@Kitonum  I like that. I haven't used 'limit' before. Will pay more attention to it in future. I am still interested in how to make Maple produce the sum. 

@tomleslie Yes I understand your point. In reality the matrix is being generated row by row and checked for the condition of M[i,1]<>M[1,1]. Does not necessarily happen though solimit loop to some upper value.

 or else it keeps running.

@vv Of course it would be probably hard to beat the Maple code. I was wondering if there was possibly some recursive approach.

@Kitonum  I managed to apply the concept to a telescoping series. Very Useful. 

sum(``(i^2-``((i-1)^2)), i = 1 .. 3) .. sum(``(i^2-``((i-1)^2)), i = -2+n .. n)

@Preben Alsholm 

I hit a problem too on a completly different issue.  All worked fine in Maple 2017.

Have a combined problem with typesetting=extended and Digits in Maple 2018.

Now what does work in typesetting =standard and Digits, this is not an issue.

With typ=extd. I was getting a incorrect 1 column in matrix. Some of the 1.0000s were 0.100000, The rest of the matrix was ok. I tries various values for Digits  no difference. I tried #Digits=15 lods ot stuff failed in the document. Removing Digits altogether produced allowed the document to run but still produced obvious errors in 1st column

Using win 10 64bit and Nvidia P2000
The new context panel is a great idea along with the plot builder.

There are some improvements that would make this really great.

Plot Builder needs to remember it’s settings. If the document is re executed the plot comes up empty and all settings are lost.

It would be good to combine Explore with Plot Builder so if you have functions like y=a x^2+b x +c you could set sliders for a,b,c.  The old plot builder (upto 2016) had this function.

At present Explore disappears when the document is re executed.

On the clickable math if you change the original equation the clickable math does not update.

                              

Edit....The below works and is lot simpler than what I was trying.  The fundamental problem is creating a procedure or module that has 2 stage inputs, data tables probably just add to that complexity.

@acer  Thank you. That is good.I simplified things by just using the matrix input pallet. And then using the the procedure to convert the matrix.

BiPolyNum := proc (N)
description "Creates Bi Polynumbers";
return ArrayTools:-Alias(N, [0 .. LinearAlgebra:-RowDimension(N)-1, 0 .. LinearAlgebra:-ColumnDimension(N)-1])
end proc;
                BiPolyNum := proc(N)  ...  end;

@acer Thank you. I have made some progress. I was using and array. Seems to cause the problem on slowness. Could be a bug.

I have it working outside of the procedure now. Still Struggling with the proc itself

I dont understand this statement "If I understand the question properly, then my Answer is as follows. The name of the unique Array/rtable/Matrix/Vector associated with a particular DataTable can be the argument to a procedure call, as can the unique string identity of a particular DataTable."

 Can you explain or show what that means?
 

Download DataTable_Experiment_rev_1.mw

this a further.

@one man Ok it all works fine now. That is a good link you posted.

Hello Tried to run your code,I get an error. It would be instructive to add explinations to your code.  

@_Maxim_ Hi, 

sb := Groebner:-NormalForm(Phi[1], `~`[`-`]([tobesbstd], [sbeqmaple18]), (tdeg@op@indets)(Phi[1]))

Could you possible explain the syntax of this line? It works great. 

@_Maxim_Thank you.  I am weak on Groebner basis. Shall experiment and see.

In Maple 18 the expand term is not needed inside algsubs.

for k to 4 do
for i to 6 do
`sb&Phi;`[1] := simplify(algsubs(tobesbstd[i] = sbeqmaple18[i], expand(`sb&Phi;`[1])))      #   This expand
end do
end do;
simplify(`sb&Phi;`[1]); sort(expand(evalf(`sb&Phi;`[1])))      #and this expand not needed in maple 18

"this is repeated until the leading monomial in f is less than the leading monomial in a" .  I think I understand this.

In my loop above set k to 1 so it only does the whole substitution once, the equation will still contain highter order terms.  On the second time around the loop in this equation they all reduce. So round 3 and 4 not needed in this case. It the coefficients are different they might be.  I had 12 other equations one required repeating the substitution set 6 times.

THe example of using algsubs(x^2 = x*y, x^3); is very simple the the complexitits don't arise.

@acer   I just tried your code. Problem occurs with 3.1, 3.41, 4.22, evalf(10/3) all returm false

Now 4.2, 10/3,  135265467/791  will return true.  Some short decimals work.

Basicially seems to be a problem with how decimals are handled

using `Maple 2017.3, X86 64 WINDOWS, Sep 27 2017, Build ID 1265877`

@Carl Love That would be interesting to see.

@Ramakrishnan Hello,

The workbook didn't upload. Can you try again please. If it doesn't upload could you describe the solution if there is one.

Ronan.