beginner questions: return on Maxima console and working with implicit functions

hi stavros---I was not an expert user.  I used Mma as a symbolic
calculator, over a span of about 20 years.  but I never wrote programs
for it.  I know nothing about Mma's internals, either.

Mma was intent on giving me irrational roots, often because it rounded
a little bit off (then I had a huge expression that was 1e-7*I).  it
is my impression (from reading some docs) that Mxa tries to restrict
itself to the rational domain.

yes, short simple expressions are in the eye of the beholder.  yes,
the problem is hard.  yes, this can take a long time, depending on the
expression.  Mma has two simplification functions.  one is called
FullSimplify[], the other is just called Simplify[].   The former can
take a lot longer.  I think an even better fullsimplify() approach
would be to let the user pick among reasonably similarly short
simplified expressions when computation power is ample and the
expression is amenable to reasonable attempts.  if the user says
"fullsimplify()", then start with and print out the result of
ratsimp(), and then continue working to see if something better comes
up (or until the user interrupts it).  print out better choices as
they come along.  for some papers, I wouldn't mind letting my computer
work overnight to see if something pops up.  for others, it's not
worth it.

regards,

/iaw



On Fri, Sep 28, 2012 at 1:45 PM, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
> Ivo,
>
> Thanks for your feedback -- very helpful to have the perspective of a
> Mathematica user.
>
> What exactly do you mean by the " 'rational' assumption"?
>
> Re FullSimplify:
>
> (self-plagiarized from an email I wrote 6 years ago):
>
> Simplification is an interesting and subtle concept.  Though sometimes you
> want the shortest possible expression, sometimes you prefer one that
> reflects the structure of the expression, or puts it in a
> particular form.  Even the simplest cases are unclear.  Consider (x+1)*(x+2)
> vs. x^2+3*x+2.  The second is slightly shorter in characters (though larger
> as a tree), and more explicit about the
> leading term (which may be of most interest for large x) and the constant
> term (which may be of most interest for small x), but the first is more
> explicit about the roots. Which is simpler: 1/(t+1)-1/(t-1) or 2/(1-t^2)?
> The second is somewhat shorter, but the first tells you more about the
> poles. How about sin(x)^2 vs.1/2-cos(2*x)/2? It is clearer that the first is
> non-negative, but the period is more explicit about the period.  Does which
> is is simpler change with a simple linear transformation: 1-2*sin(x)^2 vs.
> cos(2*x)?
>
> If the goal is the shortest representation, what about consistency between
> subparts?  Both the trigexpand and the trigreduce+ratsimp/trigrat of
> sin(5*x)+sin(x)^5 are larger than the
> original expression, but which ones are actually useful?  (Not to mention
> that it might be hard to find the unexpanded version if you're starting from
> the trigexpand'ed version.)
>
>
> Various of us have written "try hard to simplify" routines over the years.
> There are several issues there.  First, some kinds of simplifications are
> really hard to find, e.g. starting from expand( (a+b)^10 - (a-b+3)^10 ), go
> back to the unexpanded form.  Secondly, different forms are "simplest",
> depending on the purpose (see above). Third, some approaches to this will
> very quickly take impractical amounts of time.
>
> Nonetheless, some of us have thrown caution to the winds and tried some
> simple cases of this which just essentially try all combinations of some
> simplification routines and minimize tree size or string size.  I'll see if
> I can find one I wrote in my archives....
>
>               -s
>
>
>
> On Fri, Sep 28, 2012 at 12:25 PM, ivo welch <ivo.welch at gmail.com> wrote:
>>
>> thanks, volker, stavros, and andrew.  this was very helpful.
>>
>> I would put a notice about the required '$' or ';' lineend somewhere
>> in a prominent popup or startup line the first few times that Maxima
>> is invoked.  This has probably let many "silent" users to give up
