@ddaigle321 Two lists are not identical just because they might be "mathematically" equal.

Two lists are identical under evalb if they have the same memory address (see the addressof command). That is generally not the same thing as being mathematically equal -- the definition of which varies with the mathematical domain.

Perhaps see also the verify command, and in particular verify,list help topic. To compare two lists L1 and L2 as being "mathematically" equal under a general "mathematical" verification ver one could use the command,
   verify(L1, L2, list(ver))

Somewhat similar remarks may be had about sets.

Of course it is quite possible that the elements of your lists will also be identical, in which case evalb testing would suffice. We can't tell, because you won't disclose the details of what you're actually trying to accomplish.

@Carl Love Yes, I was addressing only the original Question's literal text, not your Answer.

You mentioned writing your own function with the short name RPF, with which you could wrap each plot. But that's exactly what setPlotSize does, and you can easily rename that at will (and give it default values).

I'm not talking about making things fully automatic, especially for 3D plots. But the part of your Question about writing any additional wrapping function simply doesn't add up.

On the other hand, I think that your need and expectation of a convenient way to set both default 2D and 3D plot size is very sensible.

I can think of a few ways to accomplish that, but I'm not sure which would be best, both long term and/or as quick fix. (Eg. alter behavior of plots:-setoptions, ask for new interface settings, alter PLOT/PLOT3D printing, alter individual plotting commands, etc). For a one-off quick fix it might be simplest to alter the printing... I might have time for that.

Your question does not make sense.

Please explain clearly what you are trying to do.

@Carl Love  I forget where I first saw the idea to factor the degree 8 polynomial using this field extension. It factors into a pair of quartics (which can each be solved explicitly, naturally). I have a recollection that it might have been something by Robert Israel.

Download forfun.mw

@Carl Love That's nicely done.

@Kitonum I'm curious as to your methodology. Mine didn't produce a nice form for the sin term. Did I miss something easy?

Download conv_radical.mw

@CyberRob There is no doubt a more efficient way to do this using coeff/coeffs. But I'm trying to figure out whether this is what you're after.

I still don't understand why in your second example you wanted a factor like,
   nurdel*(dnub*nur + dnur*nub)
while in your first example you wanted a factor like,
   dnub*nur*nurdel + dnur*nub*nurdel

Download collect_ac2.mw

An alternative for step1 (possibly better) might be,

step1 := proc(ee) local K;
           eval(collect(collect(ee,vars,K),K,simplify),K=(x->x));
         end proc:

@Kitonum For the very first example the OP's expected result is not the "simplest" form (lowest leaf count, shortest, fully factored, etc). So, while your comment is correct, I don't see how it figures in here.

Start by showing us the code you used to produce this plot.

@mmcdara The rotation option was introduced for the plots:-textplot command in Maple 2018.

Please don't start a new thread about how to do this kind of thing, ie. without involving the global names, etc.

Put the followup here,  instead. The whole topic should stay together.

@Stretto But it will break if the global name x is assigned a value (eg, 4) prior to calling Iter.

@Stretto Your attempt with  C@@(3)(5)  has incorrect syntax.

And your attempts using f(g) is incorrect syntax for functional composition. If it is corrected to f@g then, lo, Iter returns a result in terms of @@.

Download iter_syntax.mw

@arashghgood I have already read your post. I did that before I made various kinds of plots from it for both parts 1) and (slightly more straightforward) ii).

I would like to know precisely what kind of plots you want. It is unclear from your details provided so far what you want in the case that K or Q are not purely real or purely imaginary. It is unclear what values you want for parameters which you might want fixed.

If you are not going to provide the full details for me to choose between various approaches then I am done here.