2 How To Type a GAPDoc Document
  
  In  this chapter we give a more formal description of what you need to start
  to  type  documentation  in  GAPDoc  XML  format.  Many details were already
  explained by example in Section 1.2 of the introduction.
  
  We  do  not  answer  the  question  How  to write a GAPDoc document? in this
  chapter. You can (hopefully) find an answer to this question by studying the
  example in the introduction, see 1.2, and learning about more details in the
  reference Chapter 3.
  
  The definite source for all details of the official XML standard with useful
  annotations is:
  
  http://www.xml.com/axml/axml.html
  
  Although  this  document  must  be  quite technical, it is surprisingly well
  readable.
  
  
  2.1 General XML Syntax
  
  We  will  now  discuss  the  pieces of text which can occur in a general XML
  document.  We  start with those pieces which do not contribute to the actual
  content of the document.
  
  
  2.1-1 Head of XML Document
  
  Each XML document should have a head which states that it is an XML document
  in some encoding and which XML-defined language is used. In case of a GAPDoc
  document this should always look as in the following example.
  
    Example  
    <?xml version="1.0" encoding="UTF-8"?>
    <!DOCTYPE Book SYSTEM "gapdoc.dtd">
  
  
  See 2.1-13 for a remark on the encoding statement.
  
  (There  may  be  local  entity definitions inside the DOCTYPE statement, see
  Subsection 2.2-3 below.)
  
  
  2.1-2 Comments
  
  A  comment  in XML starts with the character sequence <!-- and ends with the
  sequence  -->. Between these sequences there must not be two adjacent dashes
  --.
  
  
  2.1-3 Processing Instructions
  
  A  processing  instruction  in  XML  starts  with  the character sequence <?
  followed  by  a  name  (xml  is  only  allowed  at the very beginning of the
  document  to  declare  it  being an XML document, see 2.1-1). After that any
  characters  may  follow,  except  that the ending sequence ?> must not occur
  within the processing instruction.
  
   
  
  And  now  we  turn  to  those  parts of the document which contribute to its
  actual content.
  
  
  2.1-4 Names in XML and Whitespace
  
  A  name  in XML (used for element and attribute identifiers, see below) must
  start  with  a letter (in the encoding of the document) or with a colon : or
  underscore  _ character. The following characters may also be digits, dots .
  or dashes -.
  
  This  is  a  simplified  description of the rules in the standard, which are
  concerned with lots of unicode ranges to specify what a letter is.
  
  Sequences  only  consisting  of  the  following characters are considered as
  whitespace:   blanks,   tabs,   carriage  return  characters  and  new  line
  characters.
  
  
  2.1-5 Elements
  
  The  actual  content of an XML document consists of elements. An element has
  some  content  with  a  leading  start  tag  (2.1-6)  and a trailing end tag
  (2.1-7).  The content can contain further elements but they must be properly
  nested.  One  can  define  elements  whose  content  is  always empty, those
  elements can also be entered with a single combined tag (2.1-8).
  
  
  2.1-6 Start Tags
  
  A  start-tag  consists of a less-than-character < directly followed (without
  whitespace)  by  an  element name (see 2.1-4), optional attributes, optional
  whitespace, and a greater-than-character >.
  
  An  attribute  consists  of some whitespace and then its name followed by an
  equal  sign  = which is optionally enclosed by whitespace, and the attribute
  value,  which  is  enclosed either in single or double quotes. The attribute
  value may not contain the type of quote used as a delimiter or the character
  <,  the  character  &  may  only  appear  to  start an entity, see 2.1-9. We
  describe in 2.1-11 how to enter special characters in attribute values.
  
  Note  especially  that  no  whitespace  is  allowed  between  the starting <
  character  and the element name. The quotes around an attribute value cannot
  be omitted. The names of elements and attributes are case sensitive.
  
  
  2.1-7 End Tags
  
  An  end  tag  consists  of  the  two  characters </ directly followed by the
  element name, optional whitespace and a greater-than-character >.
  
