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SandBoxSpeciesBayreuth

Edit detail for SandBoxSpeciesBayreuth revision 2 of 12

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Editor: Thomas Feulner Time: 2008/06/16 05:30:20 GMT-7
Note:

changed:
-A(L: LabelType): CombinatorialSpecies L == (E + X*A*A)(L) add;
-Subsets(L: LabelType): CombinatorialSpecies L == (SetSpecies*SetSpecies)(L) add;
BTree(L: LabelType): CombinatorialSpecies L == (E + X*BTree*BTree)(L) add;
MySubset(L: LabelType): CombinatorialSpecies L == (SetSpecies*SetSpecies)(L) add;

changed:
-X := A(Z)
-
-labels: SetSpecies Z := set [7::Z,8::Z,15::Z]
X := BTree(Z)

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

changed:
-X:=EmptySetSpecies(Z)
[structures(labels)$EmptySetSpecies(Z)]$ACLIST(EmptySetSpecies(Z))
[structures(labels)$SingletonSpecies(Z)]$ACLIST(SingletonSpecies(Z))
[structures(labels2)$SingletonSpecies(Z)]$ACLIST(SingletonSpecies(Z))
[structures(labels)$SetSpecies(Z)]$ACLIST(SetSpecies(Z))
subs:=[(structures(labels)$MySubset(Z))]$ACLIST(MySubset(Z))
subs.2
[structures(labels)$Subset(Z)]$ACLIST(Subset(Z))
[structures(labels)$Partition(Z)]$ACLIST(Partition(Z))
\end{axiom}

Two ways to construct LinearOrder:
\begin{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;
\end{aldor}
\begin{axiom}
X:=MyLinearOrder(Z)

changed:
-X:=SingletonSpecies(Z)
MyLinearOrder2 := Interpret([parse "Plus(EmptySetSpecies,Times(SingletonSpecies,Self))"], ACInteger);
X:=MyLinearOrder2(Z)

removed:
-X:=SingletonSpecies(Z)
-[structures(labels2)$X]$ACLIST(X)
-X:=SetSpecies(Z)
-[structures(labels)$X]$ACLIST(X)
-X:=Subsets(Z)
-subs:=[(structures(labels)$X)]$ACLIST(X)
-subs.2

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

changed:
-
-The last error occurs, because we are using the Permutation Category (?) of Axiom? 
-
-
-
-
-
Permutation does already exist within Axiom, use another name.

Now with other labels:
\begin{axiom}
labels3 : SetSpecies ACString := set ["abc"::ACString,"def"::ACString,"xyz"::ACString]
[structures(labels)$Subset(ACString)]$ACLIST(Subset(ACString))

\end{axiom}

fricas

(1) -> )cd ~/combinat/src

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

fricas

)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/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7896689979910980793-25px002.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.
"/var/lib/zope2.10/instance/axiom-wiki/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.

fricas

Z := ACInteger

$\label{eq1}\hbox{\axiomType{ACInteger}\ }$

(1)

Type: Variable(ACInteger?)

fricas

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.

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/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/7566739481302953094-25px004.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.
"/var/lib/zope2.10/instance/axiom-wiki/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.

fricas

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.

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

fricas

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.

Permutation does already exist within Axiom, use another name.

Now with other labels:

fricas

labels3 : SetSpecies ACString := set ["abc"::ACString,"def"::ACString,"xyz"::ACString]

   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(ACString)

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