Hi Simon,

On 2017-10-09, Simon Brandhorst <sbrandho...@web.de> wrote:
> "While *parents* are unique, equal *elements* of a parent in Sage are not 
> necessarily identical. "
> in
> http://doc.sagemath.org/html/en/tutorial/tour_coercion.html

Indeed that's too strict, IMHO. In
http://doc.sagemath.org/html/en/thematic_tutorials/coercion_and_categories.html,
I wrote "You are encouraged to make your parent “unique”."
and
  "Making parents unique can be quite important for an efficient implementation,
   because the repeated creation of “the same” parent would take a lot of time."

Moreover, when using non-unique parents, one has to take care to avoid
problems with coercion.

> So uniqueness is not strict. But when is a parent supposed to be unique and 
> when not?

There were cases where unique parents gave rise to memory leaks: If parents
are unique, they need to be stored somewhere. And even when using a weak
value dictionary for that (which we of course do), it can be tricky to
avoid reference chains that prevent stuff from being garbage collected.

As a rule of thumb: If the uniqueness condition is easy, then it is a good
idea to have unique parents. But certainly you should avoid that a very
costly isomorphism test of some sort is performed whenever you create
a parent.

Cheers,
Simon

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