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axiom
)cd ~/combinat/src
The current FriCAS default directory is /var/zope2/var/LatexWiki
axiom
)re ../lib/combinat.input
The file ../lib/combinat.input is needed but does not exist.

aldor
#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;
aldor
   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.

axiom
Z := ACInteger

\label{eq1}\hbox{\axiomType{ACInteger}\ }(1)
Type: Variable(ACInteger?)
axiom
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.
axiom
)set output tex off
 
axiom
)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.
axiom
)set output tex on
 
axiom
)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?:

aldor
#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;
aldor
   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.

axiom
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!

axiom
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

axiom
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 ]

\label{eq2}\left[ 1, \: 2, \: 4, \: 8, \:{16}, \:{32}, \:{64}, \:{128}, \:{256}, \:{512}, \:{1024}\right](2)
Type: List(PositiveInteger)

And what is the number of Isomorphism Types

axiom
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

\label{eq3}\hbox{\axiomType{ACMachineInteger}\ }(3)
Type: Variable(ACMachineInteger?)
axiom
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

\label{eq4}\hbox{\axiomType{CycleIndexVariable}\ }(4)
Type: Variable(CycleIndexVariable?)
axiom
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.
axiom
)set output tex off
 
axiom
)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.
axiom
)set output tex on
 
axiom
)set output algebra off




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