chap4.txt

  
  4 Visualization of the pictures created
  
  This  chapter  describes  two  easy  ways to visualize the images created by
  using  the  IntPic package. Both require LaTeX and some LaTeX packages, such
  as  Tikz  and  pgf,  to  be  installed  and working. One of the ways we will
  describe  is  almost  completely  automatic.  It  makes  use of the function
  Splash, borrowed from the Viz package. The other is not so automatic but has
  the  advantage  of not requiring other packages, besides the LaTeX ones, and
  should work in any operation system.
  
  
  4.1 Viewing using Viz
  
  Producing and displaying a picture from a tikz string tkz may me achieved in
  a simple way. (Warning: extenvive tests have only been done with Linux.) One
  just have to type the following:
  
    IP\_Splash  
    IP_Splash(tkz);
  
  
  A picture is popped up after this use of the function IP_Splash.. To see the
  name  of  the  temporary  directory created to perform the computations, and
  thus  being  able  to copy the files involved to any other place, one should
  set  the  info level InfoViz to 1 or more. The following example illustrates
  this  and  the  use of some options of the function IP_Splash. For instance,
  the pdf viewer can be changed.
  
    infoviz: temporary directory  
    gap> SetInfoLevel(InfoViz,1);
    gap> IP_Splash(tkz,rec(viewer:="okular")); 
    #I  The temporary directory used is: /tmp/tmJcpphI/
  
  
  The temporary directory /tmp/tmJcpphI/ contains the file and vizpicture.tex.
  The  file vizpicture.tex is the LaTeX document to be processed. Other files,
  namely the vizpicture.pdf are created by the pdflatex command that is called
  by the IP_Splash function.
  
  Warning: In the case of large pictures, it may happen the LaTeX memory being
  exceeded. In this case, no image is produced and the user is not warned.
  
  
  4.2 Viewing without using Viz
  
  This  section  describes a way to visualize images without sing Viz. Besides
  being  useful  in the case of not having a working copy of Viz, it is rather
  convenient  when the decision of where to save the pictures is made. In this
  case,  you  may  start  your  gap  session in the desired place, the working
  directory.  Furthermore,  if your intention is, for instance, to include the
  images  in  a document, you may just decide the name for the file containing
  the  tikz  code  and  let  your  document  input  it.  The  glogal variables
  IP_Preamble  and  Closing  can  be used to pruduce a complete LaTeX document
  rather  than  only  the  tizk code for the picture. The document may then be
  processed by using pdflatex and the picture viewed by using some pdf viewer.
  The  pdf  produced  can  be included in a LaTeX document instead of the tizk
  code.  In  the  later  case, the code is processed each time the document is
  processed, which should perhaps be avoided in the case of large images.
  
  Note  the  use of the preview package, which is used to produce the complete
  picture  without  having  to pay attention to the paper size nor to crop the
  image.  It  is  useful for viewing purposes and also to include the pdf file
  produced in a LaTeX document to be processed with pdflatex.
  
    Preamble  
    gap> Print(IP_Preamble);
    \documentclass{minimal}
    \usepackage{amsmath}
    \usepackage[active,tightpage]{preview}
    \setlength\PreviewBorder{1pt}
    \usepackage{pgf}
    \usepackage{tikz}
    \usepgfmodule{plot}
    \usepgflibrary{plothandlers}
    \usetikzlibrary{shapes.geometric}
    \usetikzlibrary{shadings}
    \begin{document}
    \begin{preview}
  
  
    Closing  
    gap> Print(IP_Closing);
    \end{preview}
    \end{document}
  
  
  
  4.2-1 A complete example
  
  Admit   you   want   to  produce  a  document  which  contains  the  picture
  corresponding to the tikz code obtained through the instructions
  
    instructions to obtain some tikz code  
    arr := [[1,2,3,4,5,6],[1,2,3,4,5],[1,2,3,4],[1,2,3],[1,2],[1]];;
    tkz := IP_TikzArrayOfIntegers([1..10],5,rec(highlights:=arr));;
  
  
  The  picture is: The elements of the set [1,2,3,4,5,6] are highlighted using
  the  first  color  (red); those of the set [1,2,3,4,5] are highlighted using
  the  second  color (green); those of the set [1,2,3,4] are highlighted using
  the  third  color (blue); those of the set [1,2,3] are highlighted using the
  fourth  color (cyan); those of the set [1,2] are highlighted using the fifth
  color  (magenta);  those of the set [1] is highlighted using the sixth color
  (yellow).
  