>> prematurely over the years.
>>
>> I am definitely warming up to Maxima over Mathematica.
>>
>> I like the "rational" assumption in Maxima, as well as its more
>> central assume feature.  Maxima seems faster, too.  Its default
>> wxMaxima notation output seems nicer.
>>
>> Mathematica seems to have a more sophisticated FullSimplify
>> simplification routine---in fact, I wonder whether Maxima there is not
>> a heuristic simplification that has some IQ and tries all sorts of
>> different approaches by itself without me having to know what packages
>> I could try.
>>
>> Mathematica puts its graphs into its notebook, while wxMaxima put them
>> into external gnuplot windows.  I believe wxplot can embed plots, but
>> when I want to use other plots, such as implicit plots, I probably
>> lose this.  I wish wxMaxima had a configure choice to integrate all
>> graphs.
>>
>> Mathematica has one big advantage, which is books.  I would purchase a
>> 150 page book that is a reasonable beginner's guide.  fortunately,
>> Mathematica's drawback is that its books are 2,000 pages.  I usually
>> just read the first few chapters.
>>
>> one thing about Maxima that cannot be changed: is that the name of the
>> package is too generic.  google searches lead to all sorts of
>> irrelevant results.  I now know a lot more about Nissan maximas.
>>
>> in any case, Maxima is an impressive package.
>>
>> Cheers.
>>
>> /iaw
>>
>>
>>
>>
>> On Fri, Sep 28, 2012 at 3:12 AM, Volker van Nek <volkervannek at gmail.com>
>> wrote:
>> >
>> > 2012/9/28 ivo welch <ivo.welch at anderson.ucla.edu>
>> >>
>> >> dear maxima experts---
>> >>
>> >> [1] I am trying to switch from Mathematica to Maxima.  I downloaded
>> >> and installed it on ubuntu linux 12.04.1 .    I can use wxMaxima
>> >> successfully.  I would like to use the basic command line interface.
>> >> I type $ maxima, and then "solve( y + 2 == 0, y)" to the (%i1) prompt
>> >> and hit enter...and nothing happens.  then I try shift-enter.  a ^c
>> >> gets me a console interrupt.
>> >
>> >
>> > Maxima needs a terminator at the end of an expression. Use ; to view the
>> > answer and $ if the answer should not be displayd.
>> >
>> > wxMaxima automatically adds a semicolon.
>> >
>> > The operator for an equation is simply =
>> >
>> >>
>> >> [2] I am trying to work with implicit functions.  an illustration of
>> >> what I want to accomplish is
>> >>
>> >> eqn : solve( y + log(y) + x = 0, y)
>> >> plot(eqn, [x,0,1])
>> >
>> >
>> >  To answer this I need to load an additional package:
>> >
>> > (%i2) eqn : y + log(y) + x = 0$
>> >
>> > (%i3) load(implicit_plot);
>> >
>> > (%o3) "/usr/local/share/maxima/5.28.0/share/contrib/implicit_plot.lisp"
>> > (%i4) implicit_plot(eqn, [x,0,1], [y,0,1])$
>> >
>> >
>> > solve cannot solve eqn. So I load another package:
>> >
>> > (%i5) load(to_poly_solve);
>> >
>> > Loading maxima-grobner $Revision: 1.6 $ $Date: 2009-06-02 07:49:49 $
>> > (%o5)
>> > "/usr/local/share/maxima/5.28.0/share/to_poly_solve/to_poly_solve.mac"
>> > (%i6) to_poly_solve(eqn, y);
>> >
>> > (%o6) %union([y = lambert_w(%e^-x)])
>> > (%i7) plot2d(lambert_w(%e^-x), [x,0,1])$
>> >
>> > To compute dy/dx I type
>> >
>> > (%i8) diff(lambert_w(%e^-x), x);
>> >
>> > (%o8) -%e^(-lambert_w(%e^-x)-x)/(lambert_w(%e^-x)+1)
>> >
>> > I don't know much about Lambert's W function. So I can't help with dy/dx
>> > >
>> > 0.
>> >
>> > I hope someone else can answer here.
>> >
>> > Volker van Nek
>> >
>> >>
>> >> I know this is wrong...but how would I do this correctly?  (I also
>> >> want to use M to ascertain whether dy/dx > 0 .)
>> >>
>> >> help for a poor beginner is appreciated.
>> >>
>> >> /iaw
>> >>
>> >>
>> >> ----
>> >> Ivo Welch (ivo.welch at gmail.com)
>> >> http://www.ivo-welch.info/
>> >> J. Fred Weston Professor of Finance
>> >> Anderson School at UCLA, C519
>> >> Editor, Critical Finance Review,
>> >> http://www.critical-finance-review.org/
>> >> _______________________________________________
>> >> Maxima mailing list
>> >> Maxima at math.utexas.edu
>> >> http://www.math.utexas.edu/mailman/listinfo/maxima
>> >
>> >
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