@Adam Ledger Carl is telling you to look at the help page for the command addcoords .

You can do that by opening the Help system with the mouse pointer and the GUI's menubar. You can also do it by executing the statement,
   ?addcoords

@Magma I have changed the Question, to be marked as Maple 15 rather than Maple 2015 as it was previously.

Those versions are quite different. Maple 15 was released in the year 2011, and is four major releases older than Maple 2015.

Marking your Question as specific to an older release is crucial if you want Responders to realize that your version may not support certain new language syntax and features.

The max[index] syntax which Carl's code utilizes was added in Maple 2015, and is not available in Maple 15.

@mwahab Carl's code uses the index command, which is not available in Maple 2016.2 (the version in which your attachments were last saved). That command was introduced in Maple 2017.

Attached is a revision which uses such a procedure, assigned to name myindex.

Download with_codes_Maple2016.mw

(I have toggled your Question as being for product Maple 2016.)

@malt1752 As submitter of the Question you could toggle the cup icon beside any one Answer, to mark it as your accepted preference.

Of course that is your choice.

You could also up vote as many separate Answers as you wish, by toggling the thumbs-up icon.

@Carl Love I eventually found what I was looking for with rsolve, and augmented my Answer.

Yes, eliminating a(n) is a good key. (I am not surprised that you found it before I did.)

Which parts of the help page for topic RandomTools,BlumBlumShub,NewBitGenerator do you not understand?

Please be clear about your precise problems. That would be much more helpful than separating your queries and issue into additional Question threads.

@Carl Love My guess is that the spirit of that is to convey that -- when called alone -- `eval` does not change the stored values.

Sure, doing so might toggle some flag or DAG bit, which could be utilized to affect subsequent rtable_eval behavior.

Getting both convenient and highly efficient behavior under all circumstances seems difficult for mutable data structures -- given the need for in-place semantics and the variety of evaluation circumstances. I suppose that it is a push-me-pull-me thing, where concessions in some respects accompany benefits in others.

@HuanLuong Nobody wants to have to type in all your code, so as to try and reproduce the issue so as to diagnose it.

A screenshot image is not code that can be easily copied.

It is impolite of you to expect an answer without providing the code to reproduce. You've even ignored a explicit request to do so.

@radaar You could use,

    catch "no improved point":

or,

    catch:

where the second of those would catch any error. You can thus catch specific errors (whose messages start a certain way), or most all errors.

@V1 ...because you couldn't be bothered to do so.

You have posted only an image of your code, and no means to reproduce or analyze it via copy & paste. That is useless.

Use the green up-arrow to attach your worksheet, or add in the code-to-reproduce as plaintext.

@nm It is a shame that you removed your Answer, for now the discussion of it seems senseless.

My point is that using an identity on a mere reformulation of itself does not demonstrate much of anything. Even now (with your new response that the identity is not "needed") it's unclear whether you actually understand this point.

@vv Thank you. I realize that it's a tough topic, but I was surprised by the slog I had trying even with cartesian coordinates.

@nm How is it meaningful to my original question to use your identity for the purpose of anything but near-trivial reformulation?

What do you think of this:

Download restatement.mw

There's not that much more going on, in using an equivalent one-off or just a reformulation. I was hoping more for a use of stock commands to provide any intermediary normalizations.

@nm 

https://web.archive.org/web/20170923195225/http://area51.stackexchange.com/proposals/107315/maple