  Let  us  explain  how  the  six  colors  used  for the cell containing 1 are
  distributed:  upper  left  corner -- red; upper right corner -- green; lower
  left  corner -- blue; lower right corner -- cyan; the number -- magenta; the
  border -- yellow.
  
  The colors of the cell containing 2 and 3 are distributed in a similar way.
  
  The  colors  of the cell containing 4: left -- red; middle -- blue; right --
  green.
  
  After the session listed below, the files tikz_pic_for_complete_document.tex
  and pic_for_complete_document.tex have been created in the current directory
  (that is, the one where the GAP session has started). For other directories,
  complete paths may have to be given.
  
    the GAP session  
    gap> tikzfile := "tikz_pic_for_complete_document.tex";;
    gap> file := "pic_for_complete_document.tex";;
    gap> 
    gap> arr := [[1,2,3,4,5,6],[1,2,3,4,5],[1,2,3,4],[1,2,3],[1,2],[1]];;
    gap> tkz := IP_TikzArrayOfIntegers([1..10],5,rec(highlights:=arr));;
    gap> 
    gap> FileString(tikzfile,tkz);
    642
    gap> FileString(file,Concatenation(IP_Preamble,tkz,IP_Closing));
    961
  
  
  Executing something like
  
    the pdf and the jpg of the picture  
    pdflatex pic_for_complete_document.tex
    convert pic_for_complete_document.pdf pic_for_complete_document.jpg
  
  
  the  pdf  and the jpg formats of the image have been created. The jpg format
  is usefull to be included into an html document, for instance.
  
  Note    that    the    tikz    code   has   been   saved   into   the   file
  tikz_pic_for_complete_document.tex.  A  complete example of a LaTeX document
  follows.
  
    a LaTeX document  
    \documentclass{article}
    \usepackage{amsmath}
    %\usepackage[active,tightpage]{preview}
    %\setlength\PreviewBorder{1pt}
    \usepackage{pgf}
    \usepackage{tikz}
    \usepgfmodule{plot}
    \usepgflibrary{plothandlers}
    \usetikzlibrary{shapes.geometric}
    \usetikzlibrary{shadings}
    \usepackage{graphicx}
    \author{Author}
    \title{How to include images in a \LaTeX\ document}
    \date{June, 2013}
    \begin{document}
    %\begin{preview}
    \maketitle
    Using the pdf file:
    
    \begin{center}
      \includegraphics[width=0.80\textwidth]{../images/pic_for_complete_document.pdf}
    \end{center}
    
    Using the PGF/TikZ code:
    
    \begin{center}
    \input{../images/tikz_pic_for_complete_document.tex}
    \end{center}
    If you want to scale this immage, please chang the ``scale'' in the file
    \textt{tikz_pic_for_complete_document.tex} 
    %\end{preview}
    \end{document}
  
  
  The output, after processing with pdflatex is as follows:
  
  
  4.3 Other examples of use of the IntPic package
  
  
  4.3-1 Varia
  
  The  following  example  shows  how  to  produce  tikz  code  for  a picture
  containing  the odd integers from 801 to 999. Each line (except the highest)
  contains 15 cells.
  
    Example  
    gap> rg := Filtered([801..889],u->(u mod 2)<>0);;
    gap> flen := 15;;
    gap> twins := Filtered(Primes, p -> p + 2 in Primes);;
    gap> arr := [Primes,Union(twins,twins+2),Filtered(rg,u->(u mod 3)=0)];;
    gap> tkz := IP_TikzArrayOfIntegers(rg,flen,rec(highlights:=arr));;
  
  
  The  picture  obtained  highlights  the  primes,  the  twin  primes  and the
  multiples  of  3.  As  the  twins  are  also  primes,  a gradient is used to
  highlight them. In this example the default list of colors is used. The same
  computations, but defining other color lists.
  
