper="PrintString"/> which returns the result
    of <Ref Oper="String"/>
</Item>

</List>

</Subsection>

<Subsection>
    <Heading>Recommendations for the implementation</Heading>

This subsection describes what methods for printing and viewing one
should implement for new &GAP; objects.

<P/>
One should at the very least install a <Ref Oper="String"/> method to
allow printing. Using the standard delegations this enables a limited
form of viewing, displaying and printing.

<P/>
If, for larger objects, nicer line breaks are needed, one should install
a separate <Ref Oper="PrintString"/> method which puts in positions for
good line breaks using the control characters <C>\&lt;</C> (ASCII 1) and
<C>\&gt;</C> (ASCII 2).

<P/>
If, for even larger objects, output performance and memory usage
matters, one should install a separate <Ref Oper="PrintObj"/> method.

<P/>
One should usually install a <Ref Oper="ViewString"/> method,
unless the above <Ref Oper="String"/> method is good enough for
<Ref Oper="ViewObj"/> purposes. Performance and memory should never
matter here, so it is usually unnecessary to install a separate <Ref
Oper="ViewObj"/> method.

<P/>
If the type of object calls for it one should install a 
<Ref Oper="DisplayString"/> method. This is the case if a human
readable verbose form is required.

<P/>
If the performance and memory usage for <Ref Oper="Display"/> matters, 
one should install a separate <Ref Oper="Display"/> method.

<P/>
Note that if only a <Ref Oper="String"/> method is installed, then
<Ref Oper="ViewObj"/> works and <Ref Oper="ViewString"/> returns <Ref
Var="DEFAULTVIEWSTRING"/>. Likewise, <Ref Oper="Display"/> works and
<Ref Oper="DisplayString"/> returns <Ref Var="DEFAULTDISPLAYSTRING"/>. If
you want to avoid this then install methods for these operations
as well.
</Subsection>

<#Include Label="View">

<ManSection>
<Func Name="Print" Arg='obj1, obj2, ...'/>

<Description>
Also <Ref Func="Print"/> shows the objects <A>obj1</A>, <A>obj2</A>... etc.
on the standard output.
The difference compared to <Ref Func="View"/> is in general that the shown
form is not required to be short,
and that in many cases the form shown by <Ref Func="Print"/> is &GAP;
readable.
<P/>
<!-- % For example for large matrices <Ref Func="Print"/> may print -->
<!-- % the full matrix, while <Ref Func="View"/> may only display the dimensions and the -->
<!-- % characteristic. -->
<Example><![CDATA[
gap> z:= Z(2);
Z(2)^0
gap> v:= [ z, z, z, z, z, z, z ];
[ Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ]
gap> ConvertToVectorRep(v);; v;
<a GF2 vector of length 7>
gap> Print( v, "\n" );
[ Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0, Z(2)^0 ]
]]></Example>
<P/>
Another difference is that <Ref Func="Print"/> shows strings without the
enclosing quotes, so <Ref Func="Print"/> can be used to produce formatted
text on the standard output
(see also chapter&nbsp;<Ref Chap="Strings and Characters"/>).
Some characters preceded by a backslash, such as <C>\n</C>, are processed
specially (see chapter&nbsp;<Ref Sect="Special Characters"/>).
<Ref Func="PrintTo"/> can be used to print to a file.
<P/>
<Example><![CDATA[
gap> for i in [1..5] do
>      Print( i, " ", i^2, " ", i^3, "\n" );
>    od;
1 1 1
2 4 8
3 9 27
4 16 64
5 25 125
gap> g:= SmallGroup(12,5);
<pc group of size 12 with 3 generators>
gap> Print( g, "\n" );
Group( [ f1, f2, f3 ] )
gap> View( g );  Print( "\n" );
<pc group of size 12 with 3 generators>
]]></Example>
</Description>
</ManSection>
<P/>
<ManSection>
<Oper Name="ViewObj" Arg='obj'/>
<Oper Name="PrintObj" Arg='obj'/>

<Description>
The functions <Ref Func="View"/> and <Ref Func="Print"/> actually call
the operations <Ref Oper="ViewObj"/> and&nbsp;<Ref Oper="PrintObj"/>,
respectively, for each argument.
By installing special methods for these operations,
it is possible to achieve special printing behavior for certain objects
(see chapter&nbsp;<Ref Chap="Method Selection"/>).
The only exceptions are strings
(see Chapter&nbsp;<Ref Chap="Strings and Characters"/>),
for which the default <Ref Oper="PrintObj"/> and <Ref Oper="ViewObj"/>
methods as well as the function <Ref Func="View"/> print also the enclosing
doublequotes, whereas <Ref Func="Print"/> strips the doublequotes.
<P/>
The default method for <Ref Oper="ViewObj"/> is to call
<Ref Oper="PrintObj"/>.
So it is sufficient to have a <Ref Oper="PrintObj"/> method for an object
in order to <Ref Func="View"/> it.
If one wants to supply a <Q>short form</Q> for <Ref Func="View"/>,
one can install additionally a method for <Ref Oper="ViewObj"/>.
</Description>
</ManSection>

