7. Installation and auxiliary functions
  
  
  7.1 Requirements
  
  The    RCWA    package   needs   at   least   GAP 4.4.7,   ResClasses 2.5.1,
  GRAPE 4.0 [Soi02],   Polycyclic 2.1 [EN06]   and   GAPDoc 1.0 [LN07].   With
  possible  exception  of  the  most  recent version of ResClasses, all needed
  packages are already present in an up-to-date standard GAP installation. The
  RCWA  package can be used under UNIX, under Windows and on the MacIntosh. It
  is  completely  written  in  the  GAP  language and does neither contain nor
  require  external  binaries.  In  particular,  warnings  concerning  missing
  binaries issued by GRAPE or other packages can savely be ignored.
  
  
  7.2 Installation
  
  Like  any  other GAP package, RCWA must be installed in the pkg subdirectory
  of the GAP distribution. This is accomplished by extracting the distribution
  file  in  this directory. If you have done this, you can load the package as
  usual via LoadPackage( "rcwa" );.
  
  
  7.3 The Info class of the package
  
  7.3-1 InfoRCWA
  
  > InfoRCWA________________________________________________________info class
  
  This  is  the  Info class of the RCWA package. See section Info Functions in
  the  GAP  Reference  Manual  for  a  description  of the Info mechanism. For
  convenience: RCWAInfo(n) is a shorthand for SetInfoLevel(InfoRCWA,n).
  
  
  7.4 The testing routine
  
  7.4-1 RCWATest
  
  > RCWATest(  ) _____________________________________________________function
  Returns:  Nothing.
  
  Performs  tests of the RCWA package. Errors, i.e. differences to the correct
  results of the test computations, are reported. The processed test files are
  in the directory pkg/rcwa/tst.
  
  
  7.5 Building the manual
  
  The  following  routine is a development tool. As all files it generates are
  included in the distribution file anyway, users will not need it.
  
  7.5-1 RCWABuildManual
  
  > RCWABuildManual(  ) ______________________________________________function
  Returns:  Nothing.
  
  This  function  builds  the  manual  of the RCWA package in the file formats
  LaTeX,  PDF,  HTML  and  ASCII  text.  This is accomplished using the GAPDoc
  package  by Frank Lübeck and Max Neunhöffer. Building the manual is possible
  only on UNIX systems and requires PDFLaTeX.
  
  
  7.6 Loading and saving bitmap pictures
  
  RCWA  provides  functions to create bitmap picture files from suitable pixel
  matrices  and  vice  versa.  The author has successfully tested this feature
  both  under  Linux  and  under  Windows,  and  the  produced pictures can be
  processed further with many common graphics programs:
  
  7.6-1 SaveAsBitmapPicture
  
  > SaveAsBitmapPicture( picture, filename ) _________________________function
  Returns:  Nothing.
  
  Writes  the  pixel  matrix  picture  to  a bitmap- (bmp-) picture file named
  filename.  The  filename  should  include  the entire pathname. The argument
  picture  can  be  a GF(2) matrix, in which case a monochrome picture file is
  generated.  In  this  case,  zeros stand for black pixels and ones stand for
  white  pixels.  The argument picture can also be an integer matrix, in which
  case  a  24-bit  True  Color  picture  file  is generated. In this case, the
  entries  of  the  matrix are supposed to be integers n = 65536 * red + 256 *
  green  +  blue in the range 0, dots, 2^24-1 specifying the RGB values of the
  colors of the pixels.
  
  The    picture    can    be   read   back   into   GAP   by   the   function
  ReadFromBitmapPicture(filename).
  
  -----------------------------  Log  ------------------------------
    
    gap> color   := n->32*(n mod 8)+256*32*(Int(n/8) mod 8)+65536*32*Int(n/64);;
    gap> picture := List([1..512],y->List([1..512],x->color(Gcd(x,y)-1)));;
    gap> SaveAsBitmapPicture(picture,"~/images/gcd.bmp");
    
  ------------------------------------------------------------------
  
  
  7.7 Running demonstrations
  
  RCWA  provides  a  routine  to run demonstrations of its functionality or of
  other features of GAP. It is intended for being used in talks.
  
  7.7-1 RunDemonstration
  
  > RunDemonstration( filename ) _____________________________________function
  Returns:  Nothing.
  
  This  function  executes  the  code  in  the file named filename. It shows a
  command  and the corresponding output, waits for a keystroke, shows the next
  command and the corresponding output, waits again for a keystroke, and so on
  until  the  end of the file. The demonstration can be stopped by pressing q.
  The  function  is  adapted  from  the  function  Demonstration  in  the file
  lib/demo.g of the main GAP distribution.
  
  
  7.8 Some general utility functions
  
  RCWA  introduces  a couple of small utility functions which can be used in a
  more  general  context: The function GeneratorsAndInverses(G) returns a list
  of  generators  of  G  and their inverses, EpimorphismByGenerators(G,H) is a
  shorthand                 for                 GroupHomomorphismByImages(G,H,
  GeneratorsOfGroup(G),GeneratorsOfGroup(H))  (there  is also an NC version of
  this),  the  function ListOfPowers(g,exp) returns the list [g,g^2,...,g^exp]
  of  powers  of g,  the  function  AllProducts(l,k)  returns  the list of all
  products of k entries of the list l, the function DifferencesList(l) returns
  the  list  of  differences  of  consecutive  entries  of the list l, and the
  function FloatQuotients(l) returns the list of floating point approximations
  of quotients of consecutive entries of the list l.
  
  There      are      also      methods      EquivalenceClasses(l,inv)     and
  EquivalenceClasses(l,rel), which decompose a list l into equivalence classes
  under an equivalence relation. The equivalence relation is given either as a
  function  inv  computing  a  class  invariant  of a given list entry or as a
  function  rel  which  takes as arguments two list entries and returns either
  true  or  false  depending  on  whether  the  arguments  belong  to the same
  equivalence class or not.