Edit detail for SandBoxSpeciesBayreuth revision 11 of 12

)cd ~/combinat/src

   The current FriCAS default directory is /var/zope2/var/LatexWiki 

)re ../lib/combinat.input

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

#includeDir "/var/lib/zope/combinat/include"
#libraryDir "/var/lib/zope/combinat/lib"
#include "combinat"

macro {
        E == EmptySetSpecies;
        X == SingletonSpecies;
        + == Plus;
        * == Times;
}
BTree(L: LabelType): CombinatorialSpecies L == (E + X*BTree*BTree)(L) add;
MySubset(L: LabelType): CombinatorialSpecies L == (SetSpecies*SetSpecies)(L) add;

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/7896689979910980793-25px002.as using 
      AXIOM-XL compiler and options 
-O -Fasy -Fao -Flsp -laxiom -Mno-ALDOR_W_WillObsolete -DAxiom -Y $AXIOM/algebra -I $AXIOM/algebra
      Use the system command )set compiler args to change these 
      options.
"/var/zope2/var/LatexWiki/7896689979910980793-25px002.as", line 3: 
#include "combinat"
^
[L3 C1] #1 (Error) Could not open file `combinat'.

   The )library system command was not called after compilation.

Z := ACInteger

(1)

X := BTree(Z)

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

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

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

labels: SetSpecies Z := set [1::Z,2::Z,4::Z]

   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(ACInteger)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
labels2 : SetSpecies Z := set[5005::Z]

   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(ACInteger)

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

)set output tex off
 

)set output algebra on

[structures(labels)$X]$ACLIST(X)

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

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

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

)set output tex on
 

)set output algebra off

[structures(labels)$EmptySetSpecies(Z)]$ACLIST(EmptySetSpecies(Z))

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

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

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
[structures(labels)$SingletonSpecies(Z)]$ACLIST(SingletonSpecies(Z))

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

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

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
[structures(labels2)$SingletonSpecies(Z)]$ACLIST(SingletonSpecies(Z))

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

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

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
[structures(labels)$SetSpecies(Z)]$ACLIST(SetSpecies(Z))

   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(ACInteger)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
subs:=[(structures(labels)$MySubset(Z))]$ACLIST(MySubset(Z))

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

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

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
subs.2

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

   Cannot find a definition or applicable library operation named subs 
      with argument type(s) 
                               PositiveInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
[structures(labels)$Subset(Z)]$ACLIST(Subset(Z))

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

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

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
[structures(labels)$Partition(Z)]$ACLIST(Partition(Z))

   The constructor Partition takes 0 arguments and you have given  1  .

Two ways to construct LinearOrder?:

#includeDir "/var/lib/zope/combinat/include"
#libraryDir "/var/lib/zope/combinat/lib"
#include "combinat"

macro {
        E == EmptySetSpecies;
        X == SingletonSpecies;
        + == Plus;
        * == Times;
}
MyLinearOrder(L:LabelType):CombinatorialSpecies L == (E + X*MyLinearOrder)(L) add;

   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/7566739481302953094-25px004.as using 
      AXIOM-XL compiler and options 
-O -Fasy -Fao -Flsp -laxiom -Mno-ALDOR_W_WillObsolete -DAxiom -Y $AXIOM/algebra -I $AXIOM/algebra
      Use the system command )set compiler args to change these 
      options.
"/var/zope2/var/LatexWiki/7566739481302953094-25px004.as", line 3: 
#include "combinat"
^
[L3 C1] #1 (Error) Could not open file `combinat'.

   The )library system command was not called after compilation.

X:=MyLinearOrder(Z)

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

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

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
[structures(labels)$X]$ACLIST(X)

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

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

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
MyLinearOrder2 := Interpret([parse "Plus(EmptySetSpecies,Times(SingletonSpecies,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.
X:=MyLinearOrder2(Z)

   There are no library operations named MyLinearOrder2 
      Use HyperDoc Browse or issue
                           )what op MyLinearOrder2
      to learn if there is any operation containing " MyLinearOrder2 " 
      in its name.

   Cannot find a definition or applicable library operation named 
      MyLinearOrder2 with argument type(s) 
                             Variable(ACInteger)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
[structures(labels)$X]$ACLIST(X)

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

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

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

I can't use the following species because of the Mathaction specific build. But they are implemented in Combinat!

X:=LinearOrder(Z)

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

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

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
X:=Cycle(Z)

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

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

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
X:=Permutation(Z)

   Permutation(Z) is not a valid type.
[structures(labels2)$X]$ACLIST(X)

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

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

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

Permutation does already exist within Axiom, use another name.

Now we are testing the generating series

X := Subset(Z)

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

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

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
es: ExponentialGeneratingSeries := generatingSeries()$X;

   The function generatingSeries is not implemented in NIL .
[coefficient(es, i) for i in 0..10]

   There are 8 exposed and 4 unexposed library operations named 
      coefficient having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op coefficient
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      coefficient with argument type(s) 
                                Variable(es)
                             NonNegativeInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   FriCAS will attempt to step through and interpret the code.
   There are 8 exposed and 4 unexposed library operations named 
      coefficient having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op coefficient
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named 
      coefficient with argument type(s) 
                                Variable(es)
                             NonNegativeInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
[count(es, i) for i in 0..10]

   There are 2 exposed and 0 unexposed library operations named count 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op count
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named count
      with argument type(s) 
                                Variable(es)
                             NonNegativeInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   FriCAS will attempt to step through and interpret the code.
   There are 2 exposed and 0 unexposed library operations named count 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op count
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named count
      with argument type(s) 
                                Variable(es)
                             NonNegativeInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
[2^i for i in 0..10 ]

(2)

And what is the number of Isomorphism Types

os: OrdinaryGeneratingSeries := isomorphismTypeGeneratingSeries()$X;

   The function isomorphismTypeGeneratingSeries is not implemented in 
      NIL .
[coefficient(os, i) for i in 0..10]

   There are 8 exposed and 4 unexposed library operations named 
      coefficient having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op coefficient
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      coefficient with argument type(s) 
                                Variable(os)
                             NonNegativeInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   FriCAS will attempt to step through and interpret the code.
   There are 8 exposed and 4 unexposed library operations named 
      coefficient having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op coefficient
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named 
      coefficient with argument type(s) 
                                Variable(os)
                             NonNegativeInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
cs: CycleIndexSeries := cycleIndexSeries()$X;

   The function cycleIndexSeries is not implemented in NIL .
I := ACMachineInteger

(3)

Q := ACFraction Z

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

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

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

(4)

T := SparseIndexedPowerProduct(V, I)

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

   Cannot find a definition or applicable library operation named 
      SparseIndexedPowerProduct with argument type(s) 
                        Variable(CycleIndexVariable)
                         Variable(ACMachineInteger)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
P := SparseDistributedPolynomial(Q, V, T)

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

   Cannot find a definition or applicable library operation named 
      SparseDistributedPolynomial with argument type(s) 
                                 Variable(Q)
                        Variable(CycleIndexVariable)
                                 Variable(T)

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

)set output tex off
 

)set output algebra on

coeffs: ACList P := [coefficient(cs, i) for i in 0..3]

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

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

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

)set output tex on
 

)set output algebra off