<#Include Label="Display">

When setting up examples, in particular if for beginning users, it sometimes
can be convenient to hide the structure behind a printing name. For many
objects, such as groups, this can be done using <Ref Func="SetName"/>. If the
objects however is represented internally, for example permutations
representing group elements, this function is not applicable. Instead the
function <Ref Func="SetNameObject"/> can be used to interface with the
display routines on a lower level.

<#Include Label="SetNameObject">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Break Loops">
<Heading>Break Loops</Heading>

When an error has occurred or when you interrupt &GAP; (usually by
hitting <B>Ctrl-C</B>) &GAP; enters a break loop,
that is in most respects like the main read eval print loop
(see&nbsp;<Ref Sect="Main Loop"/>). That is, you can
enter statements, &GAP; reads them, evaluates them, and shows the
result if any. However those evaluations happen within the context in
which the error occurred. So you can look at the arguments and local
variables of the functions that were active when the error happened and
even change them. The prompt is changed from <C>gap></C> to <C>brk></C> to
indicate that you are in a break loop.
<P/>
<Log><![CDATA[
gap> 1/0;
Rational operations: <divisor> must not be zero
not in any function
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can replace <divisor> via 'return <divisor>;' to continue
]]></Log>
<P/>
If errors occur within a break loop &GAP; enters another break loop at a
<E>deeper level</E>. This is indicated by a number appended to <C>brk</C>:
<P/>
<Log><![CDATA[
brk> 1/0;
Rational operations: <divisor> must not be zero
not in any function
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can replace <divisor> via 'return <divisor>;' to continue
brk_02>
]]></Log>
<P/>
There are two ways to leave a break loop,
see <Ref Subsect="quit"/> and <Ref Subsect="subsect:return"/>.

<Subsection Label="quit">
<Heading>quit from a break loop</Heading>

The first way to leave a break loop is to <E>quit</E> the break loop.
To do this you enter <C>quit;</C> or type the <E>eof</E>
(<E>e</E>nd <E>o</E>f <E>f</E>ile) character,
which is usually <B>Ctrl-D</B> except when using the <C>-e</C> option (see 
Section&nbsp;<Ref Sect="Command Line Options"/>).
Note that &GAP; code between <C>quit;</C> and the end of the input line
is ignored.
<P/>
<Log><![CDATA[
brk_02> quit;
brk>
]]></Log>
<P/>
In this case control returns to the break loop one level above or
to the main loop, respectively.
So iterated break loops must be left iteratively.
Note also that if you type <C>quit;</C> from a <C>gap></C> prompt,
&GAP; will exit (see&nbsp;<Ref Sect="Leaving GAP"/>).
<P/>
<E>Note:</E>
If you leave a break loop with <K>quit</K> without completing a command
it is possible (though not very likely) that data structures
will be corrupted or incomplete data have been stored in objects.
Therefore no guarantee can be given that calculations afterwards
will return correct results! If you have been using options <K>quit</K>ting
a break loop generally leaves the options stack with options you no 
longer want. The function <Ref Func="ResetOptionsStack"/>
removes all options on the options stack, and this is the sole intended
purpose of this function.

</Subsection>


<Subsection Label="subsect:return">
<Heading>return from a break loop</Heading>

<Index Key="return"><K>return</K></Index>
<Index>return from break loop</Index>
The other way to leave a break loop is to <E>return</E> from a break loop.
To do this you type <C>return;</C> or <C>return <A>obj</A>;</C>.
If the break loop was entered because you interrupted &GAP;,
then you can continue by typing <C>return;</C>.
If the break loop was entered due to an error,
you may have to modify the value of a variable before typing <C>return;</C>
(see the example for&nbsp;<Ref Func="IsDenseList"/>) or you may have to
return an object <A>obj</A>
(by typing: <C>return <A>obj</A>;</C>) to continue the computation;
in any case, the message printed on entering the break loop will 
tell you which of these alternatives is possible.
For example, if the break loop was entered because a variable had no
assigned value, the value to be returned is often a value that this 
variable should have to continue the computation.
<P/>
<Log><![CDATA[
brk> return 9;  # we had tried to enter the divisor 9 but typed 0 ...
1/9
gap> 
]]></Log>

