I cannot check right now as my Pentium machine with Win XP is at hardware maintainance. In a newer machine, I have tried running on Wine 1.4/ Linux Mint 13 32-bit, setting Windows 95 compatibility mode, but that alone does not work. I have not found yet an equivalent to the rest of the settings (256 colors, etc).

In old times, this site provided more valuable awards...

Yes, there is a bug in `limit/series`. It finds that both lateral limits are 0 because it decides that the expression is O(x) :

> trace( `limit/series`):
> L:=(x*BesselI(k-1, x)+x*BesselI(k+1, x))*BesselI(-k, x):
> limit(L,x=0);
{--> enter limit/series, args = (`limit/X`*BesselI(k-1,`limit/X`)+`limit/X`*
BesselI(k+1,`limit/X`))*BesselI(-k,`limit/X`)
                                t := O(limit/X)
<-- exit limit/series (now in limit/topright) = 0}
{--> enter limit/series, args = (-`limit/X`*BesselI(k-1,-`limit/X`)-`limit/X`*
BesselI(k+1,-`limit/X`))*BesselI(-k,-`limit/X`)
                                t := O(limit/X)
<-- exit limit/series (now in limit/topright) = 0}
                                       0

Certainly, the MultiSeries package has a better handling of asymptotic scales.

About opinions on forum bug reports, see this thread and links therein. In any case, limit is a very basic command, not only in the sense of its direct usage, but also as it is behind many other usual commands. For instance, it is used in the computation of many definite integrals via method FTOC.

I think that this is the relevant paper.

I think that this is the relevant paper.

@Markiyan Hirnyk 

The difference of the plots above for (x+y)^2=0 and (x-y)^2 arises in an externally called library. It can be seen by tracing the procedure `plots/hw_implicitplot`. In the first case a 1005x2 Array is generated:

> trace(`plots/hw_implicitplot`):
> implicitplot((x+y)^2 = 0, x = -20 .. 20, y = -20 .. 20, numpoints = 10^6, thickness = 5);
{--> enter plots/hw_implicitplot, args = fproc, Array(1..1001, [...], datatype
= float[8], order = C_order), Array(1..1001, [...], datatype = float[8], order
= C_order), 0, 0, 0, 1, 0, 0, 0, 0, 0, seg, cont0, cont1, gridn
                              lib := "libode2.so"

plots/hw_implicitplot := proc()
option
call_external, define_external(hw_implicitplot, MAPLE, LIB = "libode2.so");
    call_external(0, 16151904, true, false, args)
end proc

                          [ 1..1005 x 1..2 2-D Array ]
                          [ Data Type: float[8]      ]
                          [ Storage: rectangular     ]
                          [ Order: C_order           ]
<-- exit plots/hw_implicitplot (now in plots/implicitplot) = Array(1..1005, 1..
... 

while in the second case it is 3x2, hence the "empty" plot:

> implicitplot((x-y)^2 = 0, x = -20 .. 20, y = -20 .. 20, numpoints = 10^6, thickness = 5);
{--> enter plots/hw_implicitplot, args = fproc, Array(1..1001, [...], datatype
= float[8], order = C_order), Array(1..1001, [...], datatype = float[8], order
= C_order), 0, 0, 0, 1, 0, 0, 0, 0, 0, seg, cont0, cont1, gridn
                              lib := "libode2.so"

plots/hw_implicitplot := proc()
option
call_external, define_external(hw_implicitplot, MAPLE, LIB = "libode2.so");
    call_external(0, 5916000, true, false, args)
end proc

                                   [0.    0.]
                                   [        ]
                                   [0.    0.]
                                   [        ]
                                   [0.    0.]
<-- exit plots/hw_implicitplot (now in plots/implicitplot) = Array(1..3, 1..2,
[[...],[...],[...]], datatype = float[8], order = C_order)} 

This means that finding an explanation to this difference would require looking at the code/debugging this external library libode2. Presumably it is closed sourced.

A possible variation of this "residual effect". As a test, I have subscribed to this thread and immediatelly (within a second) unsubscribed. Yet, I have received an email notification of Will's comment that was posterior to my unsubscription.

