I have a procedure which works. ⊕(a,b) gives annwer.   a ⊕ b also gives answer. That was a surprise, discovered from a typing mistake. If b is negative is needs to be enclosed in delay evulation quotes.

2  questions 

Can anyoone expllain this useful property? Any way around having to use delay evaluation quotes for negative numbers?

Download Circle_Sum.mw

Can the procedure called Faul be made more efficient/faster? It is very slow for generating large polynomials.

Download Faulhauber_Polynomials.mw

I am trying to input data via a data table. Have several problems here.

I used an array because I want the row and column numbers to start at 0.

1st When the table appers after that the document runs hediously slow as in a second or two to enter a digit or letters appear after typing.  Like something is absorbing the computer resources. But I have a fast machine.

2nd Any data I  enter to the table vanishes but does get stored.

3rd I tried to turn it all into a procedure but cant get that to work.
 

Download DataTable_Experiment.mw

I can see my error here.Problem with Sigma(n^3). I sure i have done something stupid.

Download Sigma_problem.mw
 

Download Sigma_problem.mw

Ran into a problem with algsubs running a Maple 18 document in Maple 2017. algsubs was preforming differently i.e not working as expected. Took a while to find the cause of the problem. Eventually I had to force expansion of the equation in algsubs. This seems to have corrected the problem. Obviously there is some change in algsubs, expand, simplify or the general handling of equations.

The core of the issue has been copy/pasted here. The basic here was to substitute out higher powers of variables with expansions for them. I have had to keep resubstituting them to grind them out so to speak. That is what the outer loop "for k  to 4 do" does.  Is there a better approach to this?

Sorry the equations are long. 
 

Download Maple18_algsubs_works.mw