## 2340 Reputation

4 years, 305 days

## is(-arctan(-x, y) = arctan(x, y))?...

Maple

In the positive range Maple confirms that this is true.
In the real range Maple fails to provide an answer (see attachments).

Is this identity correct?

 (1)

 (2)

 (3)

 (4)

 (5)

But

On a unit circle

 (6)

 (7)

 (8)

 (9)

 (10)

and another maybe related case where simplification does not work

arctan_xy_simplify_2.mw

## Solve & Trig: Why is the output differen...

Maple

Solve produces different output in the attachment depending on how it is used. Why is that and how can simplification to arctan(y/z) be avoided? Arctan(y/z) only gives correct angles for positive y and z.  I prefer arctan(y,z) output that I can subsequently simplify to the y and z ranges of interest (if possible). Imagine “wrong” simplification of complex algebraic output (e.g., from inverse kinematics).

Arctan.mw

## How to get `&D;` into the favorites pale...

Maple

I got a solution to use D as a symbol that prints well in italic. For convienience I like to have it in my favorite palette.
When I drag `&D;` from a Maple Input line to the favorites palette, the ampersand and the statement operator are removed. Copy and paste have the same effect on the pasted selection. If  these characters are removed, `&D;` becomes the differential operator D. That's not what I want.
Is it possible at all to get `&D;` or simliar expressions using special characters within left single quotes into the favorite palette?

## How to get a better italic D output?...

Maple

Many formulas use a capital D to define parameters. A popular example is the second moment of area "I" of a tube. In Maple we get

Both I and D are protected symbols in Maple and are therefore printed in roman. With the "local" command, I and D can be used as unprotected symbols. However, only the unprotected "I" is printed in italic (like other symbols or names do). D is still printed in roman, which spoils Maple's excellent printout (a bit).

I hope this inconsistency can be improved one day. For the time being, I am looking for better alternatives than my workaround with a fat white space in the attachment. Are there better workarounds?

Italic_I_and_D.mw