Many thanks for your time spent on this.

I have gained an insight but I am trying to understand ‘taking the wrong branch of the radicals’.

Could I trouble you for a simpler function, than mine, for me to explore how the solving of the radicals leads to the signum functions.

Apologies if this is elementary.

Thank you Robert that is most helpful.
I have also followed up the issue of number of regions produced by lines on a plane a
and an article can be found on

PlatonicDivisionsofSpace

If I might just ask for a little more help. I am struggling to understand what is going on in the first section of your code Robert.
I have written it out in a little fuller form
L := [seq](A[i]*x + B[i]*y - C[i], i=1..8):
> CPS:=combinat[powerset]({$1..8}):
> P:= map( t -> ( map(`<`, applyop(`*`,t,L,-1) , 0) ) , CPS);
But that last line is eluding me. In particular the t in the applyop
Thank for all the help so far.

This has been answered in
Find a point in every region defined by a system of linear equations

That looks absolutely great. Thank you so much
Please ignore my other posting - I had not expected further reply

A,B,C,D,E,F are specified numbers and not ranges.
That is most helpful and clearly explained.
Many thanks

Sadly I do not have the Global Optimization toolbox
More generally can signum be used with the standard optimisation package as Maple 10 reports 'no iterations performed' when I attemp this.

Thank you as always, most informative.
My actual expression was of the form A arctan(B/C)
where A = -1 or 1, and B and C are variables and not functions.
I am glad I did not make that clear at the start; I might have missed some of the discussion!

Thank you djc and Doug.
I can not quite see how patmatch extracts x from A+B*arctan(x) where x is any expression. Am I missing something?
My original interest in this came from a wish to express
arctan(A/B) as arctan(A,B)
where A and B are any expressions.
I should have asked that specfically.

I'm using Maple 10 and find the Classic Interface comfortable.
Is the Classic Interface supported in 11?

Thank you. Aren't forums brilliant. I managed to figure out
the problem in your first posting and used
fprintf(fd ,cat(seq( "%a\t", k=1..54 ),"\n")
> ,(seq( Par_M[t,k], k=1..56 ) ) )
which seems to do the same thing as your correction.

Thank you one and all. I shall think about converting the final work to Standard

Thank you but I could not find what I was looking for.
I want to execute the whole sheet but prevent certain sections - which contain part of the code - from expanding.
It is simply to save the bother having to collapse each section that I don't need to see when I examine the results of the execution.
Have I missed something in my reading of the help section?