Re: [Maxima-discuss] How can I catch this error? "errcatch" doesn't do the trick.

[David S. <d.s...@go...>]

Dear Richard,

thank you for your very detailed response and your patience with me! :-)

integrate_use_rootsof is indeed interesting, thanks for pointing it out to
me.

However, I think that it doesn't quite work in the way it is intended to.
For example, take the function 1/(x^(1/3)+x+1). When we integrate it with
integrate_use_rootsof enabled, we get an answer that contains
rootsof(x+x^(1/3)+1). Doesn't the use of rootsof in an integral only make
sense for polynomials, since only they can be factored into factors of (x -
root_n)? Note that Wolfram Alpha gives an answer that is very similar to
Maxima's, but it involves the roots of the polynomial x^3+x+1.

Maxima's answer is wrong, there seems to be a bug in the part that uses
integrate_use_rootsof. I think this is what happens: integrate performs the
substitution u=x^(1/3), which results in 3*integrate(u^2/(u^3+u+1),u). Here
we have that polynomial u^3+u+1 (from Wolfram Alpha's answer) in the
denominator. But instead of outputting rootsof(u^3+u+1), Maxima substitutes
u=x^(1/3) back and outputs rootsof(x^(1/3)+x+1). It should not perform this
back-substitution. Unless you tell me that I'm wrong, I will file a bug
report about that ...

Thanks also for pointing me to rat3a.lisp, that was really helpful. I found
a function called ignore-rat-err, and based on that, I have now a working
solution that intercepts the error in my original integral and just returns
false instead of aborting everything:

(defmspec $ignoreraterr (form) (ignore-rat-err (mevaln (cdr form))))

(%i1) ignoreraterr(integrate(ev(ratsimp(1/(x^(5/2)+3*x^(1/3))),algebraic),x)
);
(%o1) false

The thing is that I'm calling integrate from within a Maxima program
(Maxima's programming language is much more "tangible" to me than LISP),
and I want to be able to react on errors occurring within integrate, without
my Maxima program execution being aborted. What I'm developing is an
"extended version" of integrate: If Maxima can't integrate an expression
right away, I apply ratsimp with algebraic enabled to it, and then try
integrating again. This works in many cases, like x/(x+sqrt(x^2+4)). There
may be other transformations such as trigsimp that might lead to an
integratable expression. Only if none of these work, my function will say
"I can't integrate this!". That's why I want to be able to handle errors
within my function, which is now possible, thanks to your hint.

Thanks again, and I'm really tempted now to begin learning LISP seriously.

Kind regards,
David

2015-09-08 0:57 GMT+02:00 Richard Fateman <fa...@gm...>:

