login  home  contents  what's new  discussion  bug reports     help  links  subscribe  changes  refresh  edit
SandBoxSpecies
SandBoxSpeciesAldor  ← ↑ →  SandBoxSpeciesCategory

SandBoxSpeciesBayreuth
  
last edited 16 years ago by Thomas Feulner

Edit detail for SandBoxSpeciesBayreuth revision 9 of 12
1 2 3 4 5 6 7 8 9 10 11 12
Editor: Thomas Feulner
Time: 2008/06/16 23:57:42 GMT-7
Note: 
removed:
-
-RestrictedSpecies(SetSpecies ACInteger, 2::ACInteger)


axiom
)cd ~/combinat/src
   The current FriCAS default directory is /var/lib/zope/combinat/src
axiom
)re ../lib/combinat.input

axiom
)lib cscombinatversion.ao
axiom
Reading /var/lib/zope/combinat/src/cscombinatversion.asy
   LibraryInformationCombinat is now explicitly exposed in frame 
      initial 
   LibraryInformationCombinat will be automatically loaded when needed 
      from /var/lib/zope/combinat/src/cscombinatversion
axiom
)lib csaxcompat.ao
axiom
Reading /var/lib/zope/combinat/src/csaxcompat.asy
   ACCharacter is now explicitly exposed in frame initial 
   ACCharacter will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   ACFraction is now explicitly exposed in frame initial 
   ACFraction will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   ACIntegerTools is now explicitly exposed in frame initial 
   ACIntegerTools will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   ACInteger is now explicitly exposed in frame initial 
   ACInteger will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   ACList is now explicitly exposed in frame initial 
   ACList will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   ACMachineInteger is now explicitly exposed in frame initial 
   ACMachineInteger will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   ACPrimitiveArray is now explicitly exposed in frame initial 
   ACPrimitiveArray will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   ACString is now explicitly exposed in frame initial 
   ACString will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   ACSymbol is now explicitly exposed in frame initial 
   ACSymbol will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   Array is now explicitly exposed in frame initial 
   Array will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   ACLabelType is now explicitly exposed in frame initial 
   ACLabelType will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   OutputType is now explicitly exposed in frame initial 
   OutputType will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
   TotallyOrderedType is now explicitly exposed in frame initial 
   TotallyOrderedType will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat
axiom
)lib csaxcompat2.ao
axiom
Reading /var/lib/zope/combinat/src/csaxcompat2.asy
   ExpressionTreeExpt is now explicitly exposed in frame initial 
   ExpressionTreeExpt will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTreeLeaf is now explicitly exposed in frame initial 
   ExpressionTreeLeaf will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTreePlus is now explicitly exposed in frame initial 
   ExpressionTreePlus will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTreePrefix is now explicitly exposed in frame initial 
   ExpressionTreePrefix will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTreeTimes is now explicitly exposed in frame initial 
   ExpressionTreeTimes will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTree is now explicitly exposed in frame initial 
   ExpressionTree will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
   GeneratorException is now explicitly exposed in frame initial 
   GeneratorException will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
   Generator is now explicitly exposed in frame initial 
   Generator will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionTreeOperator is now explicitly exposed in frame initial 
   ExpressionTreeOperator will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   ExpressionType is now explicitly exposed in frame initial 
   ExpressionType will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
   GeneratorExceptionType is now explicitly exposed in frame initial 
   GeneratorExceptionType will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csaxcompat2
   Partial is now explicitly exposed in frame initial 
   Partial will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csaxcompat2
Won't parse: (Type)->NIL
axiom
)lib csistruc.ao
axiom
Reading /var/lib/zope/combinat/src/csistruc.asy
