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SandBoxLeftFreeModule

Edit detail for SandBoxLeftFreeModule revision 1 of 5

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Editor: Bill Page Time: 2008/05/25 11:33:58 GMT-7
Note: Gaby's example

changed:
-
\begin{spad}
)abbrev domain LFREEMOD LeftFreeModule
LeftFreeModule(R: Ring, S: OrderedSet):
    Join(LeftModule R, IndexedDirectProductCategory(R,S)) with
      linearCombination: List Pair(S,R) -> %
 == IndexedDirectProductAbelianGroup(R,S) add
   Rep == List Pair(S,R)
   linearCombination x ==
     per [u for u in x | second u ~= 0$R ]
   if R has EntireRing then
     (r: R) * (x: %) ==
       r = 0$R => 0$%
       r = 1$R => x
       messagePrint("from LeftFreeModule")$OutputForm
       per [pair(first u, r * second u) for u in rep x]
   else
     (r: R) * (x: %) ==
       r = 0$R => 0$%
       r = 1$R => x
       messagePrint("from LeftFreeModule")$OutputForm
       per [pair(first u,c) for u in rep x | (c := r *second u) ~= 0$R]
   coerce(x: %): OutputForm ==
     x' := rep x
     null x' => 0$R :: OutputForm
     res : List OutputForm := nil
     for u in reverse x' repeat
       second u = 1$R => res := cons(first(u)::OutputForm, res)
       res := cons(second(u)::OutputForm * first(u)::OutputForm, res)
     reduce("+",res)
\end{spad}

There is no 'from LeftFreeModule' printed out.
\begin{axiom}
x := 'x::OrderedVariableList ['x,'y]
x := 'y::OrderedVariableList ['x,'y]
2 * linearCombination([pair(x,2), pair(y,3)])$LeftFreeModule(Integer,OrderedVariableList ['x,'y])
Integer has EntireRing
\end{axiom}

spad)abbrev domain LFREEMOD LeftFreeModule
LeftFreeModule(R: Ring, S: OrderedSet):
    Join(LeftModule R, IndexedDirectProductCategory(R,S)) with
      linearCombination: List Pair(S,R) -> %
 == IndexedDirectProductAbelianGroup(R,S) add
   Rep == List Pair(S,R)
   linearCombination x ==
     per [u for u in x | second u ~= 0$R ]
   if R has EntireRing then
     (r: R) * (x: %) ==
       r = 0$R => 0$%
       r = 1$R => x
       messagePrint("from LeftFreeModule")$OutputForm
       per [pair(first u, r * second u) for u in rep x]
   else
     (r: R) * (x: %) ==
       r = 0$R => 0$%
       r = 1$R => x
       messagePrint("from LeftFreeModule")$OutputForm
       per [pair(first u,c) for u in rep x | (c := r *second u) ~= 0$R]
   coerce(x: %): OutputForm ==
     x' := rep x
     null x' => 0$R :: OutputForm
     res : List OutputForm := nil
     for u in reverse x' repeat
       second u = 1$R => res := cons(first(u)::OutputForm, res)
       res := cons(second(u)::OutputForm * first(u)::OutputForm, res)
     reduce("+",res)

spad

   Compiling OpenAxiom source code from file 
      /var/zope2/var/LatexWiki/833505762114505642-25px001.spad using 
      Spad compiler.
   LFREEMOD abbreviates domain LeftFreeModule 
------------------------------------------------------------------------
   initializing NRLIB LFREEMOD for LeftFreeModule 
   compiling into NRLIB LFREEMOD 
   compiling local rep : % -> List Pair(S,R)
      LFREEMOD;rep is replaced by G1393 
Time: 0.06 SEC.
   compiling local per : List Pair(S,R) -> %
      LFREEMOD;per is replaced by G1393 
Time: 0 SEC.
   compiling exported linearCombination : List Pair(S,R) -> %
Time: 0 SEC.
****** Domain: R already in scope
augmenting R: (EntireRing)
   compiling exported * : (R,%) -> %
Time: 0.02 SEC.
   compiling exported * : (R,%) -> %
Time: 0.06 SEC.
   compiling exported coerce : % -> OutputForm
Time: 0.11 SEC.
(time taken in buildFunctor:  0)
;;;     ***       |LeftFreeModule| REDEFINED
;;;     ***       |LeftFreeModule| REDEFINED
Time: 0 SEC.
   Cumulative Statistics for Constructor LeftFreeModule
      Time: 0.25 seconds
   finalizing NRLIB LFREEMOD 
   Processing LeftFreeModule for Browser database:
--->-->LeftFreeModule((linearCombination (% (List (Pair S R))))): Not documented!!!!
--->-->LeftFreeModule(constructor): Not documented!!!!
--->-->LeftFreeModule(): Missing Description
------------------------------------------------------------------------
   LeftFreeModule is now explicitly exposed in frame initial 
   LeftFreeModule will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/LFREEMOD.NRLIB/code.o

There is no from LeftFreeModule printed out.

axiom
x := 'x::OrderedVariableList ['x,'y]

(1)

Type: OrderedVariableList? [x,y]?

axiom
x := 'y::OrderedVariableList ['x,'y]

(2)

Type: OrderedVariableList? [x,y]?

axiom
2 * linearCombination([pair(x,2), pair(y,3)])$LeftFreeModule(Integer,OrderedVariableList ['x,'y])

(3)

Type: LeftFreeModule?(Integer,OrderedVariableList? [x,y]?)

axiom
Integer has EntireRing

(4)

Type: Boolean