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spad
)abbrev domain LFREEMOD LeftFreeModule
LeftFreeModule(R: Ring, S: OrderedSet):
    Join(LeftModule R, IndexedDirectProductCategory(R,S)) with
      linearCombination: List Product(S,R) -> %
 == IndexedDirectProductObject(R,S) add
   Rep := List Product(S,R)
   rep x ==> (x@%) pretend Rep
   per x ==> (x@Rep) pretend %
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")$OutputForm per [construct(first u, r * second u) for u in rep x] else (r: R) * (x: %) == r = 0$R => 0$% r = 1$R => x messagePrint("from LeftFreeModule")$OutputForm per [construct(first u,c) for u in rep x | (c := r *second u) ~= 0$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 FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5896234725235034910-25px001.spad
      using old system compiler.
   LFREEMOD abbreviates domain LeftFreeModule 
------------------------------------------------------------------------
   initializing NRLIB LFREEMOD for LeftFreeModule 
   compiling into NRLIB LFREEMOD 
   processing macro definition rep x ==> pretend(@(x,$),Rep) 
   processing macro definition per x ==> pretend(@(x,Rep),$) 
   compiling exported linearCombination : List Product(S,R) -> $
Time: 0.02 SEC.
****** Domain: R already in scope augmenting R: (EntireRing) compiling exported * : (R,$) -> $ Time: 0.01 SEC.
compiling exported * : (R,$) -> $ Time: 0 SEC.
compiling exported coerce : $ -> OutputForm Time: 0.02 SEC.
****** Domain: R already in scope augmenting R: (OrderedAbelianMonoidSup) (time taken in buildFunctor: 10)
;;; *** |LeftFreeModule| REDEFINED
;;; *** |LeftFreeModule| REDEFINED Time: 0.01 SEC.
Warnings: [1] linearCombination: pretend$ -- should replace by @ [2] *: pretendRep -- should replace by @ [3] *: pretend$ -- should replace by @ [4] coerce: pretendRep -- should replace by @
Cumulative Statistics for Constructor LeftFreeModule Time: 0.06 seconds
finalizing NRLIB LFREEMOD Processing LeftFreeModule for Browser database: --->-->LeftFreeModule(constructor): Not documented!!!! --->-->LeftFreeModule((linearCombination (% (List (Product S R))))): Not documented!!!! --->-->LeftFreeModule(): Missing Description ; compiling file "/var/aw/var/LatexWiki/LFREEMOD.NRLIB/LFREEMOD.lsp" (written 31 JUL 2013 04:31:58 PM):
; /var/aw/var/LatexWiki/LFREEMOD.NRLIB/LFREEMOD.fasl written ; compilation finished in 0:00:00.045 ------------------------------------------------------------------------ LeftFreeModule is now explicitly exposed in frame initial LeftFreeModule will be automatically loaded when needed from /var/aw/var/LatexWiki/LFREEMOD.NRLIB/LFREEMOD

There is no from LeftFreeModule? printed out.

fricas
oV := OrderedVariableList ['x,'y]

\label{eq1}\hbox{\axiomType{OrderedVariableList}\ } ([ x , y ])(1)
Type: Type
fricas
Pro := Product(oV, Integer)

\label{eq2}\hbox{\axiomType{Product}\ } (\hbox{\axiomType{OrderedVariableList}\ } ([ x , y ]) , \hbox{\axiomType{Integer}\ })(2)
Type: Type
fricas
x := 'x::OrderedVariableList ['x,'y]

\label{eq3}x(3)
Type: OrderedVariableList([x,y])
fricas
x := 'y::OrderedVariableList ['x,'y]

\label{eq4}y(4)
Type: OrderedVariableList([x,y])
fricas
2 * linearCombination([construct(x,2)$Pro, construct(y,3)$Pro])$LeftFreeModule(Integer,OrderedVariableList ['x,'y])

\label{eq5}{4 \  y}+{6 \  y}(5)
Type: LeftFreeModule?(Integer,OrderedVariableList([x,y]))
fricas
Integer has EntireRing

\label{eq6} \mbox{\rm true} (6)
Type: Boolean
fricas
(2 * linearCombination([[x,2]$Pro, [y,3]$Pro])$LeftFreeModule(Integer,OrderedVariableList ['x,'y]))$LeftFreeModule(Integer,OrderedVariableList ['x,'y])

\label{eq7}{4 \  y}+{6 \  y}(7)
Type: LeftFreeModule?(Integer,OrderedVariableList([x,y]))




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