Re: [Maxima-discuss] Is there a way to expand ((1 + y )^ (1/n)) for y and n > 0?

[Susmita/Rajib <bkp...@gm...>]

Dr. Fateman wrote:
[quote]... The answer to part 2 depends on the particular form.  There are huge
collections of identities and special forms catalogued in math reference
books.  Steering Maxima to come up with a particular arrangement of
a formula may or may not succeed.  The question then changes to --
is there a practical reason to include this particular arrangement in
Maxima's algorithms?...[/quote]

A very deep question indeed, Sir. Unwittingly, I have just posted one
perspective, as mentioned above, in my reply to Dr. Makrakis's email.
We ignoramuses seldom seem to differ ;-)



[quote]...We can (as humans) refer to the online  collection
https://dlmf.nist.gov/...[/quote]

My profuse 'thank you' for the link provided. I had actually bought an
encyclopedia / book of functions at a sufficient cost, 8 years back. A
huge book. It lies at my ancestral place as it was difficult to bring
along with my other books.
It was unwieldy to carry.



[quote]...Less clear is how to match the capabilities of existing
(or prospective) computer systems to
make use of this kind of information in solving problems....[/quote]

None can be sure of what type of solutions might future problems need.
Nothing is redundant. So the best way is to create an exhaustive
library, depending on the user's need to download, as add-on to
maxima.
To have a self-explanatory database, with adequate explanatory note,
of add-ons so that an effort is not replicated. But of course,
combined but retaining the flavour of either of the two and something
newer than the two. Like Gestalt.



[quote]
As a very simple general statement,  if the reference document
says   A=B
should the program simplify A to B   or the reverse?
(Or neither.  Or ... depends...)
[/quote]

I believe that Dr. Raymond Rogers has adequately addressed your
present rhetoric. I can't even think of disagreeing with my seniors.
At least, normally.



[quote]
This is common in Algebraic Geometry and /should
/be common in Electronic Engineering: E-I*R=0 actually reflects reality
better than the various forms E=I*R, I=E/R, R=E/I. ...  [/quote]

I admire your understanding, Sir. E -I*R=0 makes a complete sense.
Within a closed circuit / system. Without referring to anything
outside this system/loop. The surroundings. Which is why the old
equations were restructured as Kirchoff's laws and are still extensively
used in electrical and electronic networking designs.



[quote]...  In the 80's I found
that the computer verification of identity problems could flow through
easily, whereas A=B confounded them [/quote]

Also which is why, I presume, we are superior in one way from the
computers. We can self-reflect, pause, go back and self-correct.
I believe that AI is more needed than ever to increasingly automate
more and more natural human functions that we are capable of, even
without us batting our eyelids.
To let us be aware of our unique abilities, which we take for granted.
Such reflections always leave us with minute doses of optimism.
Self-reflections are always beneficial for our health.
Regards,
Rajib