In Maple 11.02 you can do:

map(expand@(x->x/exp(B*L)),[(numer,denom)(A1)]);
algsubs(exp(B*L)+1/exp(B*L)=2*cosh(B*L),op(1,%))/
algsubs(exp(B*L)-1/exp(B*L)=2*sinh(B*L),op(2,%));
simplify(%);


A4 (cos(B L) v - v cosh(B L) - 2 sin(B L) B L)
----------------------------------------------
       v (-sinh(B L) + sin(B L))

Yet, for such a simple transformation, it is too much work. This shows, I think, the need for an improved 'algsubs' kind of tool.

In Maple 11.02 you can do:

map(expand@(x->x/exp(B*L)),[(numer,denom)(A1)]);
algsubs(exp(B*L)+1/exp(B*L)=2*cosh(B*L),op(1,%))/
algsubs(exp(B*L)-1/exp(B*L)=2*sinh(B*L),op(2,%));
simplify(%);


A4 (cos(B L) v - v cosh(B L) - 2 sin(B L) B L)
----------------------------------------------
       v (-sinh(B L) + sin(B L))

Yet, for such a simple transformation, it is too much work. This shows, I think, the need for an improved 'algsubs' kind of tool.

I see that there the page of Bruno Gauthier for the package GUESS V 1.0 wrongly states: "Maple V Release ...8". The source for this version states:

## Updated for Maple 8 by:
## Thomas Klausner

I see that there the page of Bruno Gauthier for the package GUESS V 1.0 wrongly states: "Maple V Release ...8". The source for this version states:

## Updated for Maple 8 by:
## Thomas Klausner

Just make the shift n->n-1, as 'listtorec' begins counting from 0.

Just make the shift n->n-1, as 'listtorec' begins counting from 0.

Yes, MMA 5 gives that 4F3 hypergeometric function for the definite integral, but for the indefinite integral the answer is also wrong. The function is a bit different, but it has a rather similar structure, also using dilog's. Its plot shows a bigger jump.

So, the difference is that the FTOC is not being used by MMA 5 for the definite integral. A lookup table is used instead? 

Apparently yes. Changing the upper limit to 9/10 it produces a wrong "dilog" answer that takes a much longer time and evaluates  numerically  to 0.384447-3.9169*I.

Either in this variable 't' or in the original form, and both definite or indefinite integral, Maple wrong answers have the same structure: sums over 'RootOf' of 'dilog' function calls.

To my eyes, they look much more messy than the series form. And 'dilog' is not less "abstract" than 'LerchPhi'. 

I mean mainly bug fix patches (in fact I would find ethical that Maplesoft itself provide them...). This task is probably all that could be done from the community side anyway. Along the road, some new functionality would need to be recreated. But not more than that. I do not find realistic backporting a whole package.

should be the object of an independent patch library. Surely, legal issues should be taken into account beforehand to avoid problems.

My guess is that the main difficulty for backported patches would originate from the opposite side. Plain copy of new code for a command might not work in older versions because of calls to some other new functionality. So, a whole "environment" should be additionally recreated.

Another circumstance where patches might be relevant would be in backporting  fixes or new functionality not available in earlier versions. Users of these versions could find them useful.

Yes, though I am not sure whether this 'superalgsubs' could resolve ambiguities  without providing it type information (or something equivalent) on the pattern as it is done for 'applyrule'. By the way, I largely regret that 'algsubs'  has not been enhanced for such a long time.

If this is the way to force an improvement of the underlying pattern-matching machinery, or the development of a new "PatternMatchingTools" package, for me it is OK.

Yes, I am mainly interested in "algebraic" pattern matching, as I  want to  use it for  mathematical calculations,  rather than data structure manipulations. 

My  point of view is that after so many years of development,  it is time that Maple provides a layer of abstraction that allows the user to operate in (close to)  "pure" mathematical  terms rather than being forced to think in syntactic terms. I mean here the difference between using 'subs' and 'algsubs'. So, my request is for more development in 'algsubs' kind of tools.

Indeed, I have avoided the case i=0 trying to keep the example simple. Automatic simplification is an additional nuisance here as eg I cannot have (unsimplified) alpha^0.

I keep installed all versions of Maple that I have and I can make run. You never know what has been lost along the road.

But it is really time to submit a SCR.

Yes, in Maple 10.06  it makes a plot.

'implicitplot' has been "upgraded" in Maple 11. The different behavior could arise in this change of code.