    Example  
    gap> cls := IP_ColorsCompRedTones;;
    gap> rg := Filtered([801..889],u->(u mod 2)<>0);;
    gap> flen := 15;;
    gap> twins := Filtered(Primes, p -> p + 2 in Primes);;
    gap> arr := [Primes,Union(twins,twins+2),Filtered(rg,u->(u mod 3)=0)];;
    gap> tkz := IP_TikzArrayOfIntegers(rg,flen,rec(colors := cls,highlights:=arr));;
  
  
    Example  
    gap> cls := IP_ColorsDGrayTones;;
    gap> rg := Filtered([801..889],u->(u mod 2)<>0);;
    gap> flen := 15;;
    gap> twins := Filtered(Primes, p -> p + 2 in Primes);;
    gap> arr := [Primes,Union(twins,twins+2),Filtered(rg,u->(u mod 3)=0)];;
    gap> tkz := IP_TikzArrayOfIntegers(rg,flen,rec(colors := cls,highlights:=arr));;
  
  
    Example  
    gap> cls := ["blue","-blue","black"];;
    gap> rg := Filtered([801..889],u->(u mod 2)<>0);;
    gap> flen := 15;;
    gap> twins := Filtered(Primes, p -> p + 2 in Primes);;
    gap> arr := [Primes,Union(twins,twins+2),Filtered(rg,u->(u mod 3)=0)];;
    gap> tkz := IP_TikzArrayOfIntegers(rg,flen,rec( colors := cls,highlights:=arr));;
  
  
  The following example uses the NumericalSgps package.
  
    Example  
    gap> #LoadPackage("numericalsgps");
    gap> 
    gap> ns := NumericalSemigroup(11,19,30,42,59);;
    gap> cls := ShuffleIP_Colors([IP_ColorsGreenTones,IP_ColorsCompBlueTones]);;
    gap> flen := 20;;
    gap> #some notable elements
    gap> arr := [SmallElementsOfNumericalSemigroup(ns),
    >         GapsOfNumericalSemigroup(ns),
    >         MinimalGeneratingSystemOfNumericalSemigroup(ns),
    >         FundamentalGapsOfNumericalSemigroup(ns),
    >         [ConductorOfNumericalSemigroup(ns)],
    >         PseudoFrobeniusOfNumericalSemigroup(ns)];;
    gap> 
    gap> tkz := IP_TikzArrayOfIntegers(flen,rec(colors := cls,highlights:=arr));;
  
  
  Using the default colors
  
  
  4.3-2 The banner
  
  The  code  in  the  following  example has been used to produce one possible
  banner  for  the  homepage  of the IntPic package. It is a nice picture that
  gives  an  idea  about  the  primes less than 10000. Of course, other ranges
  could  have  been  chosen.  I  warn the user that pictures involving a large
  amount of data may face the problem of exceeding TeX capacity...
  
    Example  
    gap> row_length := 200;; # the legth of each row
    gap> columns := 50;; # the number of colums
    gap> n := row_length*columns;
    10000
    gap> 
    gap> ##compute the primes less than n
    gap> # Primes is a GAP variable representing the list of primes less than 1000
    gap> mp := Maximum(Primes);
    997
    gap> newprimes := [];;
    gap> while mp < n do
    >   mp := NextPrimeInt(mp);
    >   Add(newprimes, mp);
    > od;
    gap> small_primes := Union(Primes, newprimes);;
    gap> ##compute the first element of each pair of twin primes less than n
    gap> twins := Filtered(small_primes, p -> IsPrime(p+2));;
    gap> 
    gap> rg := [1..n];;
    gap> 
    gap> arr := [Intersection(small_primes,rg),[],[], 
    >         Intersection(Union(twins,twins+2),rg),[],[],[],[],[],[],[],
    >         [],[],[],[],[],[],Difference(rg,small_primes)];;
    gap> 
    gap> tkz:=IP_TikzArrayOfIntegers([1..n],row_length,rec(highlights:=arr,
    >              cell_width := "6",colsep:="0",rowsep:="0",inner_sep:="2",
    >              shape_only:=" ",line_width:="0",line_color:="black!20" ));;