examples.xml

<?xml version="1.0" encoding="UTF-8"?>

<!--<Chapter Label="examples">
  <Heading>
    Examples of use of the <Package>IntPic</Package> package
  </Heading>
  <Index>
    <Package>IntPic</Package> - Examples
  </Index>-->
  <Section>
    <Heading>Other examples of use of the <Package>IntPic</Package> package</Heading>
    
    <Subsection>
      <Heading>Varia</Heading>
      
      The following example shows how to produce <C>tikz</C> code for a picture containing the odd integers from <M>801</M> to <M>999</M>. Each line (except the highest) contains <M>15</M> cells.
      <Example><![CDATA[
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));;
]]></Example> 
      The picture obtained highlights the primes, the twin primes and the multiples of <M>3</M>. As the twins are also primes, a gradient is used to highlight them. In this example the default list of colors is used.
      <Alt Only="LaTeX">
        \begin{center}
        \includegraphics[width=0.95\textwidth]{../images/primesandtwinsamongodd}
        \end{center}
      </Alt>
      <Alt Only="HTML">
        &#60;br&#62;&#60;center&#62;&#60;img src=&#34;../images/primesandtwinsamongodd.jpg&#34;&#62;&#60;/center&#62;&#60;br&#62;
      </Alt>
      The same computations, but defining other color lists.
      <Example><![CDATA[
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> 
      <Alt Only="LaTeX">
        \begin{center}
        \includegraphics[width=0.95\textwidth]{../images/primesandtwinsamongodd_comp_red}
        \end{center}
      </Alt>
      <Alt Only="HTML">
        &#60;br&#62;&#60;center&#62;&#60;img src=&#34;../images/primesandtwinsamongodd_comp_red.jpg&#34;&#62;&#60;/center&#62;&#60;br&#62;
      </Alt>
      <Example><![CDATA[
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> 
      <Alt Only="LaTeX">
        \begin{center}
        \includegraphics[width=0.95\textwidth]{../images/primesandtwinsamongodd_dark_gray}
        \end{center}
      </Alt>
      <Alt Only="HTML">
        &#60;br&#62;&#60;center&#62;&#60;img src=&#34;../images/primesandtwinsamongodd_dark_gray.jpg&#34;&#62;&#60;/center&#62;&#60;br&#62;
      </Alt>
      <Example><![CDATA[
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));;
]]></Example> 
      <Alt Only="LaTeX">
        \begin{center}
        \includegraphics[width=0.95\textwidth]{../images/primesandtwinsamongodd_other}
        \end{center}
      </Alt>
      <Alt Only="HTML">
        &#60;br&#62;&#60;center&#62;&#60;img src=&#34;../images/primesandtwinsamongodd_other.jpg&#34;&#62;&#60;/center&#62;&#60;br&#62;
      </Alt>
      The following example uses the 
      <Alt Not='Text'>
        <URL
   Text='NumericalSgps'>http://www.fc.up.pt/cmup/mdelgado/numericalsgps</URL>
      </Alt>
      <Alt Only='Text'>
        <Package>NumericalSgps</Package>
      </Alt>
      package.
      <Example><![CDATA[

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));;
]]></Example> 
      <Alt Only="LaTeX">
        \begin{center}
        \includegraphics[width=0.95\textwidth]{../images/numericalsgp_notable}
        \end{center}
      </Alt>
      <Alt Only="HTML">
        &#60;br&#62;&#60;center&#62;&#60;img src=&#34;../images/numericalsgp_notable.jpg&#34;&#62;&#60;/center&#62;&#60;br&#62;
      </Alt>
      Using the default colors
      <Alt Only="LaTeX">
        \begin{center}
        \includegraphics[width=0.95\textwidth]{../images/numericalsgp_notable_df_colors}
        \end{center}
      </Alt>
      <Alt Only="HTML">
        &#60;br&#62;&#60;center&#62;&#60;img src=&#34;../images/numericalsgp_notable_df_colors.jpg&#34;&#62;&#60;/center&#62;&#60;br&#62;
      </Alt>
    </Subsection>
    <Subsection>
      <Heading>The banner</Heading>
      The code in the following example has been used to produce one possible banner for the homepage of the &IntPic; package. A nice picture to give an idea about the primes less than <M>10000</M>. Of course, other ranges could be chosen. I warn the user that pictures involving a large amount of data may face the problem of exceeding &TeX; capacity...
      <Example><![CDATA[
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" ));;
]]></Example> 
      <Alt Only="LaTeX">
        \begin{center}
        \includegraphics[width=0.99\textwidth]{../images/intpic_banner.pdf}
        \end{center}
      </Alt>
      <Alt Only="HTML">
        &#60;br&#62;&#60;center&#62;&#60;img src=&#34;../images/intpic_banner.jpg&#34;&#62;&#60;/center&#62;&#60;br&#62;
      </Alt>
      
    </Subsection>
  </Section>
<!--</Chapter>-->