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Bug fixed in 10.0.0

I am having a rather unusual problem I do not understand with Mathematica where renaming one of the variables of my function causes the function to stop "working". Here is the example of the code doing what it should:

F[t_, a_, b_, l_] = x[t] /. First@
DSolve[{x'[t] == a*x[t]*(1 - (x[t]/b)) - l*x[t], x[0] == 0.4}, x[t], t];

Changing one variable name causes the code to throw out error messages. The non-working code is

F[t_, r_, b_, l_] = x[t] /. First@ DSolve[{x'[t] == r*x[t]*(1 -
(x[t]/b)) - l*x[t], x[0] == 0.4}, x[t], t];
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  • $\begingroup$ A very peculiar bug. It works if r is replaced by any of a, c, d, or e, but chokes for the other letters. What version and OS are you using, for reference? $\endgroup$
    – J. M.'s eventual burnout ♦
    May 14, 2013 at 12:53
  • $\begingroup$ It seems that only variables that begin with a c d e will work (something like aaa is also OK)… very strange! $\endgroup$
    – xzczd
    May 14, 2013 at 12:53
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    $\begingroup$ @J.M. I'm thinking about something to do with the lexicographical order of E $\endgroup$
    – Dr. belisarius
    May 14, 2013 at 12:53
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    $\begingroup$ @5xum Did you report this to [email protected] as bug? Please do if you haven't yet and link back to this question. $\endgroup$
    – Szabolcs
    May 14, 2013 at 17:13
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    $\begingroup$ @Szabolcs I reported it, will report when anything happens. It's CASE:134234 by the way $\endgroup$
    – 5xum
    May 16, 2013 at 9:15

2 Answers 2

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A little bit more. Still not fully diagnosed, but the problem isn't due to DSolve ... :

s1 = DSolve[{x'[t] == f*x[t] (1 - (x[t]/b)) - l x[t]}, x[t], t];
s2 = DSolve[{x'[t] == e*x[t] (1 - (x[t]/b)) - l x[t]}, x[t], t];

And the problem shows up when matching the initial condition:

Solve[(x[t] /. s2[[1]] /. t -> 0) == 4/10, C[1]]
(*
{{C[1] -> -(Log[1/2 (2 e - 5 b e + 5 b l)]/(b (e - l)))}}
*)

but

Solve[(x[t] /. s1[[1]] /. t -> 0) == 4/10, C[1]]

Solve::nsmet: This system cannot be solved with the methods available to Solve. >>

BTW,

Solve[(x[t] /. s1[[1]] /. t -> 0) == 4/10, C[1], Reals]

can be solved without any problem

Edit

I was able to track down the problem to: 

Solve[E^(a w) (f - e) == E^(b w), {w}]

and 

Solve[E^(a w) (f - g) == E^(b w), {w}]

only the first one gives a result!

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  • 2
    $\begingroup$ Wow. I was sure I was missing something completely obvious, but the chaotic behavior makes me think this is just a very bizzare bug... $\endgroup$
    – 5xum
    May 14, 2013 at 14:00
  • $\begingroup$ @5xum Not obvious at all ... $\endgroup$
    – Dr. belisarius
    May 14, 2013 at 14:03
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    $\begingroup$ @5xum An apparent bug indeed, and one that has persisted at least from version 7 through version 9. I'm surprised this hasn't been found and addressed in that time. $\endgroup$
    – Mr.Wizard
    May 15, 2013 at 4:36
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    $\begingroup$ I guess this is a plain bug, a pattern matching messup that makes MMA think it can solve one expression and not the other. It's funny how it can solve the last example only if at least one of the two variables you add or subtract is sorted before the letter E (or whatever you put as base to that power) $\endgroup$
    – Rojo
    May 16, 2013 at 16:58
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    $\begingroup$ @Silvia Try the Solve[] with MaxExtraConditions -> All $\endgroup$
    – Dr. belisarius
    May 17, 2013 at 1:24
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The problem can be reduced to the DSolve expressions:

DSolve[{x'[t] == a*x[t]*(1 - (x[t]/b)) - l*x[t], x[0] == 0.4}, x[t], t]

DSolve[{x'[t] == h*x[t]*(1 - (x[t]/b)) - l*x[t], x[0] == 0.4}, x[t], t]

One can see that alphabetical order appears important:

With[{a = Symbol@#},
  Shallow @ DSolve[{x'[t] == a*x[t]*(1 - (x[t]/b)) - l*x[t], x[0] == 0.4}, x[t], t]
] & /@ DeleteCases[CharacterRange["a", "z"], "b" | "l" | "t" | "x"]

{{{Rule[<<2>>]}}, {{Rule[<<2>>]}}, {{Rule[<<2>>]}}, {{Rule[<<2>>]}}, {}, {}, {},
  {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}, {}}

I suspect that this may be related to: Why does Simplify ignore an assumption?
Unfortunately I cannot think of a robust way to address the problem.

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  • $\begingroup$ Interesting. Definitely, interesting. $\endgroup$
    – rcollyer
    May 14, 2013 at 12:59
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    $\begingroup$ Finally I have a justifiable reason for using aardvark as a variable name :-) $\endgroup$
    – Simon Woods
    May 14, 2013 at 13:21
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    $\begingroup$ @SimonWoods You might then be interested in AAAAAAAAAAAAAAAAA! :D $\endgroup$
    – rm -rf ♦
    May 14, 2013 at 13:35
  • $\begingroup$ @SimonWoods DSolve[{ax'[at] == ah*ax[at]*(1 - (ax[at]/ab)) - l*ax[at], ax[0] == 0.4}, ax[at], at] seems to work... $\endgroup$
    – geordie
    May 14, 2013 at 22:29
  • $\begingroup$ If you want to "address" the problem in a robust way (as opposed to "diagnosing" the cause of the bug), I think that SetOptions[Solve,MaxExtraConditions -> All] may help $\endgroup$
    – Dr. belisarius
    May 17, 2013 at 5:16

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