Bug introduced in 14.3 or earlier and persisting through 14.3.0 or later
Consider the simple example
$Version
Series[\[Chi],{\[Chi],0,0}]
Before version 14.3, the result is
But in version 14.3, the result is
which is annoying since in most cases I'd like to drop the subleading terms by the specification of expansion order.
Is this a bug due to change of internal codes, or designed behavior? I see there is no documentation on the change of this behavior.
This problem was mentioned elsewhere, before 14.3 was available to me, and I've forgotten where. But this was a workaround I suggested:
Series[\[Chi], {\[Chi], 0, 0}] + O[\[Chi]]^1
(* O[\[Chi]]^1 *)
Or equivalently:
Series[\[Chi], {\[Chi], 0, 0}] + SeriesData[\[Chi], 0, {}, 1, 1, 1]
(* O[\[Chi]]^1 *)
Here's a couple more ideas for workarounds, based on the same idea above:
Override Series[]
Series[] is rather complicated with many cases. The following works on power/Laurent series and could be a good solution for old code until a WRI can fix the issue. It will have the default V14.3 behavior on expansions about essential singularities.
Unprotect@Series;
$fakeTheOldSeriesOrder = False;
Series[f_, {v_, c_, n_}, opts___?OptionQ] /;
TrueQ[$fakeTheOldSeriesOrder] :=
Block[{$fakeTheOldSeriesOrder = False},
With[{res = Series[f, {v, c, 0}, opts]},
If[Head@res === SeriesData && res[[3]] =!= {} && res[[5]] > n + 1,
res + SeriesData[v, c, {}, res[[4]], Max[res[[4]], n+1], 1],
res
]
]];
Protect@Series;
$fakeTheOldSeriesOrder = True;
Series[x, {x, 0, 0}]
Series[x^10, {x, 0, 0}]
Series[Exp[x]/x^5, {x, 0, -9}]
(*
O[x]^1
O[x]^10
1/O[x]^5
*)
Block[{$fakeTheOldSeriesOrder = False},
Series[x, {x, 0, 0}]]
$fakeTheOldSeriesOrder = False;
Series[x^10, {x, 0, 0}]
Series[Exp[x]/x^5, {x, 0, -9}]
(*
x+O[x]^2
x^10+O[x]^11
1/x^5+1/O[x]^4
*)
This will unset the override:
Unprotect@Series;
Series[f_, {v_, c_, n_}, opts___?OptionQ] /;
TrueQ[$fakeTheOldSeriesOrder] =.;
Protect@Series;
Series truncation utility
truncateSeries // ClearAll;
truncateSeries[sd_SeriesData, n_] :=
sd + SeriesData[sd[[1]], sd[[2]], {}, n + 1, n + 1, 1];
$fakeTheOldSeriesOrder (* check setting *)
Series[x, {x, 0, 0}]
truncateSeries[%, 0]
(*
False
x+O[x]^2
O[x]^1
*)
Efficiency
Truncating a series (that is, truncating SeriesData[]) in the way above is a very fast operation. The overhead is very small compared to the original generation of the series.
If we want to be consistent in treating coefficients of series then it is a bug. Also it must have affected/broke many codes that used this feature.
There is no reason why the first non-zero coefficient should be treated differently then the rest.
In old version - if we go backwards in the column output we see that at each step there is one coefficient less until we have zero coefficients.
But in version 14.3 the last (in reverse sense) coefficient is never removed.
Version 13.0.1
Coefficients one-by one:
Table[SeriesCoefficient[1/Log[x + 1]^4, {x, 0, k}], {k, -7, 2}]
{0, 0, 0, 1, 2, 7/6, 1/6, -(1/720), 0, 1/3024}
Series for different n:
Table[Series[1/Log[x + 1]^4, {x, 0, n}], {n, -7, 2}] // Column
Version 14.3.0 (on cloud)
Series[t^34/(2 (4*Pi^2 + (-1 + t)^2)^13*(4*Pi^3 + 9*Pi*(-1 + t)^2)^4), {t, Infinity, 1}] // AbsoluteTiming // InputFormIf I figure out a way to refix the 0-order series without reintroducing a massive slowdown I'll do so. In any case the excess term issue is an open bug report, so it won't fall off the radar. $\endgroup$