Implement reverse() for LaurentSeries

[BrentBaccala]

Power series have a reverse() method for series of valuation 1.

This enhancement wraps the power series method and makes it available for LaurentSeries of valuation 1.

sage: R.<x> = Frac(QQ[['x']])
sage: f = 2*x + 3*x^2 - x^4 + O(x^5)
sage: g = f.reverse()
sage: g
1/2*x - 3/8*x^2 + 9/16*x^3 - 131/128*x^4 + O(x^5)
sage: f(g)
x + O(x^5)
sage: g(f)
x + O(x^5)

Component: algebra

Author: Brent Baccala

Branch/Commit: ebd8f45

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/25219

[BrentBaccala]

Commit: d7ed828

[BrentBaccala]

Author: Brent Baccala

[BrentBaccala]

Branch: u/gh-BrentBaccala/25219

[BrentBaccala]

New commits:

d7ed828

Trac #25219: add reverse() method to LaurentSeries

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

90ab7ed

Merge tag '8.4' into u/gh-BrentBaccala/25219

[sagetrac-git]

Changed commit from d7ed828 to 90ab7ed

[videlec]

comment:5

Rather than type(self)(self._parent, rev) couldn't you use the parent call method? (something like self._parent(rev)?

[videlec]

comment:6

Also, I am not able to reproduce the bug that you mention in the ticket description on 8.7.beta6...

[videlec]

Reviewer: Vincent Delecroix

[embray]

comment:7

Ticket retargeted after milestone closed (if you don't believe this ticket is appropriate for the Sage 8.8 release please retarget manually)

[sagetrac-git]

Changed commit from 90ab7ed to c2e486c

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

c450c74	Merge tag '8.7' into u/gh-BrentBaccala/25219
c2e486c	Trac #25219: simplify method call syntax when creating reversed Laurent series

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

e86ed66

Trac #25219: add test case

[sagetrac-git]

Changed commit from c2e486c to e86ed66

[BrentBaccala]

comment:10

Code updated as suggested.

I can't reproduce the bug anymore, either. I added it as a test case.

[videlec]

comment:11

Does power series really behave this way

+        if rev.parent() == u.parent():
+            return self._parent(rev)
+        else:
+            P = self._parent.change_ring(rev.parent().base_ring())
+            return P(rev)

It is very counterintuitive to have methods whose output type depends on the nature of the answer. If you do 4/2 in Sage you do not obtain an integer but a rational number. I don't understand why .reverse() should be any different.

I would suggest to have reverse and reverse_unit.

I am just asking for your opinion as this is beyond the scope of the ticket.

[BrentBaccala]

comment:12

Replying to @videlec:

Does power series really behave this way

+        if rev.parent() == u.parent():
+            return self._parent(rev)
+        else:
+            P = self._parent.change_ring(rev.parent().base_ring())
+            return P(rev)

It is very counterintuitive to have methods whose output type depends on the nature of the answer. If you do 4/2 in Sage you do not obtain an integer but a rational number. I don't understand why .reverse() should be any different.

I would suggest to have reverse and reverse_unit.

I am just asking for your opinion as this is beyond the scope of the ticket.

I chose to mimic the behavior of the existing reverse method in PowerSeries_poly. Its docstring states:

If the leading coefficient is not a unit, we pass to its fraction field if possible

The Laurent series code calls the power series code, and follows its lead. So the answer to your question is yes, power series really do behave this way:

sage: R.<x> = ZZ[[]]
sage: (2*x+x^2).parent()
Power Series Ring in x over Integer Ring
sage: (2*x+x^2).reverse()
1/2*x - 1/8*x^2 + 1/16*x^3 - 5/128*x^4 + 7/256*x^5 - 21/1024*x^6 + 33/2048*x^7 - 429/32768*x^8 + 715/65536*x^9 - 2431/262144*x^10 + 4199/524288*x^11 - 29393/4194304*x^12 + 52003/8388608*x^13 - 185725/33554432*x^14 + 334305/67108864*x^15 - 9694845/2147483648*x^16 + 17678835/4294967296*x^17 - 64822395/17179869184*x^18 + 119409675/34359738368*x^19 + O(x^20)
sage: (2*x+x^2).reverse().parent()
Power Series Ring in x over Rational Field

I would tend to think that it should work this way, that 4/2 should return an integer and only 3/2 should return a rational, but I haven't thought about it enough to have a really informed opinion.

[videlec]

comment:13

The following test is working for me

sage: B.<b> = PolynomialRing(ZZ)
sage: A.<t> = LaurentSeriesRing(B)
sage: f = 2*b*t + b*t^2 + 3*b^2*t^3 + O(t^4)
sage: g = f.reverse()
sage: g(f)  # known bug - f fails to coerce properly, but next test works
t + O(t^4)

Why is it discarded?

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

ebd8f45

Trac #25219: remove TEST that was already an EXAMPLE

[sagetrac-git]

Changed commit from e86ed66 to ebd8f45

[BrentBaccala]

comment:15

Replying to @videlec:

The following test is working for me

sage: B.<b> = PolynomialRing(ZZ)
sage: A.<t> = LaurentSeriesRing(B)
sage: f = 2*b*t + b*t^2 + 3*b^2*t^3 + O(t^4)
sage: g = f.reverse()
sage: g(f)  # known bug - f fails to coerce properly, but next test works
t + O(t^4)

Why is it discarded?

It used to fail. I don't know what changed to fix it, but it was somewhere else in Sage. I'll bisect the code if you really want to track it down.

Once it was working, I added it as a test case, but forgot that it was already there as a "known bug" example. Fixed.

[vbraun]

Changed branch from u/gh-BrentBaccala/25219 to ebd8f45