Re: arithmetic operations with t_INFINITY

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Max Alekseyev [2022-10-29 13:40]:
> Bill, I do not quite follow. The issue you describe will not appear if
> comparison of oo with oo is forbidden (which should be the case).

It a general "philosophical" issue. Right PARI is highly permissive and
many operations are provided without being formally defined anywhere in
the documentation ; "sensible" defaults being provided on a case by case
basis and hardly ever tested. This is a really bad thing which took years
to fix partially. Right now the only thorough tests we have for arithmetic 
operations generate randomly complex objects and test arithmetic
properties that "should" hold. Then some exceptions are introduced in
the system to cater for exceptions, etc. E.g. a SEGV is always bad,
some errors are acceptable as are most cancellations, then some
identities just don't hold to the expected generality.

Right now, t_INFINITY is not an arihmetic type and all operations result
in an error: clean and simple. 

If we start allowing addition and multiplication, then why not division
(then \ and \/), then most arithmetic operations. And each operation on
every pair of types should be properly defined, then implemented. For
instance, 1 + I*oo can make a lot of sense (say, you're integrating on a
line Re(z) = 1), and why not quadgen(5) + oo since quadgen(5) gets
typecast to (1 + sqrt(5)) / 2, etc. And it's difficult to prevent an
arithmetic type from becoming a polynomial coefficient.

Even if we draw some arbitrary line somewhere as to what is supported
and what is not, it will take some effort to document it properly,
then really enforce it in code, then test it !

Lots of work, no motivation (except "it could be made to work, eventually").

Cheers,

    K.B.

> On Sat, Oct 29, 2022, 5:12 AM Bill Allombert <
> Bill.Allombert@math.u-bordeaux.fr> wrote:
> 
> > Le Fri, Oct 28, 2022 at 04:13:49PM -0400, Max Alekseyev a écrit :
> > > It seems reasonable to expect that "123 + oo" or "-567 * oo" should
> > > evaluate in "+oo" and "-oo", respectively, but at the moment they both
> > > result in the "forbidden" error.
> > > Can support of basic arithmetic operations for t_INFINITY be added?
> > > Of course, undefined operations such as "oo - oo" should still produce an
> > > error.
> >
> > When we added oo, we decided that we would not allow arithmetic operations
> > with
> > infinity because they are not well defined and and not obey the usual
> > equations:
> > a+x == b+x => a==b
> > etc.
> > so this can only lead to strange bugs.
> >
> > Cheers,
> > Bill.
--
Karim Belabas, IMB (UMR 5251), Université de Bordeaux
Vice-président en charge du Numérique
T: (+33) 05 40 00 29 77; http://www.math.u-bordeaux.fr/~kbelabas/
`