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Re: error with Sum and Infinity

On 8/7/09 at 5:32 AM, fateman at (Richard Fateman)

>Bill Rowe wrote: ....

>>Suppose Mathematica had functions SumA and SumB per your
>>description above.

<clarification snipped>

>I don't know how exactly to characterize a "new user" but a
>mathematician unfamiliar with computer programming would have a
>rather different understanding of the term "function" which you use
>below and that is worth considering.

I've no doubt a mathematician familiar with computer programming
would understand things as you suggest. But I am reasonably
certain the set of mathematicians that understand computer
programming is a great deal smaller than the set of new
Mathematica users. In fact, based on posts I see here it would
appear many new users lack much depth of understanding for
either computer programming or mathematics.

>>It does not help clarify things to add a new function with a
>>different name for new users.

>I disagree here.  In particular it would force the people documenting
>the "functions" to make a clear distinction.

Ideally, I agree the documentation for either function would
reference the other,make it clear why two exists and when to use
them. In practice, documentation often falls considerably short
of the ideal.

Also, you implicitly assume new users actually read and
understand the documentation. Again, posts made here suggest
this simply isn't true for many users.

>>In fact, it is more likely to cause confusion since you would now
>>have two things with similar names that don't behave the same. And
>>if the two names were not similar, you almost certainly ensure a
>>new user will not find the one with the less intuitive name.

>Instead you have one thing (Sum) that does two different things.
>Appropriate documentation or even error messages would help.

>How do you feel about Integrate and NIntegrate, Sum, NSum?

 From my personal perspective, there is no problem with these
functions. Nor is there a problem with having two separate
functions for Sum. My point is simply having more functions
doesn't reduce confusion for less experienced users. It merely
changes the nature of the confusion.

This is well supported by posts in this forum. For example, it
is not at all uncommon to see a post wondering why
N[Integrate[...]] doesn't get the same result as NIntegrate[...].

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