</Subsection>


<ManSection>
<Var Name="OnBreak"/>

<Description>
By default, when a break loop is entered, &GAP; prints a trace of the 
innermost 5 commands currently being executed. This behaviour can be
configured by changing the value of the global variable
<Ref Func="OnBreak"/>. When a break loop is entered,
the value of <Ref Func="OnBreak"/> is
checked. If it is a function, then it is called with no arguments. By
default, the value of <Ref Func="OnBreak"/> is <Ref Func="Where"/>.
<P/>
<Example><![CDATA[
gap> OnBreak := function() Print("Hello\n"); end;
function(  ) ... end
]]></Example>
<P/>
<Log><![CDATA[
gap> Error("!\n");
Error, !
Hello
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;
]]></Log>
<P/>
In cases where a break loop is entered during a function that was  called
with options (see Chapter&nbsp;<Ref Chap="Options Stack"/>),
a <C>quit;</C> will also cause the
options stack to be reset  and  an  <C>Info</C>-ed  warning  stating  this  is
emitted at <Ref Var="InfoWarning"/> level 1
(see Chapter&nbsp;<Ref Sect="Info Functions"/>).
<!-- %This is actually controlled by -->
<!-- % -->
<!-- %\>OnQuit() F -->
<!-- % -->
<!-- %which, like <Ref Func="OnBreak"/>, is a no-argument function. It is executed -->
<!-- %when a user elects to <C>quit;</C> a non-kernel-induced break loop. -->
<!-- %<C>OnQuit</C> is set read-only to a variant of <C>ResetOptionsStack</C> -->
<!-- %that warns when it does something rather than the other way round. -->
<!-- %It can be redefined after executing <C>MakeReadWriteGlobal( "OnQuit" );</C>. -->
<!-- %Currently, <C>OnQuit</C> is not  advertised, since exception handling  -->
<!-- %may make it obsolete. -->
<P/>
Note that for break loops entered by a call to <Ref Func="Error"/>,
the lines after <Q><C>Entering break read-eval-print loop ...</C></Q>
and before the <C>brk></C> prompt can also be customised,
namely by redefining <Ref Func="OnBreakMessage"/>.
<P/>
<Index Key="ErrorNoTraceBack"><C>ErrorNoTraceBack</C></Index>
Also, note that one can achieve the effect of changing <Ref Func="OnBreak"/>
<E>locally</E>.
As mentioned above, the default value of <Ref Func="OnBreak"/> is
<Ref Func="Where"/>. Thus,
a call to <Ref Func="Error"/> generally gives a trace back up to
five levels of calling functions. Conceivably, we might like to have
a function like <Ref Func="Error"/> that does not trace back without globally
changing <Ref Func="OnBreak"/>.
Such a function we might call <C>ErrorNoTraceBack</C>
and here is how we might define it.
(Note <C>ErrorNoTraceBack</C> is <E>not</E> a &GAP; function.)
<P/>
<Example><![CDATA[
gap> ErrorNoTraceBack := function(arg) # arg is special variable that GAP
>                                      # knows to treat as list of arg's
>      local SavedOnBreak, ENTBOnBreak;
>      SavedOnBreak := OnBreak;        # save current value of OnBreak
> 
>      ENTBOnBreak := function()       # our `local' OnBreak
>      local s;
>        for s in arg do
>          Print(s);
>        od;
>        OnBreak := SavedOnBreak;      # restore OnBreak afterwards
>      end;
> 
>      OnBreak := ENTBOnBreak;
>      Error();
>    end;
function( arg ) ... end
]]></Example>
<P/>
Here is a somewhat trivial demonstration of the use of
<C>ErrorNoTraceBack</C>.
<P/>
<Log><![CDATA[
gap> ErrorNoTraceBack("Gidday!", " How's", " it", " going?\n");
Error, Gidday! How's it going?
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;
]]></Log>
<P/>
Now we call <Ref Func="Error"/> with the same arguments to show the difference.
<P/>
<Log><![CDATA[
gap> Error("Gidday!", " How's", " it", " going?\n");
Error, Gidday! How's it going?
Hello
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;
]]></Log>
<P/>
Observe that the value of <Ref Func="OnBreak"/> before the
<C>ErrorNoTraceBack</C> call was restored.
However, we had changed <Ref Func="OnBreak"/> from its default value;
to restore <Ref Func="OnBreak"/> to its default value,
we should do the following.
<P/>
<Example><![CDATA[
gap> OnBreak := Where;;
]]></Example>
</Description>
</ManSection>

