Hi Nils,

On 2015-02-21, Nils Bruin <nbr...@sfu.ca> wrote:
> I'm not so sure. How does x+3 make unambiguous sense?

If there is a coercion then (by definition of coercion in contrast to
conversion) it is unique.

> We can map ZZ onto 
> any cyclic subgroup.

Yes, but at most one map is a coercion.

> On the other hand,  x*0 should work: A commutative additive group is a left 
> and right ZZ-module, so x*0 and 0*x should match as scalar multiplication. 

Actually, in the case at hand it will probably work, because there is a
module action of ZZ on the parent. So, I should perhaps withdraw my
example, as n*x should work for any element n of ZZ and any element x of
a commutative additive group P, as P is a ZZ-module.

But what I don't need to withdraw is the general statement that coercion should
work on the level of parents, not on the level of elements. I.e., I
withdraw my example, because there is an action (involving the *whole*
parents). However, element-wise rules such as "if the first factor lives in an
additive group and the right factor is the neutral element for the additive 
group
of its parent, then the product shall be the zero element of the left factor"
should be banned.

Best regards,
Simon


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