[Axiom-developer] Another strange coercion

[Franz Lehner]

Hello,

> There are many easy examples of this when you use the Axiom interpreter.
Perhaps the following is related:

Trying to implement free products of monoids
FreeProductMonoid(M1:Monoid,M2:Monoid)
(see attachment, not very elegant, but I don't know how to avoid "mixed 
lists" otherwise). I am stuck at the following problem: 
There are two converters

coerce:M1 -> %
coerce:M2 -> %

but somehow always the first converter is called,
in the order where they are found in the source file,
leading to strange results:


(1) -> Z2:=CyclicGroup(2,'a)

   (1)  CyclicGroup(2,a)
                                                       Type: Domain
(2) -> Z3:=CyclicGroup(3,'b)

   (2)  CyclicGroup(3,b)
                                                       Type: Domain
(3) -> G:=FreeProductMonoid(Z2,Z3)

   (3)  FreeProductMonoid(CyclicGroup(2,a),CyclicGroup(3,b))
                                                       Type: Domain
(4) -> a1:=a::Z2

   (4)  a
                                                       Type: CyclicGroup(2,a)
(5) -> b1:=b::Z3

   (5)  b
                                                       Type: CyclicGroup(3,b)
(6) -> a2:=a1::G

   (6)  a
                   Type: FreeProductMonoid(CyclicGroup(2,a),CyclicGroup(3,b))
(7) -> b2:=b1::G

   (7)  a
                   Type: FreeProductMonoid(CyclicGroup(2,a),CyclicGroup(3,b))

(8) -> b2a:= (b1^2) ::G

         2
   (8)  a
                   Type: FreeProductMonoid(CyclicGroup(2,a),CyclicGroup(3,b))


(9) -> b2a * 1::G

   (9)  1

(10) -> b::Z2

   >> System error:
   wrong symbol


Especially (8) is pretty strange. (9) shows that indeed b made it 
into M1 and is the identity element. (10) shows that coercion in 
CyclicGroup filters out the wrong symbols as it should.
What am I missing? Somehow the interpreter is confused by two almost equal 
signatures (both M1 and M2 are Monoids). Is this forbidden?
Renaming the converters to coerce1 and coerce2 makes it work.

regards
Franz

free.as
Description: Text document

cyclic.as
Description: Text document