Re: Newby Q: How to specify reals

• To: mathgroup at smc.vnet.net
• Subject: [mg110557] Re: Newby Q: How to specify reals
• From: "David Park" <djmpark at comcast.net>
• Date: Fri, 25 Jun 2010 07:28:07 -0400 (EDT)

```Maybe ComplexExpand should have been called ComplexSimplify or ComplexReduce
- but it's too late now and I don't know if that, in itself, would alleviate
the problem for beginners.

It's not that it's not readily accessible in the documentation. Using:

?*Complex* will bring it up on a short list. But will a beginner recognize
it as useful?

It is in the See Also section of most related Function pages. (Im, Re,
Complex, Reals) But not Complexes. It is easy for beginners to ignore the

If you enter "Complex" in the DC Search box, and then use "Search for all
pages containing Complex" it also comes up on the list.

But the real crux of the problem is the lack of basic information in the
"More Information" notes and in the "Basic Examples". WRI tends to be too
formalistic instead of putting examples of common usages. For example, on
the Complex page, which will probably be the root page new users will look
at, they write in the notes:

"You can enter a complex number in the form x + I y." Of course, if you
enter x + I y you will not obtain an expression with Head Complex but an
expression. They should add "where x and y are numbers" - even though it is
rather implied.

Then they should add a note: "Symbolic expressions containing I will contain
Complex numbers as subparts. Complex symbolic expressions can be simplified
with ComplexExpand." Even though this is not formally part of the
description of Complex, EVERYONE NEEDS TO KNOW IT.

Then in the "Basic Examples" section they could add the examples:

"Complex symbolic expressions will contain Complex numbers as subparts:"

a + I b // FullForm

Plus[a,Times[Complex[0,1],b]]

"Complex symbolic expressions can be simplified with ComplexExpand."

Im[a + I b] // ComplexExpand

b

Even though this isn't a direct formal description of Complex, it is such a
common usage that users have to see it RIGHT AWAY.

I bet that would go a long way to cutting down questions.

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

From: AES [mailto:siegman at stanford.edu]

In article <hvs7n2\$8v0\$1 at smc.vnet.net>,
"David Park" <djmpark at comcast.net> wrote:

> When working with complex expressions your best friend is the
ComplexExpand
> command. For some reason, this command doesn't immediately jump to the
> notice of beginners and this leads to frequent questions on MathGroup.

1)  Unlike familiar commands or functions or operators such as Sin, Cos,
Exp, SquareRoot, or even Re[-] or Im[-] or complex conjugate, there is
no such command or operator in "ordinary mathematics."

No one _says_ "ComplexExpand" in ordinary mathematical discourse, and
the term would not have been encountered by the ordinary high school or

2)  It's bizarrely named.  SeriesExpand _expands_ into a series.
ComplexExpand[Re[expr]] trims, or selects.

3)  And, because of Mathematica's generally dysfunctional documentation
-- e.g. "ComplexExpand" is not even mentioned in tutorial/ComplexNumbers
and if it's mentioned in ref/Conjugate, it's buried somewhere down in
the nested and closed subsections and therefore cannot be _searched_ for
using any kind of Find command.

Would anyone suggest that the occurrence of "frequent questions on
MathGroup" might indicate a weakness, or even a product defect, in this
particular Mathematica design decision?

```

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