Re: [Maxima-discuss] Feature request: step by step

[Richard F. <fa...@gm...>]

If you are expecting Maxima to improve your math skills as in some of the
on-line tutoring programs,
by some nearly automatic process  (like tracing existing programs), that is
highly unlikely to work.

Elaborating on Stavros' note -- typically Maxima DOES NOT USE THE STEPS
USED BY BEGINNING
STUDENTS OF ALGEBRA, CALCULUS, ETC.

So what to do?
Say, take an algebra example.  "Solve for x".
A person reasonably familiar with the classroom / textbook method writes
down the steps:
step 1: move all additive terms containing x to the left hand side.  e.g.
  3*x^2+4 = 5*x  ===>  3*x^2+5*x+4 =0
step 2:  ...
step 3: ....
.....
solution: ....

  next, A person reasonably familiar with Maxima writes out a procedure to
go from step 1 to step 2,  etc.
The procedure would provide explanation of what is being done, and would go
on to step 2.  It would be
nice but not essential that this person is the same as the previous one.
................
Now take the next example of interest.
Say,  "reduce to lowest terms ..."  or ... or ...  differentiate ...
integrate ...
ETC. for all math "lessons".

If you do this right you could set up a web site to help with homework,
charge money, sell advertising space..
{I had envisioned such a scheme, years ago. Who would buy ad space?  I
thought, maybe skin cream for
acne-prone nerds? Caffeinated soft drinks? Unhealthful snack chips?}

Now there are AI programs that will "show steps", and they might be right.
If the test / homework questions are
the very standard ones that are solved repeatedly, with answers in the back
of the book, there is a higher
probability that the AI answers are correct.  I'm not sure what the
relationship is between
"AI, please scan this homework assignment and provide a printout of the
solution showing steps"
   and
learning math.

 Returning to the earlier suggestion...
Note that intermediate steps are, as Stavros notes, generally NOT HOW
MAXIMA WORKS.
If you wish to learn how computer algebra system algorithms work, there are
books, many papers, etc
on these topics.  Why aren't these methods (say, for doing integral
calculus) taught in calculus courses?

Maybe 3 reasons
1. The algorithms are efficient, effective, but somewhat tedious to do by
hand.
2. There is a mystique of "calculus is hard, uses heuristics, requires
intelligence and problem-solving" promoted by
teachers, textbooks, etc.
3. The teachers, textbook authors , are ignorant of reason 1.
(I would love to be corrected on items 3, and maybe 2.  I have, in fact,
taught calculus most recently in 1973.  My
students learned item 1, but other sections of the course did not see
this.  )

Have fun. Learn math..
RJF




On Wed, Jan 14, 2026 at 8:56 AM Stavros Macrakis <mac...@gm...> wrote:

> Thanks for the interesting request.
>
> Unfortunately, the existing code base doesn't support a step-by-step mode.
>
> You can of course trace the internal functions, but right now, we don't
> have an end-user friendly tracing solution -- you have to study the Lisp
> code to know what to trace, and the printout uses the internal form (that
> would be pretty easy to improve, though). Also, a lot of the code is not
> structured in a way that tracing the functions gives much insight. More
> seriously, the internal logic often doesn't correspond to what a human user
> would consider an "explanation" and it's hard to isolate what are
> meaningful "steps".
>
> That said, if you or others would like to work on it, it would be great to
> have it.
>
>            -s
>
>
>
> On Wed, Jan 14, 2026 at 8:31 AM Jérémy Bézairie <jer...@gm...>
> wrote:
>
>> Already asked
>> https://maxima-discuss.narkive.com/PTZcHypd/maxima-step-by-step-mode but
>> here I request the feature.
>>
>> I trust PC & Maxima for the result but step by step would help me to
>> better understand & improve me in math.
>>
>> Your competitor wolframalpha.com has it but paying...
>> _______________________________________________
>> Maxima-discuss mailing list
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>>
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