<ManSection>
<Var Name="OnBreakMessage"/>

<Description>
<Index>Break loop message</Index>
When a break loop is entered by a call to <Ref Func="Error"/>
the message after the
<Q><C>Entering break read-eval-print loop ...</C></Q> line is produced
by the function <C>OnBreakMessage</C>,
which just like <Ref Func="OnBreak"/>
is a user-configurable global variable
that is a <E>function</E> with <E>no arguments</E>.
<P/>
<Example><![CDATA[
gap> OnBreakMessage(); # By default, OnBreakMessage prints the following
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
]]></Example>
<P/>
Perhaps you are familiar with what's possible in a break loop, and so
don't need to be reminded. In this case, you might wish to do the
following (the first line just makes it easy to restore the default 
value later).
<P/>
<Example><![CDATA[
gap> NormalOnBreakMessage := OnBreakMessage;; # save the default value 
gap> OnBreakMessage := function() end;        # do-nothing function
function(  ) ... end
gap> OnBreakMessage();
gap> OnBreakMessage := NormalOnBreakMessage;; # reset
]]></Example>
<P/>
With <Ref Func="OnBreak"/> still set away from its default value,
calling <Ref Func="Error"/> as we did above, now produces:
<P/>
<Log><![CDATA[
gap> Error("!\n");
Error, !
Hello
Entering break read-eval-print loop ...
brk> quit; # to get back to outer loop
]]></Log>
<P/>
However, suppose you are writing a function which detects an error
condition and <C>OnBreakMessage</C> needs to be changed only <E>locally</E>,
i.e., the instructions on how to recover from the break loop need
to be specific to that function. The same idea used to define 
<C>ErrorNoTraceBack</C> (see <Ref Func="OnBreak"/>) can be adapted to achieve 
this. The function <Ref Func="CosetTableFromGensAndRels"/>
is an example in the &GAP; code where the idea is actually used.
</Description>
</ManSection>
<P/>
<ManSection>
<Func Name="Where" Arg='nr'/>

<Description>
<Index Subkey="GAP3 name for Where">Backtrace</Index>
<Index>Stack trace</Index>
shows the last <A>nr</A> commands on the execution stack during whose execution
the error occurred. If not given, <A>nr</A> defaults to 5. (Assume, for the
following example, that after the last example <Ref Func="OnBreak"/>
has been set back to its default value.)
<P/>
<Log><![CDATA[
gap> StabChain(SymmetricGroup(100)); # After this we typed ^C  
user interrupt at
bpt := S.orbit[1];
 called from
SiftedPermutation( S, (g * rep) ^ -1 ) called from
StabChainStrong( S.stabilizer, [ sch ], options ); called from
StabChainStrong( S.stabilizer, [ sch ], options ); called from
StabChainStrong( S, GeneratorsOfGroup( G ), options ); called from
StabChainOp( G, rec(
     ) ) called from
...
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> Where(2);
 called from
SiftedPermutation( S, (g * rep) ^ -1 ) called from
StabChainStrong( S.stabilizer, [ sch ], options ); called from
...
]]></Log>
<P/>
Note that the variables displayed even in the first line of the
<Ref Func="Where"/> list
(after the <C>called from</C> line) may be already one environment level higher 
and <Ref Func="DownEnv"/> may be necessary to access them.
<P/>
At the moment this backtrace does not work from within compiled code (this
includes the method selection which by default is compiled into the kernel).
If this creates problems for debugging, call &GAP; with the <C>-M</C> option
(see&nbsp;<Ref Sect="Command Line Options"/>)
to avoid loading compiled code.
<P/>
(Function calls to <Ref Func="Info"/> and methods installed for
binary operations are handled in a special way.
In rare circumstances it is possible therefore that they do not show up
in a <Ref Func="Where"/> log but the log refers to the <E>last</E>
proper function call that happened before.)
<P/>
The command line option <C>-T</C> to &GAP; disables the break loop. This
is mainly intended for testing purposes and for special
applications. If this option is given then errors simply cause &GAP;
to return to the main loop.
</Description>
</ManSection>

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Variable Access in a Break Loop">
<Heading>Variable Access in a Break Loop</Heading>

In a break loop access to variables of the current break level and higher
levels is possible, but if the same variable name is used for different
objects or if a function calls itself recursively, of course only the
variable at the lowest level can be accessed.

