Asymptotic Ring: cannot construct 2^n when coefficient ring is SR

[cheuberg]

The following is unexpected:

sage: A.<n> = AsymptoticRing('QQ^n * n^QQ', SR)
sage: 2^n
Traceback (most recent call last):
...
ArithmeticError: Cannot construct 2^n in Growth Group QQ^n * n^QQ
> *previous* TypeError: unsupported operand parent(s) for '*':
'Growth Group QQ^n * n^QQ' and 'Growth Group SR^n'

The only work-around I found until now is

sage: A(AsymptoticRing(growth_group='QQ^n', coefficient_ring=ZZ)('2^n'))
2^n

Once this is fixed, the work-around should be removed from #19532 (asymptotic_expansions.SingularityAnalysis).

Depends on #19961

CC: @dkrenn @behackl

Component: asymptotic expansions

Author: Daniel Krenn

Branch: 1259201

Reviewer: Clemens Heuberger

Issue created by migration from https://trac.sagemath.org/ticket/19946

[dkrenn]

Replying to @cheuberg:

The only work-around I found until now is

sage: A(AsymptoticRing(growth_group='QQ^n', coefficient_ring=ZZ)('2^n'))
2^n

The workaround

sage: n.rpow(2)
2^n

works. However, for some reason (I still have to track this down) the parent changes to

sage: n.rpow(1/2).parent()
Asymptotic Ring <QQ^n * n^SR> over Symbolic Ring

[dkrenn]

Branch: u/dkrenn/t/19946

[dkrenn]

Author: Daniel Krenn

[dkrenn]

Commit: 1b62954

[dkrenn]

comment:4

I've fixed the original problem. However, there is the following:

            sage: T = TermMonoid('exact', GrowthGroup('QQ^n * n^QQ'), SR)
            sage: n = T('n')
            sage: n.rpow(2)
            2^n
            sage: _.parent()
            Exact Term Monoid QQ^n * n^SR with coefficients in Symbolic Ring

        Above, we get ``QQ^n * n^SR`` since
        ::

            sage: (n^SR(1)).parent()
            Exact Term Monoid QQ^n * n^SR with coefficients in Symbolic Ring

        and that is because of

            sage: (QQ(2)^SR(1)).parent(), (QQ(1)*SR(1)).parent()
            (Rational Field, Symbolic Ring)

For me this is fine; although it is not nice. What do you think?

---

New commits:

1fc00c7	Trac #19946: fix `_pushout_` for cartesian product of growth groups
1b62954	Trac #19946: add doctests to document behavior

[cheuberg]

Changed branch from u/dkrenn/t/19946 to u/cheuberg/t/19946

[cheuberg]

comment:6

Reviewed your changes, main bug is fixed; two reviewer commits added; but I do not understand the explanation why we fall into QQ^n * n^SR. For future investigations I would prefer to have a good explanation once we intend to fix this pushout explosion. But that would be another ticket.

---

New commits:

24c153c	Trac #19946: reviewer commit: ReSt error
7918417	Trac #19946: additional doctest

[cheuberg]

Changed commit from 1b62954 to 7918417

[dkrenn]

Changed branch from u/cheuberg/t/19946 to u/dkrenn/t/19946

[dkrenn]

comment:8

Replying to @cheuberg:

two reviewer commits added;

Cross-reviewed.

but I do not understand the explanation why we fall into QQ^n * n^SR. For future investigations I would prefer to have a good explanation once we intend to fix this pushout explosion.

Rewritten.

But that would be another ticket.

Ok.

I've merged #19961 and made a link from there to this new explaination.

---

New commits:

1471336	Trac #19946: rewrite and improve explaination of 1b62954
9f9a23f	Trac #19961: document rpow
101e4de	Merge branch 'u/dkrenn/t/19961' of trac.sagemath.org:sage into t/19946
7179c78	Trac #19946: link from general doc to detailed explaination

[dkrenn]

Changed commit from 7918417 to 7179c78

[dkrenn]

Dependencies: #19961

[dkrenn]

comment:9

Replying to @cheuberg:

For future investigations I would prefer to have a good explanation once we intend to fix this pushout explosion. But that would be another ticket.

Follow-up is #19965.

[cheuberg]

comment:10

LGTM, thank you.

[cheuberg]

Reviewer: Clemens Heuberger

[cheuberg]

Changed branch from u/dkrenn/t/19946 to u/cheuberg/t/19946

[cheuberg]

Changed commit from 7179c78 to 1259201

[cheuberg]

comment:12

had forgotten to push the fix for one typo.

---

New commits:

1259201

Trac #19946: fix typo

[vbraun]

Changed branch from u/cheuberg/t/19946 to 1259201

[jdemeyer]

comment:14

This ticket has added a few doctests of the form

            sage: A.<n> = AsymptoticRing('QQ^n * n^QQ', SR)
            sage: n.rpow(2)
            2^n
            sage: _.parent()
            Asymptotic Ring <QQ^n * n^SR> over Symbolic Ring

With #19945, the last result will change to

            Asymptotic Ring <SR^n * n^SR> over Symbolic Ring

I think that this change makes sense, since a coercion of QQ and SR should end up in SR. If you object, please comment at #19945.

[jdemeyer]

Changed commit from 1259201 to none