   SparseAdditiveArray is now explicitly exposed in frame initial 
   SparseAdditiveArray will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csistruc
   SparseFiniteMonoidRing is now explicitly exposed in frame initial 
   SparseFiniteMonoidRing will be automatically loaded when needed from
      /var/lib/zope/combinat/src/csistruc
   IndexedFreeAdditiveCombinationType is now explicitly exposed in 
      frame initial 
   IndexedFreeAdditiveCombinationType will be automatically loaded when
      needed from /var/lib/zope/combinat/src/csistruc
   IndexedFreeArithmeticType is now explicitly exposed in frame initial
   IndexedFreeArithmeticType will be automatically loaded when needed 
      from /var/lib/zope/combinat/src/csistruc
axiom
)lib csdistpoly.ao
axiom
Reading /var/lib/zope/combinat/src/csdistpoly.asy
   SparseDistributedPolynomial is now explicitly exposed in frame 
      initial 
   SparseDistributedPolynomial will be automatically loaded when needed
      from /var/lib/zope/combinat/src/csdistpoly
axiom
)lib csstream.ao
axiom
Reading /var/lib/zope/combinat/src/csstream.asy
   DataStream is now explicitly exposed in frame initial 
   DataStream will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csstream
axiom
)lib csseries.ao
axiom
Reading /var/lib/zope/combinat/src/csseries.asy
   SeriesOrder is now explicitly exposed in frame initial 
   SeriesOrder will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csseries
   FormalPowerSeries is now explicitly exposed in frame initial 
   FormalPowerSeries will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csseries
   FormalPowerSeriesCategory is now explicitly exposed in frame initial
   FormalPowerSeriesCategory will be automatically loaded when needed 
      from /var/lib/zope/combinat/src/csseries
axiom
)lib csidxpp.ao
axiom
Reading /var/lib/zope/combinat/src/csidxpp.asy
   SparseIndexedPowerProduct is now explicitly exposed in frame initial
   SparseIndexedPowerProduct will be automatically loaded when needed 
      from /var/lib/zope/combinat/src/csidxpp
axiom
)lib cssiprimes.ao
axiom
Reading /var/lib/zope/combinat/src/cssiprimes.asy
   SmallIntegerPrimes is now explicitly exposed in frame initial 
   SmallIntegerPrimes will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/cssiprimes
axiom
)lib cssitools.ao
axiom
Reading /var/lib/zope/combinat/src/cssitools.asy
   SmallIntegerTools is now explicitly exposed in frame initial 
   SmallIntegerTools will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/cssitools
axiom
)lib csgseries.ao
axiom
Reading /var/lib/zope/combinat/src/csgseries.asy
   CycleIndexSeries is now explicitly exposed in frame initial 
   CycleIndexSeries will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csgseries
   CycleIndexVariable is now explicitly exposed in frame initial 
   CycleIndexVariable will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csgseries
   ExponentialGeneratingSeries is now explicitly exposed in frame 
      initial 
   ExponentialGeneratingSeries will be automatically loaded when needed
      from /var/lib/zope/combinat/src/csgseries
   OrdinaryGeneratingSeries is now explicitly exposed in frame initial 
   OrdinaryGeneratingSeries will be automatically loaded when needed 
      from /var/lib/zope/combinat/src/csgseries
axiom
)lib csmultinom.ao
axiom
Reading /var/lib/zope/combinat/src/csmultinom.asy
   MultinomialTools is now explicitly exposed in frame initial 
   MultinomialTools will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csmultinom
axiom
)lib csspexpr.ao
axiom
Reading /var/lib/zope/combinat/src/csspexpr.asy
   SpeciesExpression is now explicitly exposed in frame initial 
   SpeciesExpression will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspexpr
axiom
)lib csspecies.ao
axiom
Reading /var/lib/zope/combinat/src/csspecies.asy
   RestrictedSpecies is now explicitly exposed in frame initial 
   RestrictedSpecies will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   SetSpecies is now explicitly exposed in frame initial 
   SetSpecies will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   SingletonSpecies is now explicitly exposed in frame initial 
   SingletonSpecies will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   ACIsomorphismType is now explicitly exposed in frame initial 
   ACIsomorphismType will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   Augment is now explicitly exposed in frame initial 
   Augment will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   Subset is now explicitly exposed in frame initial 