<ManSection>
<Heading>DownEnv and UpEnv</Heading>	
<Func Name="DownEnv" Arg='nr'/>
<Func Name="UpEnv" Arg='nr'/>

<Description>
<Ref Func="DownEnv"/> moves down <A>nr</A> steps in the environment and
allows one to inspect variables on this level;
if <A>nr</A> is negative it steps up in the environment again;
<A>nr</A> defaults to 1 if not given.
<Ref Func="UpEnv"/> acts similarly to <Ref Func="DownEnv"/>
but in the reverse direction
(the mnemonic rule to remember the difference between 
<Ref Func="DownEnv"/> and <Ref Func="UpEnv"/> is the order in which commands
on the execution stack are displayed by <Ref Func="Where"/>).
<P/>
<Log><![CDATA[
gap> OnBreak := function() Where(0); end;; # eliminate back-tracing on
gap>                                       # entry to break loop
gap> test:= function( n )
>    if n > 3 then Error( "!\n" ); fi; test( n+1 ); end;;
gap> test( 1 );
Error, !
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> Where();
 called from
test( n + 1 ); called from
test( n + 1 ); called from
test( n + 1 ); called from
<function>( <arguments> ) called from read-eval-loop
brk> n;
4
brk> DownEnv();
brk> n;
3
brk> Where();
 called from
test( n + 1 ); called from
test( n + 1 ); called from
<function>( <arguments> ) called from read-eval-loop
brk> DownEnv( 2 );
brk> n;
1
brk> Where();
 called from
<function>( <arguments> ) called from read-eval-loop
brk> DownEnv( -2 );
brk> n;
3
brk> quit;
gap> OnBreak := Where;; # restore OnBreak to its default value
]]></Log>
<P/>
Note that the change of the environment caused by <Ref Func="DownEnv"/>
only affects variable access in the break loop.
If you use <K>return</K> to continue a
calculation &GAP; automatically jumps to the right environment level
again.
<P/>
Note also that search for variables looks first in the chain of outer
functions which enclosed the definition of a currently executing
function, before it looks at the chain of calling functions which led
to the current invocation of the function. 
<P/>
<Log><![CDATA[
gap> foo := function()
> local x; x := 1;
> return function() local y; y := x*x; Error("!!\n"); end;
> end;
function(  ) ... end
gap> bar := foo();
function(  ) ... end
gap> fun := function() local x; x := 3; bar(); end;
function(  ) ... end
gap> fun();
Error, !!
 called from
bar(  ); called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> x;
1
brk> DownEnv(1);
brk> x;
3
]]></Log>
<P/>
Here the <C>x</C> of <C>foo</C> which contained the definition of <C>bar</C>
is found before that of <C>fun</C> which caused its execution.
Using <Ref Func="DownEnv"/> we can access the <C>x</C> from <C>fun</C>.
</Description>
</ManSection>

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sect:Error">
<Heading>Error and ErrorCount</Heading>

<ManSection>
<Func Name="Error" Arg='messages ...'/>

<Description>
<Ref Func="Error"/> signals an error from within a function.
First the messages <A>messages</A> are printed,
this is done exactly as if <Ref Func="Print"/>
(see&nbsp;<Ref Sect="View and Print"/>)
were called with these arguments.
Then a break loop (see&nbsp;<Ref Sect="Break Loops"/>) is
entered, unless the standard error output is not connected to a terminal.
You can leave this break loop with <C>return;</C> to continue execution with
the statement following the call to <Ref Func="Error"/>.
</Description>
</ManSection>


<ManSection>
<Func Name="ErrorCount" Arg=''/>

<Description>
<Ref Func="ErrorCount"/> returns a count of the number of errors
(including user interruptions) which have occurred in the &GAP; session
so far.
This count is reduced modulo <M>2^{28}</M> on <M>32</M> bit systems,
<M>2^{60}</M> on <M>64</M> bit systems.
The count is incremented by each error, even if &GAP; was
started with the <C>-T</C> option to disable the break loop.
</Description>
</ManSection>

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Leaving GAP">
<Heading>Leaving GAP</Heading>

<Index Subkey="in emergency">quit</Index>
<Index>exit</Index>
<Index>at exit functions</Index>
<Index>saving on exit</Index>
The normal way to terminate a &GAP; session is to enter either
<C>quit;</C> (note the semicolon) or an end-of-file character (usually
<B>Ctrl-D</B>) at the <C>gap> </C> prompt in the main read eval print loop. 

