that this issue was already discussed at alec's blog over a year ago.

Sadly I do not have access to the articles in the ACM Portal.

is useful in collecting this information:

FunctionAdvisor("branch_points",ln);
FunctionAdvisor("singularities",ln);
FunctionAdvisor("branch_cuts",ln);

[ln(z), z  in  [0, infinity + infinity I]]

[ln(z), "No isolated singularities"]

[ln(z), z < 0]

Finding the domain of a function is algorithmic?

is useful in collecting this information:

FunctionAdvisor("branch_points",ln);
FunctionAdvisor("singularities",ln);
FunctionAdvisor("branch_cuts",ln);

[ln(z), z  in  [0, infinity + infinity I]]

[ln(z), "No isolated singularities"]

[ln(z), z < 0]

Finding the domain of a function is algorithmic?

For something quick you have the Wikipedia articles Quantum field theory and Renormalization (you may read also the discussion). As anything in Wikipedia take with caution. They have references to some standard text books. And there are many more text books around. If you want more I can send you later on a longer list.

Now, if accesible means QFT/renormalization for mathematicians, I am not sure. I remember once reading in a catalog a title like that, but I am not sure where and when.

As usual, digestion of these subjects is slow (as it occurs when I am reading papers written by mathematicians). So, keep your pills at hand!

For something quick you have the Wikipedia articles Quantum field theory and Renormalization (you may read also the discussion). As anything in Wikipedia take with caution. They have references to some standard text books. And there are many more text books around. If you want more I can send you later on a longer list.

Now, if accesible means QFT/renormalization for mathematicians, I am not sure. I remember once reading in a catalog a title like that, but I am not sure where and when.

As usual, digestion of these subjects is slow (as it occurs when I am reading papers written by mathematicians). So, keep your pills at hand!

My feeling is that alternative methods at some point  also involve a dirty trick, within the framework of standard analysis. It would be interesting if you find a "tidy" way to do it so that you could show that my feeling is wrong.

My feeling is that alternative methods at some point  also involve a dirty trick, within the framework of standard analysis. It would be interesting if you find a "tidy" way to do it so that you could show that my feeling is wrong.

to the exact phrase "on gods green earth" are not quite useful as I get 24.100 results. Clearly it is a common phrase in English. So common and obvious, apparently, for native English speakers that it is not so easy to find an explanation out of so many pages where it is just used.

That is why, I think, a good online "dictionary" of English phrases would be very useful for me in this case. May be that I should ask at a forum on the English language...

that is the trick :)

This one, in fact, is naive. Look at the literature on field theory and the methods of renormalization on how to obtain finite predictions from ill defined theories that produce divergent integrals, products of distributions, etc.

That is real fun, not for delicate stomachs though. Nevertheless, results are got that agree with experiments in some cases to 12 digits o so. Hence, in some sense, these tricks should be right.

that is the trick :)

This one, in fact, is naive. Look at the literature on field theory and the methods of renormalization on how to obtain finite predictions from ill defined theories that produce divergent integrals, products of distributions, etc.

That is real fun, not for delicate stomachs though. Nevertheless, results are got that agree with experiments in some cases to 12 digits o so. Hence, in some sense, these tricks should be right.

May be but I do not know. I would like to know. I just do it, as physicists has been doing regularization and renormalization for decades without a formal theory behind.

Or may be that it has already been explored in the mathematical literature, but  because  of communication issues most physicists  have missed  it.  Moreover,  as I have said elsewhere, it seems to me that there is a connection with this  transseries issue, but I have not  studied it yet.

May be but I do not know. I would like to know. I just do it, as physicists has been doing regularization and renormalization for decades without a formal theory behind.

Or may be that it has already been explored in the mathematical literature, but  because  of communication issues most physicists  have missed  it.  Moreover,  as I have said elsewhere, it seems to me that there is a connection with this  transseries issue, but I have not  studied it yet.

There are problems here with the documentation.

In ?convert/FormalPowerSeries , section Options:

method: one of default, hypergeometric, rational, or exponential. Specifies the method that will be used; the default method uses an internal selection strategy. See the Examples below for an illustration of the various methods.

An illustration is not enough for me. I need a an explanation in proper detail of what these methods do, and what I get by using any of them. I see these four examples. Very nice, but in any other case, how do I know which (if any) should be used?

Six papers are cited in the references. I guess that a lot of work is behind this option. May be that some day I will be able to read them (if I can get the copies). But, until then, I would find much more useful that the documentation of Maple provide me enough information to make profit of this command option. Writing a details help page is much less work than writing the code and six papers. But this critical final task is missing.

There are problems here with the documentation.

In ?convert/FormalPowerSeries , section Options:

method: one of default, hypergeometric, rational, or exponential. Specifies the method that will be used; the default method uses an internal selection strategy. See the Examples below for an illustration of the various methods.

An illustration is not enough for me. I need a an explanation in proper detail of what these methods do, and what I get by using any of them. I see these four examples. Very nice, but in any other case, how do I know which (if any) should be used?

Six papers are cited in the references. I guess that a lot of work is behind this option. May be that some day I will be able to read them (if I can get the copies). But, until then, I would find much more useful that the documentation of Maple provide me enough information to make profit of this command option. Writing a details help page is much less work than writing the code and six papers. But this critical final task is missing.

If you expect that the posters will collaborate to improve to the content of a thread by editing their articles acordingly, it should be no problem allowing all necesary edits. It is the same principle of wikis.

Moreover I would like the posibility of  moving/copying subthreads of "mixed" threads (ie single subject sequences of posts within threads with several "simultaneous" subjects )  to  new  threads  to get a more useful  result.