@Christian Wolinski  Sorry. I meant to remove that line. There is a procedure at the start called Trunc. It is normally stored in my package called RonanRoutines. I copied and pasted it into the doc so it should work for you.

@Christian Wolinski Thank you. Very workable. I would love to give you best answer, thumbs up. They are not available.

@Joe Riel That is nice proc and a big step towards the end goal. At this point, I am going to start a new question on reducing the equations as this one was primarily about plotting.

@Joe Riel Thank you. I have the same problem. I can't figure out how to get Maple to reduce (x^2 + y^2 -1)^2 to  x^2 + y^2 -1. I am trying to find a way to do this automatically. Do you have any ideas on how to?  It could be for example  (x^2 + y^2 -1)^6.  I just picked the circle equation as a representative example.

Another good example is; because it has no constant term.

(-27*x^2*y^2-27*y^4+4*x^3)^2

Christian Wolinski Very nice and powerful. I was just going to post a similar question. I have a couple of questions and a problem.

The code doesn't seem to need Y or am I missing something?

k doesn't match my variable x but it works with k?

I found a situation where it returns a squared version of the desired answer. Is there a way around this? 
 

Download sometimes_not_full_reduction.mw

@acer That is great. So useful. Is there a way to extend the functionality to handle for example trig functions? I multiplied one side by sin(x) and the other by tan(x).

fact := proc (expr::equation) options operator, arrow; frontend(gcd, [numer(lhs(expr)), numer(rhs(expr))])/frontend(gcd, [denom(lhs(expr)), denom(rhs(expr))]) end proc;
 eq1 := F*R = (1/2)*M*R^2*(a/R); eq1/fact(eq1); 
eq2 := (F+G)*R*sin(x)/sqrt(W-1) = (1/2)*M*R^2*tan(x)*(a/(R*sqrt(W-1)));
 fact(eq2); eq2/fact(eq2)

(F+G)*sin(x) = (1/2)*M*tan(x)*a

@Carl Love I found that line of code here on Maple Primes as a stand alone way to truncate an equation.

map(select, proc (q) options operator, arrow; evalb(degree(q, b) <= odr) end proc, a)

I put it inside the  procedure. 

I see that yours works alone too.

select(proc (q) options operator, arrow; evalb(degree(q, [x, y]) <= 2) end proc, E2)

Thank you,

Both answers are execellent.

@Kitonum That is some nice disassembly of the function in Addition 2. 

In Addition 1 I found using the inert form Sum and then setting u=v gives the correct evaluation of the limit.

I was originally trying to convert that expression automaticially to the sum for an abrtitary m. An example of something similar is   which assuming n>m can be represented as  but outside of actual numbers I can't get Maple to factor to that. That then evaluates to .

These functions are rather elementry and I am surprised Maple doesn't seem handle this. 

In the original document I attached, I notice something odd with

The second sum is from 0 to infinity. How could that be? 

@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.