<ManSection>
<Var Name="QUIT"/>

<Description>
An emergency way to leave &GAP; is to enter 
<Index Key="QUIT" Subkey="emergency quit"><K>QUIT</K></Index>
<K>QUIT</K>
at any <C>gap></C>
or <C>brk></C> or <C>brk_<A>nn</A>></C> prompt. 
</Description>
</ManSection>


<ManSection>
<Func Name="InstallAtExit" Arg='func'/>
<Var Name="QUITTING"/>

<Description>
Before actually terminating, &GAP; will call (with no arguments) all
of the functions that have been installed using <C>InstallAtExit</C>. These
typically perform tasks such as cleaning up temporary files created
during the session, and closing open files. If an error occurs during
the execution of one of these functions, that function is simply
abandoned, no break loop is entered. 
<P/>
<!-- Cannot test this as manual example -->
<Log><![CDATA[
gap> InstallAtExit(function() Print("bye\n"); end);
gap> quit;
bye
]]></Log>
<P/>
During execution of these functions, the global variable <C>QUITTING</C>
will be set to <K>true</K> if &GAP; is exiting because the user typed
<K>QUIT</K> and <K>false</K> otherwise.
Since <K>QUIT</K> is considered as an emergency measure,
different action may be appropriate.
</Description>
</ManSection>

<ManSection>
<Var Name="SaveOnExitFile"/>

<Description>
If, when &GAP; is exiting due to a <K>quit</K> or end-of-file (i.e. not due
to a <K>QUIT</K>) the variable <Ref Var="SaveOnExitFile"/> is bound
to a string value,
then the system will try to save the workspace to that file.
</Description>
</ManSection>

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Line Editing">
<Heading>Line Editing</Heading>

In most installations &GAP; will be compiled to use the
Gnu readline library (see the line <C>Libs used:</C> on &GAP; startup).
In that case skip to the next section <Ref Sect="sec:readline"/>.
(The line editing commands described in the rest of this section were
available in previous versions of &GAP;, they will work almost the same 
in the standard configuration of the Gnu readline library.)
<P/>
&GAP; allows one you to edit the current input line with a number of editing
commands. Those commands are accessible either as <E>control keys</E> or as
<E>escape keys</E>.
You enter a control key by pressing the <B>Ctrl</B> key, and,
while still holding the <B>Ctrl</B> key down,
hitting another key <C>key</C>.
You enter an escape key by hitting <B>Esc</B> and then hitting another
key <C>key</C>.
Below we denote control keys by <B>Ctrl-</B><C>key</C> and escape keys by
<B>Esc-</B><C>key</C>.
The case of <C>key</C> does not matter, i.e., <B>Ctrl-A</B> and
<B>Ctrl-a</B> are equivalent.
<P/>
Normally, line editing will be enabled if the input is connected to a
terminal. Line editing can be enabled or disabled using the command line
options <C>-f</C> and <C>-n</C> respectively
(see&nbsp;<Ref Sect="Command Line Options"/>), however
this is a machine dependent feature of &GAP;.
<P/>
Typing <B>Ctrl-key</B> or <B>Esc-key</B> for characters not mentioned below
always inserts <B>Ctrl-</B><C>key</C> resp.&nbsp;<B>Esc-</B><C>key</C>
at the current cursor position.
<P/>
The first few commands allow you to move the cursor on the current line.
<P/>
<List>
<Mark><B>Ctrl-A</B></Mark>
<Item>
  move the cursor to the beginning of the line.
</Item>
<Mark><B>Esc-B</B></Mark>
<Item>
  move the cursor to the beginning of the previous word.
</Item>
<Mark><B>Ctrl-B</B></Mark>
<Item>
  move the cursor backward one character.
</Item>
<Mark><B>Ctrl-F</B></Mark>
<Item>
  move the cursor forward one character. 
</Item>
<Mark><B>Esc-F</B></Mark>
<Item>
  move the cursor to the end of the next word. 
</Item>
<Mark><B>Ctrl-E</B></Mark>
<Item>
  move the cursor to the end of the line.
</Item>
</List>
<P/>
The next commands delete or kill text.
The last killed text can be reinserted, possibly at a different position,
with the <Q>yank</Q> command <B>Ctrl-Y</B>.
<List>
<Mark><B>Ctrl-H</B> or <A>del</A></Mark>
<Item>
  delete the character left of the cursor. 
</Item>
<Mark><B>Ctrl-D</B></Mark>
<Item>
  delete the character under the cursor. 
</Item>
<Mark><B>Ctrl-K</B></Mark>
<Item>
  kill up to the end of the line. 
</Item>
<Mark><B>Esc-D</B></Mark>
<Item>
  kill forward to the end of the next word. 
</Item>
<Mark><B>Esc-del</B></Mark>
<Item>
  kill backward to the beginning of the last word. 
</Item>
<Mark><B>Ctrl-X</B></Mark>
<Item>
  kill entire input line, and discard all pending input. 
</Item>
<Mark><B>Ctrl-Y</B></Mark>
<Item>
  insert (yank) a just killed text.
</Item>
</List>
<P/>
The next commands allow you to change the input.
<P/>
<List>
<Mark><B>Ctrl-T</B></Mark>
<Item>
  exchange (twiddle) current and previous character. 
</Item>
<Mark><B>Esc-U</B></Mark>
<Item>
  uppercase next word. 
</Item>
<Mark><B>Esc-L</B></Mark>
<Item>
  lowercase next word. 
</Item>
<Mark><B>Esc-C</B></Mark>
<Item>
  capitalize next word.
</Item>
</List>
<P/>
The <B>Tab</B> character,
which is in fact the control key <B>Ctrl-I</B>, looks at
the characters before the cursor, interprets them as the beginning of an
identifier and tries to complete this identifier. If there is more than
one possible completion, it completes to the longest common prefix of all
those completions. If the characters to the left of the cursor are
already the longest common prefix of all completions hitting <B>Tab</B> a
second time will display all possible completions.
<P/>
<List>
<Mark><B>tab</B></Mark>
<Item>
  complete the identifier before the cursor.
</Item>
</List>
<P/>
The next commands allow you to fetch previous lines, e.g., to correct
typos, etc. 
<P/>
<List>
<Mark><B>Ctrl-L</B></Mark>
<Item>
  insert last input line before current character.
</Item>
<Mark><B>Ctrl-P</B></Mark>
<Item>
  redisplay the last input line,
  another <B>Ctrl-P</B> will redisplay the line before that, etc.
  If the cursor is not in the first column only the lines starting with the
  string to the left of the cursor are taken.
</Item>
<Mark><B>Ctrl-N</B></Mark>
<Item>
  Like <B>Ctrl-P</B> but goes the other way round through the history.
</Item>
<Mark><B>Esc-&lt;</B></Mark>
<Item>
  goes to the beginning of the history.
</Item>
<Mark><B>Esc-></B></Mark>
<Item>
  goes to the end of the history.
</Item>
<Mark><B>Ctrl-O</B></Mark>
<Item>
  accepts this line and perform a <B>Ctrl-N</B>.
</Item>
</List>
<P/>
Finally there are a few miscellaneous commands.
<P/>
<List>
<Mark><B>Ctrl-V</B></Mark>
<Item>
  enter next character literally, i.e., enter it even if it
  is one of the control keys.
</Item>
<Mark><B>Ctrl-U</B></Mark>
<Item>
  execute the next line editing command 4 times.
</Item>
<Mark><B>Esc-</B><C>num</C></Mark>
<Item>
  execute the next line editing command <C>num</C> times.
</Item>
<Mark><B>Esc-Ctrl-L</B></Mark>
<Item>
  redisplay input line.
</Item>
</List>
<P/>
The four arrow keys (cursor keys) can be used instead of
<B>Ctrl-B</B>, <B>Ctrl-F</B>, <B>Ctrl-P</B>, and <B>Ctrl-N</B>,
respectively.