  
  2.1-8 Combined Tags for Empty Elements
  
  Elements  which  always have empty content can be written with a single tag.
  This   looks   like  a  start  tag  (see 2.1-6)  except  that  the  trailing
  greater-than-character > is substituted by the two character sequence />.
  
  
  2.1-9 Entities
  
  An  entity in XML is a macro for some substitution text. There are two types
  of entities.
  
  A  character entity can be used to specify characters in the encoding of the
  document  (can  be useful for entering non-ASCII characters which you cannot
  manage  to  type in directly). They are entered with a sequence &#, directly
  followed  by either some decimal digits or an x and some hexadecimal digits,
  directly  followed  by  a semicolon ;. Using such a character entity is just
  equivalent to typing the corresponding character directly.
  
  Then  there  are  references  to  named  entities.  They are entered with an
  ampersand character & directly followed by a name which is directly followed
  by  a  semicolon  ;.  Such  entities  must be declared somewhere by giving a
  substitution text. This text is included in the document and the document is
  parsed  again  afterwards. The exact rules are a bit subtle but you probably
  want  to  use  this only in simple cases. Predefined entities for GAPDoc are
  described in 2.1-10 and 2.2-3.
  
  
  2.1-10 Special Characters in XML
  
  We  have  seen  that the less-than-character < and the ampersand character &
  start  a  tag  or  entity reference in XML. To get these characters into the
  document  text  one  has  to use entity references, namely &lt; to get < and
  &amp;  to  get &. Furthermore &gt; must be used to get > when the string ]]>
  appears  in  element  content  (and  not  as  delimiter  of  a CDATA section
  explained below).
  
  Another possibility is to use a CDATA statement explained in 2.1-12.
  
  
  2.1-11 Rules for Attribute Values
  
  Attribute values can contain entities which are substituted recursively. But
  except  for the entities &lt; or a character entity it is not allowed that a
  <  character  is introduced by the substitution (there is no XML parsing for
  evaluating the attribute value, just entity substitutions).
  
  
  2.1-12 CDATA
  
  Pieces  of text which contain many characters which can be misinterpreted as
  markup  can  be  enclosed  by  the  character  sequences  <![CDATA[ and ]]>.
  Everything  between these sequences is considered as content of the document
  and  is  not further interpreted as XML text. All the rules explained so far
  in  this  section  do  not  apply  to  such a part of the document. The only
  document  content  which cannot be entered directly inside a CDATA statement
  is  the  sequence  ]]>.  This  can  be  entered  as ]]&gt; outside the CDATA
  statement.
  
    Example  
    A nesting of tags like <a> <b> </a> </b> is not allowed.
  
  
  
  2.1-13 Encoding of an XML Document
  
  We  suggest  to use the UTF-8 encoding for writing GAPDoc XML documents. But
  the  tools  described  in  Chapter  5  also  work  with ASCII or the various
  ISO-8859-X  encodings  (ISO-8859-1  is  also  called  latin1 and covers most
  special characters for western European languages).
  
  
  2.1-14 Well Formed and Valid XML Documents
  
  We  want  to mention two further important words which are often used in the
  context of XML documents. A piece of text becomes a well formed XML document
  if all the formal rules described in this section are fulfilled.
  
  But  this  says  nothing  about  the  content  of the document. To give this
  content  a  meaning one needs a declaration of the element and corresponding
  attribute  names as well as of named entities which are allowed. Furthermore
  there  may  be restrictions how such elements can be nested. This definition
  of  an  XML  based markup language is done in a document type definition. An
  XML  document  which  contains only elements and entities declared in such a
  document  type  definition  and  obeys the rules given there is called valid
  (with respect to this document type definition).
  
  The  main  file  of  the  GAPDoc package is gapdoc.dtd. This contains such a
  definition  of  a  markup  language.  We are not going to explain the formal
  syntax rules for document type definitions in this section. But in Chapter 3
  we will explain enough about it to understand the file gapdoc.dtd and so the
  markup language defined there.
  