A "ray" is shown in the CLI:

    |\^/|     Maple 16 (IBM INTEL LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2012
 \  MAPLE  /  All rights reserved. Maple is a trademark of
   Waterloo Maple Inc.
      |       Type ? for help.
> with(plots):
> implicitplot(sqrt(x^2+y^2)-sqrt((x-4)^2+(y-3)^2) = 5, x = -20 .. 20, y = -20 .. 20,numpoints = 10^6, thickness = 5, scaling = constrained);
                       14 +                          H                         
                          +                                                    
                          +                       H                            
                          +                     H                              
                       12 +                                                    
                          +                   H                                
                          +                  H                                 
                          +                 H                                  
                       10 +               HH                                   
                          +                                                    
                          +            HH                                      
                        8 +           HH                                       
                          +          H                                         
                          +        H                                           
                          +       H                                            
                        6 +                                                    
                          +                                                    
                          +   H                                                
                          +                                                    
                        4 +                                                    
                          *+++++++++++++++++++++++++++                         
                             6   8 10  12  14  16 18                           

No, it was primes1 that used Drupal! That changed in June 2010. Presumably, after Bryon's site change plan, primes2 uses home grown board code written in Visual Studio. He said: "Among other things, one of the primary benefits of this change is that we will have increased capacity within our web development team to troubleshoot and update the site."...

The issue is whether Derive (or other CAS) is successful in finding that no discontinuity occurs within the integration interval, or it does not check for discontinuities at all.

The issue is whether Derive (or other CAS) is successful in finding that no discontinuity occurs within the integration interval, or it does not check for discontinuities at all.

@Axel Vogt 

Indeed, branch cuts is the bigger issue in the FTOC discontinuity problem, as it has been discussed many times here. In particular, some six years ago, Jacques said "that there is very little that has been done on the theoretical side for this problem."  And I have the impression that this issue is still stagnated. 

In Maple, the more comprenhensive collection of information on branch cuts is probably contained in the MathematicalFunctions package, in a table-based form. E.g.:

eval(MathematicalFunctions:-FunctionInfo["ln"]["branch_cuts"]);
                                   a -> a < 0

And via the FunctionAdvisor front end, some elementary functionality for function composition is available, so that this case could be handled:

bc:=FunctionAdvisor(branch_cuts,ln(2*x^5+1));
                                     5          5
                        bc := [ln(2 x  + 1), 2 x  < -1]

 solve(op(2,bc),{x},explicit);
                                          4/5
                                         2
                                  {x < - ----}
                                          2
 solve(op(2,bc) and 0<=x and x<=1,[x]) ;
                                       []

It is likely that the original intention of the MathematicalFunctions project was becoming a central server for information on mathematical functions to the other routines of the system, but I think that little has been done in this direction. On the other hand, I have heard about some research on an algorithmic approach for the computation of branch cuts, but I do not know where is the state of the art.

@Axel Vogt 

Indeed, branch cuts is the bigger issue in the FTOC discontinuity problem, as it has been discussed many times here. In particular, some six years ago, Jacques said "that there is very little that has been done on the theoretical side for this problem."  And I have the impression that this issue is still stagnated. 

In Maple, the more comprenhensive collection of information on branch cuts is probably contained in the MathematicalFunctions package, in a table-based form. E.g.:

eval(MathematicalFunctions:-FunctionInfo["ln"]["branch_cuts"]);
                                   a -> a < 0

And via the FunctionAdvisor front end, some elementary functionality for function composition is available, so that this case could be handled:

bc:=FunctionAdvisor(branch_cuts,ln(2*x^5+1));
                                     5          5
                        bc := [ln(2 x  + 1), 2 x  < -1]

 solve(op(2,bc),{x},explicit);
                                          4/5
                                         2
                                  {x < - ----}
                                          2
 solve(op(2,bc) and 0<=x and x<=1,[x]) ;
                                       []

It is likely that the original intention of the MathematicalFunctions project was becoming a central server for information on mathematical functions to the other routines of the system, but I think that little has been done in this direction. On the other hand, I have heard about some research on an algorithmic approach for the computation of branch cuts, but I do not know where is the state of the art.

Indeed, I am writing this comment after logging out... I have observed this interesting feature long time ago (may be a year or so).

@Kitonum 

Yes, though this is an independent bug. Really, weaknesses and bugs of is would be the subject for another thread. For a simpler example:

is(х>0) assuming x>0;
                                     false

For additional information see this thread.