Actually, I think that Wolfram Mathematica is cool.

For example,

KnotData[{6,2}]

Isn't that cool?

Alec

Wolfram Mathematica has several mathematicians among its developers, so it does such things right,

In[1]:= Sin[x]/x  /. x -> 0

During evaluation of In[1]:= Power::infy: Infinite expression 1/0 \
encountered. >>

During evaluation of In[1]:= \[Infinity]::indet: Indeterminate \
expression 0 ComplexInfinity encountered. >>

Out[1]= Indeterminate

Without the mentioned line in the eval help page, Maple would be close to be correct. Even if it produces only an error, without giving the correct answer "undefined", it is much better than saying that the answer is 1.

Alec

The correct answer for the value of sin(x)/x at x=0 is "undefined".

Singularity is a very vague term. Very often it means that the derivative of a function is discontinuous at that point (like for abs(x) at x=0). What singularity means in Maple, is hard to tell. I'll check the "Dictionary" after posting that.

The problem with that is that it is a typical situation in Calculus course during studying limits. Many students get confused enough with that even without Maple.

Alec

I don't download worksheets from here. First - for security reasons. Second - because I use Maple remotely and doing that would cause some trouble.

Alec

I don't download worksheets from here. First - for security reasons. Second - because I use Maple remotely and doing that would cause some trouble.

Alec

I almost wrote that at the end - that Jacques, probably, meant dismantle when he wrote disassemble.

Alec

Also, dismantle can be used,

dismantle(op(RealDomain:-limit));
PROC(10)
   EXPSEQ(1)
   EXPSEQ(1)
   EXPSEQ(1)
   EXPSEQ(1)
   STATSEQ(4)
      ASSIGN(3)
         NAME(8): _EnvSolveOverReals
         NAME(5): true #[protected]
      FUNCTION(3)
         NAME(8): NumericEventHandler #[protected]
         EXPSEQ(2)
            EQUATION(3)
               UNEVAL(2)
                  NAME(7): real_to_complex #[protected]
               LEXICAL(2): [1]
      FUNCTION(3)
         LEXICAL(2): [3]
         EXPSEQ(2)
            FUNCTION(3)
               NAME(6): `assuming` #[_syslib]
               EXPSEQ(3)
                  LIST(2)
                     EXPSEQ(2)
                        FUNCTION(3)
                           LEXICAL(2): [-2]
                           EXPSEQ(2)
                              PARAM(2): [-1]
                  LIST(2)
                     EXPSEQ(2)
                        UNEVAL(2)
                           NAME(5): real #[protected, _syslib]
   EXPSEQ(1)
   EXPSEQ(1)
   EXPSEQ(7)
      NAME(6): r2c_handler
      NAME(6): RealDomain:-r2c_handler #[modulename = RealDomain]
      NAME(4): p
      NAME(5): limit #[protected, _syslib]
      NAME(5): clean
      NAME(5): RealDomain:-clean #[modulename = RealDomain]
   BINARY(2)
      0

Alec

It evaluates automatically if a procedure is executed. So running showstat after that should work OK. Originally, showstat was a debugging command, and it was usually run in the debugger after executing (or after starting to execute) a procedure, so such a problem, probably, didn't arise.

Alec

Another way to get a more correct reading from showstat is to evaluate the lexical table of a procedure before using showstat. In this example,

eval(op(7,op(RealDomain:-limit))):
showstat(RealDomain:-limit);

RealDomain:-limit := proc()
   1   _EnvSolveOverReals := true;
   2   NumericEventHandler(('real_to_complex') = RealDomain:-r2c_handler);
   3   RealDomain:-clean(`assuming`([limit(args)],['real']))
end proc

Alec

1) I think, it is called removable, because the function can be made a continuous function after defining its value at that point being equal to the limit. For the other types of discontinuities that can not be done.

2) The jump discontinuities have the left and the right limits, but they are different. Infinite discontinuities have either left, or right limit infinite. "Oscillating" discontinuity doesn't have eiher left, or right limit. As one can see, all of them have some specific features. In many cases (but not all) the function is not defined at the discontinuity point. So it is usually good to check first. If a function is not defined - then it is a discontinuity and you don't even have to evaluate the limit to tell that. In particular, in your original example,

f:=x->(x^2-2)/(x-sqrt(2)):
f(sqrt(2));
Error, (in f) numeric exception: division by zero

One should be careful with that though, because Maple is not very good with that. See that thread, for example.

3) I think, it misses the singularity in most examples. It would be interesting actually to find an example in which the plot command would hit the discontinuity exactly, and see what happens. I don't know.

4) I tried to post a plot, but all the exports looked very bad. See that one, for example.

Also, there is a good SAGE tutorial for Calculus at that link. You might try it in addition (or instead) of Maple. SAGE developers are mathematicians, so Calculus in SAGE may be more mathematically correct than in Maple.

Alec

Well, I don't know them personally, and I am certainly not a Maple's or their enemy. Just having some fun in my spare time :)

Alec

Well, I don't know them personally, and I am certainly not a Maple's or their enemy. Just having some fun in my spare time :)

Alec

Jacques,

Do you think they read posts here?

I don't think actually that my comments matter.

Alec

Jacques,

Do you think they read posts here?

I don't think actually that my comments matter.

Alec

That was from Maple 12 on 32-bit Vista, build 347164. I don't have an access to the development version.

Alec