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: 0.03 SEC.
****** Domain: R already in scope
augmenting R: (EntireRing)
compiling exported * : (R,$) -> $
Time: 0 SEC.
compiling exported * : (R,$) -> $
Time: 0.01 SEC.
compiling exported coerce : $ -> OutputForm
****** comp fails at level 4 with expression: ******
error in function coerce
(SEQ (|:=| |x'| (|pretend| (@ |x| $) |Rep|))
(|exit| 1
(IF | << |
(|null| |x'|)
| >> |
(|::| (|Sel| R 0) (|OutputForm|))
(SEQ (|:=| (|:| |res| (|List| (|OutputForm|))) |nil|)
(REPEAT (IN |u| (|reverse| |x'|))
(SEQ
(|:=| (|:| #1=#:G674 (|Boolean|))
(= (|second| |u|) (|Sel| R 1)))
(|exit| 1
(IF #1#
(|:=| |res|
(|cons| (|::| (|first| |u|) (|OutputForm|))
|res|))
(|:=| |res|
(|cons|
(* (|::| (|second| |u|) (|OutputForm|))
(|::| (|first| |u|) (|OutputForm|)))
|res|))))))
(|exit| 1 (|reduce| "+" |res|))))))
****** level 4 ******
$x:= (null x')
$m:= (Boolean)
$f:=
((((|x'| #) (|x| # #) (|per| #) (|rep| #) ...)))
>> Apparent user error:
NoValueMode
is an unknown modeThere is no from LeftFreeModule? printed out.
fricas
oV := OrderedVariableList ['x,'y]
Type: Type
fricas
Pro := Product(oV, Integer)
Type: Type
fricas
x := 'x::OrderedVariableList ['x,'y]
fricas
x := 'y::OrderedVariableList ['x,'y]
fricas
2 * linearCombination([construct(x,2)$Pro, construct(y,3)$Pro])$LeftFreeModule(Integer,OrderedVariableList ['x,'y])
LeftFreeModule is an unknown constructor and so is unavailable. Did
you mean to use -> but type something different instead?
![\label{eq1}\hbox{\axiomType{OrderedVariableList}\ } ([ x , y ])](images/5509962614798529383-16.0px.png "\label{eq1}\hbox{\axiomType{OrderedVariableList}\ } ([ x , y ])")
![\label{eq2}\hbox{\axiomType{Product}\ } (\hbox{\axiomType{OrderedVariableList}\ } ([ x , y ]) , \hbox{\axiomType{Integer}\ })](images/3160640450652175172-16.0px.png "\label{eq2}\hbox{\axiomType{Product}\ } (\hbox{\axiomType{OrderedVariableList}\ } ([ x , y ]) , \hbox{\axiomType{Integer}\ })")
