@Rouben Rostamian  Possibly. But I had elliminated a first and then used isolve to get b and c. Then used those values to solve for a. I gusss that assumed there would be an integer solution for a.

@Kitonum Wow! That is a great solution.

I think that is the way it has always been. I ran into that around 2018.

@C_R I should have pinned Maple 2026 not Maple 2026 (Shared Server) to the task bar.

@C_R A self created problem. I had pinned Maple (Shared Server) to the task bar.

@nm I cannot get that setting to stick. "Create a new engine for each document". Everytime I restart Maple it has reverted to "Share one engine among alll documents".

I was trying that because if i open a tab in a window Maple is very prone to hanging.
I'm using Maple 2026.1 and windows 10.

@janhardo  Now I see what you mean. Yes that is where I hava put it now. Yesterday I  put it here "C:\Program_Files\Maple\Users\maple.ini". Both actually work.

@acer  Ah that link clarifies things. So I moved the file from Maple2026/Users to C:\Users\Ronan.  That way my older versions of Maple can access it too.

@acer @janhardo I set the lifbary to as suggested by acer. The nest step is the package "mapel.ini" file needs to be placed in "C:\Program Files\Maple 2026\Users". My install of Maple did not have the "Users" folder. Maybe because it is a home user license?

@janhardo That is great. So do downloaded the package. Can you explain the steps you took, screenshots  and what is in it's maple.ini file?

Edit:- what Maple version?

@janhardo That looks like it alright.  Well done!  You could also show on the diagram the matching inner twincircles. The green blue and pink ellipses should be tangent to thier corresponding outer ones. the red  should be an ellipse/circle through the 3 points.

@acer  Basicaly that finds the package alright. But produces an error on loading

restart
with(eClifford)
       _known_types = [eclibasmon, eclimon, eclipolynom]

      _known_sortings = [sort/byegrade, sort/byegradenum, 

        sort/byegradesymb]

   _known_conversions = [convert/binarytuple_to_eclibasmon, 

     convert/clibas_to_eclibas, convert/eclibas_to_clibas, 

     convert/eclibasmon_to_binarytuple]

  _revisions_additions = [eClifford:-eLC, eClifford:-ecinv, 

    eClifford:-ecinv1, eClifford:-ecinv2, eClifford:-ecmulCh, 

    eClifford:-eminpoly]

Error, (in eClifford:-ModuleLoad) could not open `savelibname/Walshpackage.m` for reading

Same here. I have had yhat error before and just had it now. The I tried again. and got this. I don't thing a have used a mi;;ion credits this month as I don't use Maple AI that much.

@janhardo Sorry but, I don't have the time to analise the code.
1st forget about ideal points. 

2nd  Twin circles are in matched pairs. So use one colour for each pair.

3rd Tangency usually occurs between pairs of twin circles. 

Look at the example I posted last week. It covers all the above.

@janhardo So the null conic is the black one. What is the cyan coloured blue conic? You have twin circles blue and circumcircles orange. They all are twin circles. You would be better off pairing them in matched colours. You still have the basic problem. The twincircles cannot pass throught the null conic. Yours do (as far as I can make out). My original question was on the type of matrix normailsation being used. I already had and have a working solution. You need to study the relevant section of the paper and understand it for yourself. AI will not do that for you. Where did the "Ideal points" come from? All this applies to non null points to the best of my current understanding.