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

**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 ]

**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

**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

**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