  
  2.2 Entering GAPDoc Documents
  
  Here are some additional rules for writing GAPDoc XML documents.
  
  
  2.2-1 Other special characters
  
  As  GAPDoc  documents  are  used  to  produce  LaTeX and HTML documents, the
  question arises how to deal with characters with a special meaning for other
  applications  (for  example  &,  #,  $,  %,  ~,  \, {, }, _, ^,   (this is a
  non-breakable  space, ~ in LaTeX) have a special meaning for LaTeX and &, <,
  >  have a special meaning for HTML (and XML). In GAPDoc you can usually just
  type  these  characters  directly,  it is the task of the converter programs
  which  translate  to  some  output  format  to  take  care  of  such special
  characters. The exceptions to this simple rule are:
  
      & and < must be entered as &amp; and &lt; as explained in 2.1-10.
  
      The  content of the GAPDoc elements <M>, <Math> and <Display> is LaTeX
        code, see 3.8.
  
      The  content of an <Alt> element with Only attribute contains code for
        the specified output type, see 3.9-1.
  
  Remark:  In former versions of GAPDoc one had to use particular entities for
  all  the  special  characters  mentioned  above  (&tamp;,  &hash;, &dollar;,
  &percent;, &tilde;, &bslash;, &obrace;, &cbrace;, &uscore;, &circum;, &tlt;,
  &tgt;). These are no longer needed, but they are still defined for backwards
  compatibility with older GAPDoc documents.
  
  
  2.2-2 Mathematical Formulae
  
  Mathematical  formulae  in  GAPDoc  are  typed as in LaTeX. They must be the
  content of one of three types of GAPDoc elements concerned with mathematical
  formulae:  Math,  Display,  and  M  (see  Sections 3.8-1  and 3.8-2 for more
  details).  The  first  two  correspond to LaTeX's math mode and display math
  mode.  The last one is a special form of the Math element type, that imposes
  certain  restrictions  on the content. On the other hand the content of an M
  element is processed in a well defined way for text terminal or HTML output.
  The Display element also has an attribute such that its content is processed
  as in M elements.
  
  Note  that  the  content  of  these  element  is LaTeX code, but the special
  characters  <  and  &  for  XML  must  be entered via the entities described
  in 2.1-10 or by using a CDATA statement, see 2.1-12.
  
  
  2.2-3 More Entities
  
  In GAPDoc there are some more predefined entities:
  
      ┌─────────────┬─────────┐
      │ &GAP;       │ GAP     │ 
      ├─────────────┼─────────┤
      │ &GAPDoc;    │ GAPDoc  │ 
      ├─────────────┼─────────┤
      │ &TeX;       │ TeX     │ 
      ├─────────────┼─────────┤
      │ &LaTeX;     │ LaTeX   │ 
      ├─────────────┼─────────┤
      │ &BibTeX;    │ BibTeX  │ 
      ├─────────────┼─────────┤
      │ &MeatAxe;   │ MeatAxe │ 
      ├─────────────┼─────────┤
      │ &XGAP;      │ XGAP    │ 
      ├─────────────┼─────────┤
      │ &copyright; │ ©       │ 
      ├─────────────┼─────────┤
      │ &nbsp;      │       │ 
      ├─────────────┼─────────┤
      │ &ndash;     │ –       │ 
      └─────────────┴─────────┘
  
       Table: Predefined Entities in the GAPDoc system
  
  
  Here &nbsp; is a non-breakable space character.
  
  Additional  entities  are defined for some mathematical symbols, see 3.8 for
  more details.
  
  One can define further local entities right inside the head (see 2.1-1) of a
  GAPDoc XML document as in the following example.
  
    Example  
    <?xml version="1.0" encoding="UTF-8"?>
    
    <!DOCTYPE Book SYSTEM "gapdoc.dtd"
      [ <!ENTITY MyEntity "some longish <E>text</E> possibly with markup">
      ]>
  
  
  These  additional  definitions go into the <!DOCTYPE tag in square brackets.
  Such new entities are used like this: &MyEntity;