</Section>

<#Include Label="readline">

<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Editing Files">
<Heading>Editing Files</Heading>

In most cases, it is preferable to create longer input (in particular &GAP;
programs) separately in an editor,
and to read in the result via <Ref Func="Read"/>.
Note that <Ref Func="Read"/> by default reads from the directory
in which &GAP; was started (respectively under Windows the directory
containing the &GAP; binary),
so you might have to give an absolute path to the file.
<P/>
If you cannot create several windows,
the <Ref Func="Edit"/> command may be used to leave &GAP;, start an editor,
and read in the edited file automatically.

<#Include Label="Edit">

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Editor Support">
<Heading>Editor Support</Heading>

<Index>utilities for editing GAP files</Index>
<Index Key="vi"><C>vi</C></Index>
<Index Key="vim"><C>vim</C></Index>
<Index Key="emacs"><C>emacs</C></Index>
In the <F>etc</F> subdirectory of the &GAP; installation
we provide some setup files for the editors <C>vim</C> and
<C>emacs</C>/<C>xemacs</C>.
<P/>
<C>vim</C> is a powerful editor that understands the basic <C>vi</C> commands
but provides much more functionality. You can find more information about it
(and download it) from <URL>http://www.vim.org</URL>.
<P/>
To get support for &GAP; syntax in vim, create in your home directory a
directory <F>.vim</F> with  subdirectories  <F>.vim/syntax</F> and
<F>.vim/indent</F>
(If you are not using Unix, refer to the <C>vim</C> documentation
on where to place syntax files).
Then copy the file <F>etc/gap.vim</F> to <F>.vim/syntax/gap.vim</F> 
and  the file <F>etc/gap_indent.vim</F> to <F>.vim/indent/gap.vim</F>.
<P/>
Then edit the <F>.vimrc</F> file in your home directory.
Add lines as in the following example:
<P/>
<Log><![CDATA[
if has("syntax")
  syntax on             " Default to no syntax highlightning 
endif

