Edit detail for SandBoxSpeciesAldor revision 4 of 11

removed:
-*Want loading of libraries with no output.*

changed:
-X := A(ACInteger)
I := ACMachineInteger
Z := ACInteger
Q := ACFraction Z
V := CycleIndexVariable
T := SparseIndexedPowerProduct(V, I)
P := SparseDistributedPolynomial(Q, V, T)
S := CycleIndexSeries;
X := A(Z)

changed:
-labels := set [i::ACInteger for i in 1..3]
labels := set [i::Z for i in 1..3]

removed:
-I := ACMachineInteger
-Q := ACFraction ACInteger
-V := CycleIndexVariable
-T := SparseIndexedPowerProduct(V, I)
-P := SparseDistributedPolynomial(Q, V, T)
-S := CycleIndexSeries;

removed:
-coeffs3: List P := [coefficient(cs, i) for i in 0..5]

changed:
-Ooops, it seems that elements of P cannot be printed in Axiom. :-(
-
-So let's find the problem. P is the polynomial domain in infinitely many variables with rational coefficients.
The output of the next command apparently causes a "Proxy Error" on the mathaction server.
This can be avoided by changing the output from LaTeX to ASCII mode:


\begin{axiom}
)set output tex off
)set output algebra on
coeffs3: ACList P := [coefficient(cs, i) for i in 0..5]
)set output tex on
)set output algebra off
\end{axiom}

P is the polynomial domain in infinitely many variables with rational coefficients.

changed:
-Hmm, prints fine...
-
-\begin{axiom}
-coefficient(cs, 0)
-coefficient(cs, 1)
-coefficient(cs, 2)
-coefficient(cs, 3)
-coefficient(cs, 4)
-coefficient(cs, 5)
-\end{axiom}
-
-The output of the next command apparently causes a "Proxy Error" on the mathaction server. This can be avoided by changing the output from LaTeX to ASCII mode:
-\begin{axiom}
-)set output tex off
-)set output algebra on
-coeffs4: ACList P := [coefficient(cs, i) for i in 0..5]
-)set output tex on
-)set output algebra off
-\end{axiom}
-
-Let's do some more advanced stuff. See
-the "functorial composition testpage":http://www.risc.uni-linz.ac.at/people/hemmecke/AldorCombinat/combinatsu78.html#x117-16400029.2

Let's do some more advanced stuff with
"Aldor-Combinat":http://www.risc.uni-linz.ac.at/people/hemmecke/AldorCombinat/ .
See the
"functorial composition testpage":http://www.risc.uni-linz.ac.at/people/hemmecke/AldorCombinat/combinatsu78.html#x117-16400029.2

added:
Here we compute the cycleindex series of simple graphs.

Test species in axiom/FriCAS?.

The species project is written in Aldor. Thus we need to load the libraries explicitly:

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.

Let's define a binary tree.

aldor

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

macro {
        E == EmptySetSpecies;
        X == SingletonSpecies;
        + == Plus;
        * == Times;
}

A(L: LabelType): CombinatorialSpecies L == (E + X*A*A)(L) add;

aldor

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5200085684951427974-25px002.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/5200085684951427974-25px002.as", line 3: 
#include "combinat"
^
[L3 C1] #1 (Error) Could not open file `combinat'.

   The )library system command was not called after compilation.

fricas

I := ACMachineInteger

(1)

Type: Variable(ACMachineInteger?)

fricas

Z := ACInteger

(2)

Type: Variable(ACInteger?)

fricas

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.

The output of the next command apparently causes a "Proxy Error" on the mathaction server. This can be avoided by changing the output from LaTeX? to ASCII mode:

fricas

)set output tex off
 

fricas

)set output algebra on

coeffs3: ACList P := [coefficient(cs, i) for i in 0..5]

   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.

P is the polynomial domain in infinitely many variables with rational coefficients.

fricas

p: P := 1$P

   P is not a valid type.

Let's do some more advanced stuff with Aldor-Combinat . See the functorial composition testpage for more details.

Here we compute the cycleindex series of simple graphs.

fricas

e: S := cycleIndexSeries() $ SetSpecies(Z);

   S is not a valid type.