   Subset will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   CharacteristicSpecies is now explicitly exposed in frame initial 
   CharacteristicSpecies will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   Times is now explicitly exposed in frame initial 
   Times will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   Combination is now explicitly exposed in frame initial 
   Combination will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   Compose is now explicitly exposed in frame initial 
   Compose will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   Derivative is now explicitly exposed in frame initial 
   Derivative will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   DropEmpty is now explicitly exposed in frame initial 
   DropEmpty will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   EmptySetSpecies is now explicitly exposed in frame initial 
   EmptySetSpecies will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   FunctorialCompose is now explicitly exposed in frame initial 
   FunctorialCompose will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   MultiCompose is now explicitly exposed in frame initial 
   MultiCompose will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   MultiDerivative is now explicitly exposed in frame initial 
   MultiDerivative will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   MultiPlus is now explicitly exposed in frame initial 
   MultiPlus will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   MultiSetCombination is now explicitly exposed in frame initial 
   MultiSetCombination will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   MultiSetPartition is now explicitly exposed in frame initial 
   MultiSetPartition will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   MultiSet is now explicitly exposed in frame initial 
   MultiSet will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   MultiSubset is now explicitly exposed in frame initial 
   MultiSubset will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   CombinatorialSpecies is now explicitly exposed in frame initial 
   CombinatorialSpecies will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   MultiTimes is now explicitly exposed in frame initial 
   MultiTimes will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   Multiple is now explicitly exposed in frame initial 
   Multiple will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   NonEmpty is now explicitly exposed in frame initial 
   NonEmpty will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   IsomorphismTypeCategory is now explicitly exposed in frame initial 
   IsomorphismTypeCategory will be automatically loaded when needed 
      from /var/lib/zope/combinat/src/csspecies
   Partition is now explicitly exposed in frame initial 
   Partition will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
   Plus is now explicitly exposed in frame initial 
   Plus will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csspecies
axiom
)lib csexamples.ao
axiom
Reading /var/lib/zope/combinat/src/csexamples.asy
   ACBinaryTree is now explicitly exposed in frame initial 
   ACBinaryTree will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csexamples
   SetSpecies is already explicitly exposed in frame initial 
   SetSpecies will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csexamples
   Combination is already explicitly exposed in frame initial 
   Combination will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csexamples
   Generator is already explicitly exposed in frame initial 
   Generator will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csexamples
Won't parse: (ACLabelType)->NIL
Won't parse: (Type)->NIL
axiom
)lib csinterp.ao
axiom
Reading /var/lib/zope/combinat/src/csinterp.asy
   Interpret is now explicitly exposed in frame initial 
   Interpret will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csinterp
   InterpretingTools is now explicitly exposed in frame initial 
   InterpretingTools will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csinterp
   LabelSpecies is now explicitly exposed in frame initial 
   LabelSpecies will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csinterp
axiom
)lib csparse.ao
axiom
Reading /var/lib/zope/combinat/src/csparse.asy
   MyParser is now explicitly exposed in frame initial 
   MyParser will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/csparse

