Dear Hsin-Po Wang,

On 2018-01-30, Hsin-Po Wang <a.simple.peo...@gmail.com> wrote:
> But it is still interesting to see if this is an unintentional bug in, say, 
> the coercion model and can be fixed.

We have
  sage: S4.has_coerce_map_from(S4.subgroups()[19])
  True

Hence, the coercion model is supposed to *automatically* convert the
element S4.subgroups()[19][1] into an element of S4, and then do the
multiplication.

Oddly enough,
  sage: S4[1]*S4.subgroups()[19][1]
  (1,4,2,3)
works (i.e., the right factor is automatically converted into the parent
of the left factor), but
  sage: S4.subgroups()[19][1]*S4[1]
doesn't work (as you reported).

The coercion model chooses coercion to the left factor's parent, if
there are coercions available in *both* directions. However, if there
only is a coercion from the left factor's parent to the right factor's
parent but not vice versa, that coercion is supposed to be used.

So, shortly, it is a clear bug. I created
https://trac.sagemath.org/ticket/24612 for it.

Thank you for reporting it!
Best regards,
Simon

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