bug in a simple series expansion

[fchapoton]

Steps To Reproduce

sage: var('t')
sage: v = -125/24*e^(-5*t)/t - 8/3*e^(-4*t)/t^2 - 3/2*e^(-3*t)/t^3 - e^(-2*t)/t^4 - e^(-t)/t^5 + 1/t^5; v
-125/24*e^(-5*t)/t - 8/3*e^(-4*t)/t^2 - 3/2*e^(-3*t)/t^3 - e^(-2*t)/t^4 - e^(-t)/t^5 + 1/t^5
sage: v.series(t,2)
54/5 + (-3731/90)*t + Order(t^2)
sage: v.series(t,4)
54/5 + (-29849/720)*t + 139459/1680*t^2 + (-2305729/20160)*t^3 + Order(t^4)
sage: v.series(t,6)
54/5 + (-29849/720)*t + 139459/1680*t^2 + (-1537153/13440)*t^3 + 43947619/362880*t^4 + (-10845131/103680)*t^5 + Order(t^6)

Expected Behavior

answer should be correct up to the required order.

Actual Behavior

last term is always wrong

Additional Information

No response

Environment

• OS: Ubuntu 24.04
• Sage Version: 10.5.beta8

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[mantepse]

u=t

[S17A05]

#37368 had similar issues, though I'm not sure whether these are related

[fchapoton]

if needed, I can provide many similar examples. The smallest is

-e^(-5*t)/t - 4*e^(-t)/t^5 + 6*e^(-2*t)/t^5 - 4*e^(-3*t)/t^5 + e^(-4*t)/t^5 + 1/t^5

Failure seems to happen only but systematically in complicated enough cases.

[fchapoton]

a simplified failing case

sage: g=-e^(-2*t) - e^(-t)/t^3
sage: bool(g.series(t,2)==g.series(t,4).series(t,2))
True
sage: g=-e^(-2*t) - e^(-t)/t^4
sage: bool(g.series(t,2)==g.series(t,4).series(t,2))
False

Note that this works in GiNaC 1.8.7 using ginsh

> series(-exp(-2*t) - exp(-t)/t^4,t==0,2);
(-1)*t^(-4)+1*t^(-3)+(-1/2)*t^(-2)+1/6*t^(-1)+(-25/24)+241/120*t+Order(t^2)
> series(-exp(-2*t) - exp(-t)/t^4,t==0,4);
(-1)*t^(-4)+1*t^(-3)+(-1/2)*t^(-2)+1/6*t^(-1)+(-25/24)+241/120*t+(-1441/720)*t^2+6721/5040*t^3+Order(t^4)

[mantepse]

Worse:

sage: g = e^(t) - e^(t)/t^6
sage: g.series(t, 1)
(-1)*t^(-6) + (-1)*t^(-5) + (-1/2)*t^(-4) + (-1/6)*t^(-3) + 1 + Order(t)
sage: g.series(t, 2)
(-1)*t^(-6) + (-1)*t^(-5) + (-1/2)*t^(-4) + (-1/6)*t^(-3) + (-1/24)*t^(-2) + 1 + 1*t + Order(t^2)

[maxale]

Is it related by any chance to the bug in taylor() reported at https://ask.sagemath.org/question/79842 ?

[fchapoton]

I do not think so. The method series is handled by pynac/ginac, but taylor is done by maxima.

[fchapoton]

Worse:

sage: g = e^(t) - e^(t)/t^6
sage: g.series(t, 1)
(-1)*t^(-6) + (-1)*t^(-5) + (-1/2)*t^(-4) + (-1/6)*t^(-3) + 1 + Order(t)
sage: g.series(t, 2)
(-1)*t^(-6) + (-1)*t^(-5) + (-1/2)*t^(-4) + (-1/6)*t^(-3) + (-1/24)*t^(-2) + 1 + 1*t + Order(t^2)

This also works fine in GiNaC V1.8.7

[fchapoton]

many fixes have been made to the series code in ginac, see

https://www.ginac.de/ginac.git/?p=ginac.git&a=search&h=HEAD&st=commit&s=series

Our ginac code base is an old and very obsolete version. The copyright statements are saying 2008.