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-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra
      Use the system command )set compiler args to change these 
      options.
#1 (Warning) Deprecated message prefix: use `ALDOR_' instead of `_AXL'
   Compiling Lisp source code from file 
      ./7896689979910980793-25px002.lsp
   Issuing )library command for 7896689979910980793-25px002
   Reading /var/lib/zope/combinat/src/7896689979910980793-25px002.asy
   BTree is now explicitly exposed in frame initial 
   BTree will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/7896689979910980793-25px002
   MySubset is now explicitly exposed in frame initial 
   MySubset will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/7896689979910980793-25px002

axiom
Z := ACInteger
LatexWiki Image(1)
Type: Domain
axiom
X := BTree(Z)
LatexWiki Image(2)
Type: Domain
axiom
labels: SetSpecies Z := set [1::Z,2::Z,4::Z]
LatexWiki Image(3)
Type: SetSpecies? ACInteger?
axiom
labels2 : SetSpecies Z := set[5005::Z]
LatexWiki Image(4)
Type: SetSpecies? ACInteger?
axiom
)set output tex off

axiom
)set output algebra on
[structures(labels)$X]$ACLIST(X)
   (5)
   [((1, "nil"), ((2, "nil"), ((4, "nil"), "nil"))),
    ((1, "nil"), ((4, "nil"), ((2, "nil"), "nil"))),
    ((1, "nil"), ((2, ((4, "nil"), "nil")), "nil")),
    ((1, "nil"), ((4, ((2, "nil"), "nil")), "nil")),
    ((2, "nil"), ((1, "nil"), ((4, "nil"), "nil"))),
    ((2, "nil"), ((4, "nil"), ((1, "nil"), "nil"))),
    ((2, "nil"), ((1, ((4, "nil"), "nil")), "nil")),
    ((2, "nil"), ((4, ((1, "nil"), "nil")), "nil")),
    ((1, ((2, "nil"), "nil")), ((4, "nil"), "nil")),
    ((2, ((1, "nil"), "nil")), ((4, "nil"), "nil")),
    ((4, "nil"), ((1, "nil"), ((2, "nil"), "nil"))),
    ((4, "nil"), ((2, "nil"), ((1, "nil"), "nil"))),
    ((4, "nil"), ((1, ((2, "nil"), "nil")), "nil")),
    ((4, "nil"), ((2, ((1, "nil"), "nil")), "nil")),
    ((1, ((4, "nil"), "nil")), ((2, "nil"), "nil")),
    ((4, ((1, "nil"), "nil")), ((2, "nil"), "nil")),
    ((2, ((4, "nil"), "nil")), ((1, "nil"), "nil")),
    ((4, ((2, "nil"), "nil")), ((1, "nil"), "nil")),
    ((1, ((2, "nil"), ((4, "nil"), "nil"))), "nil"),
    ((1, ((4, "nil"), ((2, "nil"), "nil"))), "nil"),
    ((1, ((2, ((4, "nil"), "nil")), "nil")), "nil"),
    ((1, ((4, ((2, "nil"), "nil")), "nil")), "nil"),
    ((2, ((1, "nil"), ((4, "nil"), "nil"))), "nil"),
    ((2, ((4, "nil"), ((1, "nil"), "nil"))), "nil"),
    ((2, ((1, ((4, "nil"), "nil")), "nil")), "nil"),
    ((2, ((4, ((1, "nil"), "nil")), "nil")), "nil"),
    ((4, ((1, "nil"), ((2, "nil"), "nil"))), "nil"),
    ((4, ((2, "nil"), ((1, "nil"), "nil"))), "nil"),
    ((4, ((1, ((2, "nil"), "nil")), "nil")), "nil"),
    ((4, ((2, ((1, "nil"), "nil")), "nil")), "nil")]
Type: ACList? BTree? ACInteger?
axiom
)set output tex on

