User brings a follow up question, would this still work with:

1. A  polynomial of degree 4 in two variables X,Y can be described as 

Hi @brian.paul.hanley ,

The Maple development team are reviewing the all of the reports,symptoms and worksheets including the CPU graphs.

We find this latest symptom to be strange indeed. Is the Maple Start page set to Maple Portal?

Was Help > Maple Portal navigated to?

Hi @brian.paul.hanley ,

We apologize for the issues affecting Maple performance with large worksheets.

Our development team are looking into it with the worksheets provided. 

At least one issue they believe will be improved in a future version.

The issues are unlikely to be isolated to remote development, since our guidance,

How do I avoid corrupting document/worksheet files and/or crashing/freezing Maple?

i.e. to disable auto-save, split into multiple worksheets in a workbook, etc. has existed for some time. 

We'll see what their investigation uncovers, though.  

Hi @Carl Love, the team investigated, and improvements to the documentation should appear in a future version of Maple.

Hello @emendes ,

We reached out by the support case.

Our Grid team started to investigate.

They're not going to be able to make progress on the case unless we have a smaller example.

Update for @tomleslie: Our developers had a chance to investigate. They found that,

This is a bug that should be fixed in a future version of Maple. It is caused by the very specific situation where one of two possible variable eliminations are essentially identical, and one is chosen arbitrarily by the lexical order of the variables using the lexorder command. Since upper and lower case letters sort differently with respect to the underscore (the character with which all internal variables start) that led to the reported behavior.  That code will be changed to be less dependent on variable names.

Thank you for the detailed report and discussion @tomleslie,

Our developers are looking into it.  

In the second question from the original post, if looking for polynomials h1,h2,...,h9 to make F = h1*g1 + h2*g2 ... h9*g9,

We would need to express the basis elements in terms of the original elements. 

The suggested Maple becomes

with(Groebner):
G := [g1, g2, ..., gn];
nG := numelems(G);
ord := tdeg(x,y,z); # replace x, y, z with the appropriate variables; you can also use other variable orders -- see ?Groebner,MonomialOrders
b, transform := Basis(G, ord, 'output' = 'extended');
nb := numelems(b);
# for verification - this should be all zeroes:
[seq(expand(b[i] - add(transform[i][j] * G[j], j = 1 .. nG)), i=1..nb)];

n := NormalForm(f, b, ord, 'Q');
# if n = 0 then f is in the ideal; Q is the list of coefficients w.r.t. b.
f - add(Q[i] * b[i], i = 1 .. nb); # this will be equal to n.
# Now because b[i] = add(transform[i][j] * G[j], j = 1 .. nG), we have:
# n = f - add(Q[i] * add(transform[i][j] * G[j], j = 1 .. nG), i = 1 .. nb)
# = f - add(G[j] * add(transform[i][j] * Q[i], i = 1 .. nb), j = 1 .. nG)
R := [seq(expand(add(transform[i][j] * Q[i], i = 1 .. nb)), j = 1 .. nG)];
f - add(R[j] * G[j], j = 1 .. nG); # this will be equal to n.

Hello everyone,

We apologize for the inconvenience caused by unintended double-character inputs on MacOS. 

It now looks like the issue is not isolated to Danish users, but rather users of MacOS versions 11.2 and 12.2. 

If possible, users can update to other MacOS versions, i.e. 11.6 or 12.3 (beta)

The Maplesoft Development team are also looking into the issue and possible fixes for Maple 2021.2. 

[Update Feb 8, 2022] Maplesoft development plans to relese an update to Maple 2021.2 products imminently to address the issue. 

Please keep an eye on our Support article for all developments:

Why are Characters Typed into Maplesoft Products Doubled on Apple Systems?

[Update Feb 9,2022] See this post for details of an update to address the issue:

Critical fix for Maplesoft products on macOS

We're sorry to hear about trouble with double input on MacOS 12.2. 

Another option for Maple is to join our beta program for access to an early release of Maple 2022, as described in our article,

[Edit Feb 8, 2022] We are no longer recommending installation of Beta versions. Maple development plans to release an update to Maple 2021.2 products imminently. The article will have the latest developments. Flow should have a similar update. 

Why are Characters Typed into Maplesoft Products Doubled on Apple Systems?

We are investigating options for Maple Flow at this time.

[Update Feb 9, 2022] See this post for details of an update to address the issue:

Critical fix for Maplesoft products on macOS

Hello @nm ,

Thank you for brining this to our attention. 

Our documentation team will look into improving the ?object article in future versions of Maple. 

In the meantime, the "message-passing form" link may be be intended to link to the bullet "Using the Message Passing Mechanism" further down the ?object,methods article.

An example of how it can be used as of Maple 2021 with a StringBuffer is provided in the next bullet point immediately following your screenshot of ?object,methods (in additon to your sample code)

Hello @Tereso ,

Could you use the green up arrow to upload your worksheet so that the MaplePrimes community might be able to identify the issue with it?

Thanks for the feedback on the help article @Carl Love.

Our Documentation team will look into possible improvements. 

Hi @Anthrazit ,

We apologize for the inconvenience of not being able to re-order files in the workbook navigator.

As @Scot Gould mentions, this is a known issue in Maple 2021.2. We expect it to be improved in future versions of Maple.

If anyone's interested in early access to Maple 2022, they should consider joining the beta program.

This problem has been fixed in the Maple 2021.2 update. Thank you for letting us know about it.