> Because it's really inconvenient to always have to manually cast to
> the same parent. Imagine I have a loop.
>
> while a < 1:
> [do stuff to a to make it smaller]
>
> Would this fail if a was not an integer. What if it started out as an
> integer but then I divided it by something and it became a rational.
> It's much cleaner to write the above than
>
> while a < a.parent()(1):
> [...]
>
> There is are natural morphisms (in Sage called coercion morphism) Z -
> > Q, Z -> Z[x], and Z -> Z/nZ that are used to equate objects across
> parents.
As you can guess, I am a lot for the new coercion system. And having
the very basic embeddings done automatically is definitely useful (say
int into rationals). But there is a tight balance to maintain, and my
feeling is that Sage is really going too far currently. And I am quite
worried about this in the long run. This leads to slower membership
and equality testing, subtle errors, more complicated code to handle
all sorts of possible cases, ...
I typically write things like:
class MyParent
def bla(self, x)
assert x in self
...
I really mean that x should be an element of self; not something that
could be converted into it.
Just yesterday, I lost 1 hour around this because membership testing
for a Weyl group ultimately led to listing all the elements of the
group. Which is problematic for an infinite group. And it was not easy
to straighten this up cleanly.
In short: for < = in, if it was just me, I would only use the most
absolutely trivial coercions. And in particular avoid there all the
coercions that involve projections and not embedding (like Z -> Z/nZ)
Just my own feeling ...
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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