" For GAP files
augroup gap
  " Remove all gap autocommands
  au!
autocmd BufRead,BufNewFile *.g,*.gi,*.gd set filetype=gap comments=s:##\ \ ,m:##\ \ ,e:##\ \ b:#

" I'm using the external program `par' for formating comment lines starting
" with `##  '. Include these lines only when you have par installed.
  autocmd BufRead,BufNewFile *.g,*.gi,*.gd set formatprg="par w76p4s0j"
  autocmd BufWritePost,FileWritePost *.g,*.gi,*.gd set formatprg="par w76p0s0j"
augroup END
]]></Log>
<P/>
See the headers  of the two mentioned files for  additional comments and
adjust details according to  your personal taste.
Send comments  and suggestions to <Email>support@gap-system.org</Email>.
Setup files for <C>emacs</C>/<C>xemacs</C> are contained in the
<F>etc/emacs</F> subdirectory.

</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="sect:SizeScreen">
<Heading>Changing the Screen Size</Heading>

<ManSection>
<Func Name="SizeScreen" Arg='[sz]'/>

<Description>
Called with no arguments, <Ref Func="SizeScreen"/> returns the size of the
screen as a list with two entries.
The first is the length of each line, the second is the number of lines.
<P/>
Called with one argument that is a list <A>sz</A>,
<Ref Func="SizeScreen"/> sets the size of the screen;
The first entry of <A>sz</A>, if bound, is the length of each line,
and the second entry of <A>sz</A>, if bound, is the number of lines.
The values for unbound entries of <A>sz</A> are left unaffected.
The function returns the new values.
<P/>
Note that those parameters can also be set with the command line options
<C>-x</C> for the line length and <C>-y</C> for the number of lines
(see Section&nbsp;<Ref Sect="Command Line Options"/>).
<P/>
To check/change whether line breaking occurs for files and streams 
see&nbsp;<Ref Func="PrintFormattingStatus"/>
and&nbsp;<Ref Func="SetPrintFormattingStatus"/>.
<P/>
The line length must be between <M>20</M> and <M>4096</M> characters
(inclusive) and the number of lines must be at least <M>10</M>.
Values outside this range will be adjusted to the nearest endpoint of the
range.
</Description>
</ManSection>
</Section>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<Section Label="Teaching Mode">
<Heading>Teaching Mode</Heading>

When using &GAP; in the context of (undergraduate) teaching it is often
desirable to simplify some of the system output and functionality defaults
(potentially at the cost of making the printing of objects more expensive).
This can be achieved by turning on a teaching mode:

<ManSection>
<Func Name="TeachingMode" Arg='[switch]'/>
<Description>
When called with a boolean argument <A>switch</A>, this function will turn
teaching mode respectively on or off.
<Example><![CDATA[
gap> a:=Z(11)^3;
Z(11)^3
gap> TeachingMode(true);
#I  Teaching mode is turned ON
gap> a;
ZmodnZObj(8,11)
gap> TeachingMode(false);
#I  Teaching mode is turned OFF
gap> a;
Z(11)^3
]]></Example>

At the moment, teaching mode changes the following things
<P/>
<List>
<Mark>Prime Field Elements</Mark>
<Item>
Elements of fields of prime order are printed as
<Ref Func="ZmodnZObj" Label="for two integers"/>
instead as power of a primitive root.
</Item>
<Mark>Quadratic Irrationalities</Mark>
<Item>
Elements of a quadratic extension of the rationals are printed using the
square root <Ref Func="ER"/> instead of using roots of unity.
</Item>
<Mark>Creation of some small groups</Mark>
<Item>
The group creator functions
<Ref Func="CyclicGroup"/>,
<Ref Func="AbelianGroup"/>,
<Ref Func="ElementaryAbelianGroup"/>, and
<Ref Func="DihedralGroup"/>
create by default (if no other representation is specified) not a pc group,
but a finitely presented group, which makes the generators easier to
interpret.
</Item>
</List>

</Description>
</ManSection>

</Section>
</Chapter>


<!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
<!-- %% -->
<!-- %E -->

