Math 696 -- Misunderstandings

Misunderstandings

Misunderstandings

Some of Maple's mistakes are really mistakes by the operator. If you ask Maple a dumb question, you may get a dumb answer.

For example, if you ask Maple to sum a divergent infinite series, do not be surprised if Maple gives a strange response. Maple 7 correctly reports that the divergent series
```
sum( (-2)^n, n=1..infinity);
```
is "undefined", but Maple 6 blithely returns the answer -2/3. Maple 7 correctly sums the convergent series
```
sum( (-exp(-1))^n, n=1..infinity);
```
but does not report the divergent series
```
sum( (-exp(1))^n, n=1..infinity);
```
as undefined. Instead Maple 7 issues the curious message
```
Error, (in convert/hypergeom) cannot evaluate boolean: exp(1) < 1
```
If you tell Maple that x is equal to 0 and then ask it to divide both sides of the equation by x, it will tell you that 1=0. Indeed, both of the following pairs of commands produce that result.
```
x=0: %/x;
x:=0: x/x=0/x;
```
If you give Maple the command
```
10e10 + 1 - 10e10;
```
with the default setting of Digits, then you will get the wrong answer 0 instead of the right answer 1. Do you see why?
Roots of negative numbers often cause confusion. Here is a common example in which the user gets an unanticipated result:
```
(-8.0)^(1/3);             
     
     1.000000000 + 1.732050807 I
```
Maple did not give the "correct" answer of -2, but it did give a valid complex cube root of -8. What the user should have input was "surd(-8.0,3);".

It is possible to disguise the preceding error by complicating the problem. Calculus students are guaranteed to be confused about why Maple evaluates
```
limit( ( (x-1)^(1/3) -1 )^3, x=0 );
```
to the value 1 instead of the "correct" value -8.
A user was surprised that the following command fails to produce the expected result of 6.
```
> evalf(solve(n!=720, n));
                   -.9986122210
```
If you know about the Gamma function, you will understand that Maple's result is meaningful. The question the user should have asked Maple is fsolve(n!=720, n=2..10);.
A student was surprised that although the Maple command "sign(-2);" produces the value -1, the command "plot(sign(x), x);" displays a horizontal line segment at height 1. The reason is that Maple's "sign" function returns the sign of the leading term of a polynomial. It is the "signum" function that yields the sign of a number.

Misunderstandings