Edit detail for SandBoxSpecies revision 3 of 8

Test species in axiom/FriCAS?.

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

(1) -> )version

"FriCAS 1.4.0 compiled at Fri 16 Oct 16:10:51 CEST 2026"

)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.

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.
#1 (Warning) Could not use archive file `libfricas.al'.
"/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5200085684951427974-25px003.as", line 3: 
#include "combinat"
^
[L3 C1] #2 (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 are 3 
      unexposed operations with that name. Use HyperDoc Browse or issue
                              )display op parse
      to learn more about the available operations.

   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.