axiom
)set output algebra off
[structures(labels)$EmptySetSpecies(Z)]$ACLIST(EmptySetSpecies(Z))
LatexWiki Image(5)
Type: ACList? EmptySetSpecies? ACInteger?
axiom
[structures(labels)$SingletonSpecies(Z)]$ACLIST(SingletonSpecies(Z))
LatexWiki Image(6)
Type: ACList? SingletonSpecies? ACInteger?
axiom
[structures(labels2)$SingletonSpecies(Z)]$ACLIST(SingletonSpecies(Z))
LatexWiki Image(7)
Type: ACList? SingletonSpecies? ACInteger?
axiom
[structures(labels)$SetSpecies(Z)]$ACLIST(SetSpecies(Z))
LatexWiki Image(8)
Type: ACList? SetSpecies? ACInteger?
axiom
subs:=[(structures(labels)$MySubset(Z))]$ACLIST(MySubset(Z))
LatexWiki Image(9)
Type: ACList? MySubset? ACInteger?
axiom
subs.2
LatexWiki Image(10)
Type: MySubset? ACInteger?
axiom
[structures(labels)$Subset(Z)]$ACLIST(Subset(Z))
LatexWiki Image(11)
Type: ACList? Subset ACInteger?
axiom
[structures(labels)$Partition(Z)]$ACLIST(Partition(Z))
LatexWiki Image(12)
Type: ACList? Partition ACInteger?

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-AXL_W_WillObsolete -DAxiom -Y $AXIOM/algebra
      Use the system command )set compiler args to change these 
      options.
#1 (Warning) Deprecated message prefix: use `ALDOR_' instead of `_AXL'
   Compiling Lisp source code from file 
      ./7566739481302953094-25px004.lsp
   Issuing )library command for 7566739481302953094-25px004
   Reading /var/lib/zope/combinat/src/7566739481302953094-25px004.asy
   MyLinearOrder is now explicitly exposed in frame initial 
   MyLinearOrder will be automatically loaded when needed from 
      /var/lib/zope/combinat/src/7566739481302953094-25px004

axiom
X:=MyLinearOrder(Z)
LatexWiki Image(13)
Type: Domain
axiom
[structures(labels)$X]$ACLIST(X)
LatexWiki Image(14)
Type: ACList? MyLinearOrder? ACInteger?
axiom
MyLinearOrder2 := Interpret([parse "Plus(EmptySetSpecies,Times(SingletonSpecies,Self))"],
ACInteger);
Type: Domain
axiom
X:=MyLinearOrder2(Z)
LatexWiki Image(15)
Type: Domain
axiom
[structures(labels)$X]$ACLIST(X)
LatexWiki Image(16)
Type: ACList? Interpret([CONCATPlus(PAREN (AGGLST (CONCAT (NOTHING) EmptySetSpecies) (CONCAT Times (PAREN (AGGLST (CONCAT (NOTHING) SingletonSpecies) (CONCAT (NOTHING) Self))))))]?,ACInteger?)

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)
                                   Domain
      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.
X:=Cycle(Z)
   There are no library operations named Cycle
      Use HyperDoc Browse or issue
                               )what op Cycle
      to learn if there is any operation containing " Cycle " in its
      name.
   Cannot find a definition or applicable library operation named Cycle
      with argument type(s)
                                   Domain
      Perhaps you should use "@" to indicate the required return type,
      or "$" to specify which version of the function you need.
X:=Permutation(Z)
LatexWiki Image(17)
Type: Domain
axiom
[structures(labels2)$X]$ACLIST(X)
   The function structures is not implemented in Permutation ACInteger
      .

Permutation does already exist within Axiom, use another name.

Now we are testing the generating series 

axiom
X := Subset(Z)
LatexWiki Image(18)
Type: Domain
axiom
es: ExponentialGeneratingSeries := generatingSeries()$X;
Type: ExponentialGeneratingSeries?
axiom
[coefficient(es, i) for i in 0..10]
LatexWiki Image(19)
Type: List ACFraction? ACInteger?
axiom
[count(es, i) for i in 0..10]
LatexWiki Image(20)
Type: List ACInteger?
axiom
[2^i for i in 0..10 ]
LatexWiki Image(21)
Type: List PositiveInteger?

And what is the number of Isomorphism Types 

axiom
os: OrdinaryGeneratingSeries := isomorphismTypeGeneratingSeries()$X;
Type: OrdinaryGeneratingSeries?
axiom
[coefficient(os, i) for i in 0..10]
LatexWiki Image(22)
Type: List ACInteger?