Bug introduced in 9.0 or earlier and fixed in 11.0.0
In:
D[Sum[Sin[x],x],x]
D[Sum[f[x],x],x]
Out:
1/2 Cos[1/2 (-1 - Pi + 2 x)] Csc[1/2]
0
Function f is undefined, but Mathematica 9 counts it as constant?
Mathematica 8 returns
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9
1 Answer
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5
Probably this is just a bug. Especially since it "works" in 8. You could fix it by doing
SetOptions[D, NonConstants -> {Sum}]
first, or by putting this in your init.m file.
answered Dec 19, 2012 at 20:47
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1$\begingroup$ Sorry, but I wouldn't do that. Even in version 8 you would expect
D[Sum,x] == 0to beTrue, wouldn't you? $\endgroup$– JensCommented Dec 19, 2012 at 22:02 -
1$\begingroup$ Well, we are supposed to use lower case letters for variables. Anyway, of course this is not a real fix, just a hack as a reminder that something is fishy in 9.0.0 (waiting for 9.0.1 anyway any day, aren't you, too?) $\endgroup$ Commented Dec 19, 2012 at 22:38
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$\begingroup$ Actually, I think I'm just waiting to get version 5.2 back one day... $\endgroup$– JensCommented Dec 19, 2012 at 22:42
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$\begingroup$ Sum[f[x],x] gave an error there ... $\endgroup$ Commented Dec 19, 2012 at 22:47
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$\begingroup$ Well, are things better now? Anyway, I'm only kidding about the good old times... they weren't that good, either, I guess. $\endgroup$– JensCommented Dec 19, 2012 at 22:52
Sin[x]it simplifies it first to the expression dependent of x. So it's not a bug. $\endgroup$Sum[f[x],x]is the same asSum[f[y],{y,0,x-1}]. But without specifying the limits it's not a function, because x is an index variable not an upper limit. $\endgroup$D[Sum[Sin[x],x],x]has a nonzero value, thenD[Sum[f[x],x],x]cannot be zero in general, since we might havef==Sin. $\endgroup$