Re: Arctan rational

On Mar 31, 12:56 am, quasi <qu...@xxxxxxxx> wrote:
Let's try Maple.

As a trivial check of prerequisites, I tried

   > x:=arctan(1);

result: Pi/4

Note -- Maple simplifies it automatically.

Next, a warmup ...

   > x:=arctan(1/2) + arctan(1/3);
   > simplify(x);

result: Pi/4

Although Maple had to be asked to simplify it, the result is fine.

Next, the real problem ...

   > x:=arctan(1/2) + arctan(1/5) + arctan(1/8);
   > simplify(x);

result:  arctan(1/2) + arctan(1/5) + arctan(1/8)

In other words, Maple has no clue on this one.

Had it succeeded, I would have let it have a shot at the expression
Robert Israel posted, the one which equals 5*Pi/4.

But since Maple couldn't handle the above sum with 3 terms, there's
essentially no chance for it to handle Robert's more complicated
expression. Since I knew it would fail, I didn't bother trying -- I
wouldn't want to hurt Maple's feelings.

How about Mathematica or Maxima?

Can either of those contenders simplify

   arctan(1/2) + arctan(1/5) + arctan(1/8)

without being led by the hand?

quasi

Derive has no trouble simplifying these expressions (Including
Robert's). Too bad Texas Instruments decided to discontinue it.
.

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