> Incidentally, Mathematica 10.0  returns an expression, the first 1/3 of
> which looks like
>
> -(2/13) 3^(
>  4/13) (2 ArcTan[(x^(1/6) Sec[(3 \[Pi])/26])/3^(1/13) -
>       Tan[(3 \[Pi])/26]] Cos[\[Pi]/26] +
>    2 ArcTan[Cot[(2 \[Pi])/13] + (x^(1/6) Csc[(2 \[Pi])/13])/3^(1/13)]
> .....
>
> whereas Wolfram Alpha's answer returns
> -2/13 *3^(4/13)* ( Log( .....)  ...
>
> RJF
>
>
>
> On Mon, Sep 7, 2015 at 3:50 PM, Richard Fateman <fa...@gm...> wrote:
>
>> A bunch of responses:
>>
>> 1. Thanks for providing a brief way of producing this error message.
>> 2. If you really want an answer, you could try
>>
>> integrate_use_rootof:true;
>>
>> integrate(1/(x^(5/2)+3*x^(1/3)),x);
>>
>> though I'm not sure the answer returned is correct or
>> even sensible.
>>
>> It returns
>> 6*lsum(log(x^(1/6)-%r1)/(13*%r1^9),%r1,rootsof(x^(13/6)+3))
>>
>> Mathematica produces an answer, but one which is quite large.
>> Wolfram Alpha produces an answer that is different but is
>> also large, and runs out of time, it seems, in analyzing the
>> expression.  Incidentally, it apparently allows the Maxima syntax :)
>>
>> I'm not sure the answer is correct or even sensible. The
>> Mathematica system 10 could not simplify the derivative back
>> to the input, at least not before I lost patience.
>>
>>
>>
>> 3. My understanding of algebraic:true  is that it uses
>> only roots of integers  (absent in your expression)
>> %i (also absent),  and tellrat() info  (also absent).
>> So setting algebraic to true is maybe not the right thing to do.
>>
>> Introducing  both sqrt(x) and x^(1/3) by a single algebraic
>> extension of degree 6  is possible via tellrat.  I'm not
>> sure this gets you to where you want.
>>
>> Or even if you really want this integral or are just poking at Maxima.
>>
>> 4. If you really want to try to patch this bug in the handling of
>> algebraic:true,
>> + integrate + ratsimp,  not by fixing the bug, but by catching it in a
>> different
>> place, you can look at code in src/rat3a.lisp  where you can see that the
>> polynomial division  in the function pquotient, at some point says, in
>> effect,
>> HEY!  you want me to divide exactly -- that's what pquotient does -- but
>> the remainder is not zero.  There's no bug in pquotient, but there is a
>> bug
>> in someone who called it on bad argumemtns.   (This is probably because
>> the GCD routine in use  fails when there are algebraically dependent
>> indeterminates,  but this handling of algebraics is touchy. maybe because
>> of comment 1. (thanks) someone can find this???   Anyway, this
>> error-catch of the throw in pquotient is what you would have to change,
>> so that
>> it doesn't just vomit all the way to the top, but to some other err-catch.
>> Maybe you can figure out enough from the comments and the code to
>> do this.   The main body of code (but not all the comments) are almost
>> 50 years old,  circa 1966 I think.
>>
>> 5. I am not sure what you mean by "throw to the outside" and how this
>> makes
>> life easier.  Perhaps you are resisting the "easy" way -- which is to use
>> the Maxima  read-meval-print loop to call your functionality --   and
>> calling
>> Maxima  via some other language at the end of a pipe?
>> (Why easy?   load into Maxima some lisp function from a file foo, by
>> load("c:/..../foo.lisp");
>>
>> and in the file foo.lisp
>>
>> (defun $sherfgen(x)  (call_whatever_you_want_next    x))
>>
>> ;; call_whatever .... can link to fortran, python, jscript, java, most
>> any  windows dll, typical unix .o files, libraries etc
>>
>> And the load()  command can be put into a maxima initialization file so
>> it is loaded up without user attention.
>>
>>
>> Anyway. I  hope this info is useful, and you take the opportunity to
>> learn more lisp and
>> Maxima stuff.
>>
>> RJF
>>
>>
>> On Mon, Sep 7, 2015 at 12:54 AM, David Scherfgen <
>> d.s...@go...> wrote:
>>
>>> Hello,
>>>
>>> the following integral results in an error "quotient by zero":
>>>
>>> integrate(ev(ratsimp(1/(x^(5/2)+3*x^(1/3))),algebraic),x);
>>>
>>> Unfortunately, I can't catch the error using errcatch. It goes right
>>> through it, i.e. the whole evaluation is aborted, and I don't get any
>>> result (usually, errcatch would give me an empty list if it caught an
>>> error).
>>>
>>> I've had a similar problem with questions being asked by Maxima - there
>>> is no official way to intercept them. This is really bad if you run Maxima
>>> "automatedly" - without anybody being there to answer questions.
>>>
>>> But luckily, there is Robert Dodier's noninteractive package that
>>> re-defines the Maxima functions that are responsible for asking those
>>> questions. The re-defined functions don't ask the questions, but throw
>>> them, so that it can be caught from the outside.
>>>
>>> I tried to do something similar with the function that's responsible for
>>> generating the error, the function merror in merror.lisp.
>>>
>>> This is my attempt at it:
>>>
>>> ; If this is enabled, errors will be intercepted and thrown.
>>> (defmvar $no_errors t)
>>>
>>> ; A wrapper around MERROR in merror.lisp.
>>> (defvar *real-merror* (symbol-function 'merror))
>>> (defun merror (sstring &rest l)
>>>   (if $no_errors
>>>     (meval `(($throw) '(($merror) ,sstring ,@ l)))
>>>     (apply *real-merror* sstring l)))
>>>
>>> In a simple test case, it seems to work:
>>>
>>> (%i1) catch(1/0);
>>> (%o1) merror("expt: undefined: 0 to a negative exponent.")
>>>
>>> It throws the error instead of aborting the evaluation, just as I want.
>>>
>>> But in my original problem, it doesn't work, but crashes Maxima instead:
>>>
>>> (%i1) catch(integrate(ev(ratsimp(1/(x^(5/2)+3*x^(1/3))),algebraic),x));
>>> Maxima encountered a Lisp error:
>>>  Condition in MEVAL [or a callee]: INTERNAL-SIMPLE-ERROR: Bind stack
>>> overflow.
>>> Automatically continuing.
>>> To enable the Lisp debugger set *debugger-hook* to nil.
>>>
>>> Unfortunately, my LISP knowledge is basically nonexistent.
>>>
>>> Does anyone of you know why this doesn't work? Why can't errcatch catch
>>> the error in the first place? Is there something wrong with my merror
>>> wrapper?
>>>
>>> Thanks for any help!
>>>
>>> Best regards,
>>> David
>>>
>>>
>>> ------------------------------------------------------------------------------
>>>
>>> _______________________________________________
>>> Maxima-discuss mailing list
>>> Max...@li...
>>> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>>>
>>>
>>
>