Confused about power series ring identity

[Nils Bruin]

From "PowerSeriesRing" docstring:

   There is a unique power series ring over each base ring with given
   variable name. Two power series over the same base ring with
   different variable names are not equal or isomorphic.

However (and I think it should be like that):

sage: P1.<x>=PowerSeriesRing(QQ,default_prec=30)
sage: P2.<x>=PowerSeriesRing(QQ,default_prec=20)
sage: P1 == P2
False

So .. I think a mistake in the documentation?

This bit is a little more questionable:

sage: (P1.0+P2.0).parent() == P1
True
sage: (P1.0+P2.0).parent() == P2
False
sage: (P2.0+P1.0).parent() == P2
True

I'm not quite sure if P1 or P2 should be preferred, but I think preferring just the left parent might not be desirable.

[David Roe]

On Fri, Feb 17, 2023 at 6:04 AM Nils Bruin <nbr...@sfu.ca> wrote:

From "PowerSeriesRing" docstring:

   There is a unique power series ring over each base ring with given
   variable name. Two power series over the same base ring with
   different variable names are not equal or isomorphic.

However (and I think it should be like that):

sage: P1.<x>=PowerSeriesRing(QQ,default_prec=30)
sage: P2.<x>=PowerSeriesRing(QQ,default_prec=20)
sage: P1 == P2
False

So .. I think a mistake in the documentation?

I agree, this is a mistake in the documentation.

 

This bit is a little more questionable:

sage: (P1.0+P2.0).parent() == P1
True
sage: (P1.0+P2.0).parent() == P2
False
sage: (P2.0+P1.0).parent() == P2
True

I'm not quite sure if P1 or P2 should be preferred, but I think preferring just the left parent might not be desirable.

Since elements of power series rings track their own precision, I would suggest choosing the parent with higher precision.  This is what is done for p-adic capped relative and capped absolute rings:

sage: R1 = Qp(5, 30)

sage: R2 = Qp(5, 20)

sage: (R1(1) + R2(1)).parent() is R1

True

sage: (R2(1) + R1(1)).parent() is R1

True

David

 

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