Edit detail for SandBoxCombinat revision 4 of 8

(1) -> <aldor>
#include "axiom.as"

macro CCC == CombinatorialClassCategory;
import from Integer;
import from List Integer;
import from OutputForm;

CombinatorialClassCategory: Category == with {        
        list: Integer -> List %;
        count: Integer -> Integer;
        import from NonNegativeInteger;
        default count(i: Integer): Integer == (#list(i))::Integer;
        coerce: % -> OutputForm;
} 

Primitive(n: Integer): CombinatorialClassCategory == add {
        Rep == Integer;
        count(i: Integer): Integer == if i=n then 1 else 0;
        list(i: Integer): List % == if i=n then [per 1] else [];
        coerce(x: %): OutputForm == message(" ")
}

Epsilon: CombinatorialClassCategory == Primitive(0) add;

Atom: CombinatorialClassCategory == Primitive(1) add;

UnionClass(S1: CCC, S2: CCC): CCC == add {
        Rep == Union(s1: S1, s2: S2);
        count(i: Integer): Integer == count(i)$S1 + count(i)$S2;
        import from Rep;
        import from List S1;
        import from List S2;
        list(i: Integer): List % == {
                result: List % := [];
                for a in list(i)$S1 repeat result := cons(per union a, result);
                for b in list(i)$S2 repeat result := cons(per union b, result);
                result;
        }
        coerce(x: %): OutputForm == {
                (rep x) case s1 => ((rep x).s1)::OutputForm;
                ((rep x).s2)::OutputForm;
        }
}

CrossClass(S1: CCC, S2: CCC): with {
        CombinatorialClassCategory
} == add {
        Rep == Record(t1: S1, t2: S2);
        count(i: Integer): Integer == {
                result := 0;
                for k in 1 .. i-1 repeat {
                        result := result + count(k)$S1 * count(i-k)$S2;
                }
                result;
        }
        import from Rep;
        import from List S1;
        import from List S2;
        list(i: Integer): List % == {
                result: List % := [];
                for k in 1..i-1 repeat {
                  for a in list(k)$S1 repeat {
                    for b in list(i-k)$S2 repeat {
                      result := cons(per record(a, b), result);
                    }
                  }
                }
                result;
        }
        coerce(x: %): OutputForm == {
                a := ((rep x).t1)::OutputForm;
                b := ((rep x).t2)::OutputForm;
                c: List OutputForm := [a, b];
                vconcat [hconcat [hspace 1, message("o")], hconcat [hspace 1, message("/"), hspace 1, message("\")], hconcat [a,hspace 3,b]]
        }
}

TreeClass: CombinatorialClassCategory == UnionClass(Atom, CrossClass(TreeClass, TreeClass)

) add;</aldor>

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/386348539091125073-25px001.as
      using Aldor compiler and options 
-O -Fasy -Fao -Flsp -lfricas -Mno-ALDOR_W_WillObsolete -DFriCAS -Y $FRICAS/algebra -I $FRICAS/algebra
      . Use the system command )set compiler args to change these 
      options.
#1 (Warning) Could not use archive file `libfricas.al'.
"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/386348539091125073-25px001.as", line 1: 
#include "axiom.as"
^
[L1 C1] #2 (Error) Could not open file `axiom.as'.

   The )library system command was not called after compilation.

[count(i)$TreeClass for i in 1..7]

   TreeClass is not a valid type.

)set output tex off
 

)set output algebra on

(list(5)$TreeClass)::List OutputForm

   TreeClass is not a valid type.

Test species in axiom/FriCAS?.

)cd ~/combinat/src

   The current FriCAS default directory is /var/aw/var/LatexWiki 

)re ../lib/combinat.input

   The file ../lib/combinat.input is needed but does not exist.

This should give the set partitions of {1,2,3,4}

lab: SetSpecies ACINT := set [i::ACINT for i in 1..4]

   There are no library operations named SetSpecies 
      Use HyperDoc Browse or issue
                             )what op SetSpecies
      to learn if there is any operation containing " SetSpecies " in 
      its name.

   Cannot find a definition or applicable library operation named 
      SetSpecies with argument type(s) 
                               Variable(ACINT)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

#include "combinat"

macro {
        E == EmptySetSpecies;
        X == SingletonSpecies;
        + == Plus;
        * == Times;
}

A(L: LabelType): CombinatorialSpecies L == (E + X*A*A)(L) add;

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/6037167008170035778-25px006.as
      using Aldor compiler and options 
-O -Fasy -Fao -Flsp -lfricas -Mno-ALDOR_W_WillObsolete -DFriCAS -Y $FRICAS/algebra -I $FRICAS/algebra
      . Use the system command )set compiler args to change these 
      options.
#1 (Warning) Could not use archive file `libfricas.al'.
"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/6037167008170035778-25px006.as", line 1: 
#include "combinat"
^
[L1 C1] #2 (Error) Could not open file `combinat'.

   The )library system command was not called after compilation.