Test species in axiom/FriCAS.

The species project is written in Aldor. Thus we need to load the libraries explicitly:

(1) -> )version

"FriCAS 1.3.12 compiled at Sat  7 Jun 23:54:49 CEST 2025"

)cd /var/lib/zope/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.

We took the decision not to rely on the Axiom algebra. Unfortunately, this means that integration in Axiom is a little unsatisfactory. Eg., instead of Integer and List, we need to use ACInteger and ACList. Often explicit coercions are necessary.

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

l: 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.

#includeDir "/var/lib/zope/combinat/include"
#libraryDir "/var/lib/zope/combinat/lib"
#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/5200085684951427974-25px003.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.
"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5200085684951427974-25px003.as", line 3: 
#include "combinat"
^
[L3 C1] #1 (Error) Could not open file `combinat'.

   The )library system command was not called after compilation.

Due to types not being first class objects in the Axiom interpreter, we had to write a little interpreter to allow for user specified species:

T := Interpret([parse "Plus(SingletonSpecies, Times(Self, Self))"], ACInteger);

   There are no exposed library operations named parse but there is one
      unexposed operation with that name. Use HyperDoc Browse or issue
                              )display op parse
      to learn more about the available operation.

   Cannot find a definition or applicable library operation named parse
      with argument type(s) 
                                   String

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

We are still not 100% sure how to represent isomorphism types. So far, we had two ideas: in the iso-experiment branch, we have separate (but tightly connected) representation:

m: MultiSet ACINT := multiset([1$ACINT for i in 1..3]::ACList ACINT)

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

   Cannot find a definition or applicable library operation named 
      MultiSet 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.

IsoT := ACIsomorphismType(ACINT, T)

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

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

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

debugging needed here... On my computer, the last statement yields

On my computer, the last statement yields:

  (13)  [r([1], ([1], [1])),r(([1], [1]), [1])]

Very likely, the bug is due to the broken aldor interface. Ralf is working hard on that.

)cl all

   All user variables and function definitions have been cleared.
G := Interpret([parse "FunctorialCompose(Subset, Combination(2)))"], ACINT)

   There are no exposed library operations named parse but there is one
      unexposed operation with that name. Use HyperDoc Browse or issue
                              )display op parse
      to learn more about the available operation.

   Cannot find a definition or applicable library operation named parse
      with argument type(s) 
                                   String

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

)lisp  (use-fast-links nil)

   Your user access level is compiler and this command is therefore not
      available. See the )set userlevel command for more information.
--)se br br
next! s;

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

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

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