Re: Bug Report: Maxima hangs on definite integration and simplification

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Troll?

On Sun, Jun 14, 2026 at 4:44 PM Stavros Macrakis <[email protected]> wrote:

> These are interesting examples, although I'm not sure how important they
> are in practice. I think practical problems tend to be messier....
>
> If your goal is to solve these as practical problems, there are several
> useful approaches:
>
>    - Try *scanmap(trigsimp,...,bottomup)* -- that will simplify from the
>    "bottom up".
>    - For problems including *EX^10000*, try solving them with *EX^a* and
>    then substituting back in.
>
> If your goal is to show that Maxima doesn't use the optimal strategy in
> all cases, that's certainly true. In many math problems, there are multiple
> possible tricks (a.k.a. heuristics) that might be useful, and they can be
> tried in different orders. One way to try multiple heuristics is to try
> more than one, but limit the "effort" on each (time, size of intermediate
> results, aches, each time-limited, e.g., try expanding, try trig
> simplifications bottom-up, try factoring, etc. That's a tactic that Maxima
> never uses, as far as I know.
>
> It does seem obvious in this case that *trigsimp* should be applied
> bottom-up before trying anything else, but in other cases, some other
> approach might be better.
>
>
> On Sun, Jun 14, 2026 at 2:38 PM sexymaxima via Maxima-discuss <
> [email protected]> wrote:
>
>> Description
>>
>> Maxima correctly handles the symbolic simplification and indefinite
>> integration of the expression (sin(x)^2 + cos(x)^2)^1000000, but fails
>> (hangs indefinitely) when a definite integral is requested or when the
>> exponent is a large concrete integer in certain contexts.
>> **Bug Report: Maxima hangs on definite integration and simplification of
>> `(sin(x)^2 + cos(x)^2)^N` for large integer N**
>>
>> *Steps to Reproduce*
>>
>> 1. Indefinite integral works:
>>    ```maxima
>>    integrate((sin(x)^2 + cos(x)^2)^1000000, x);
>>    ```
>>    → Returns `x` (correct, since `sin(x)^2 + cos(x)^2 = 1`).
>>
>> 2. Definite integral hangs:
>>    ```maxima
>>    integrate((sin(x)^2 + cos(x)^2)^1000000, x, 0, %pi);
>>    ```
>>    → Maxima becomes unresponsive / hangs.
>>
>> 3. Symbolic exponent works with `trigsimp`:
>>    ```maxima
>>    trigsimp((sin(x)^2 + cos(x)^2)^a);
>>    ```
>>    → Correctly returns `1`.
>>
>> 4. Integer exponent fails with `trigsimp`:
>>    ```maxima
>>    trigsimp((sin(x)^2 + cos(x)^2)^1000000);
>>    ```
>>    → Maxima hangs or fails to simplify.
>>
>> *Expected Behavior*
>> Maxima should recognize that `sin(x)^2 + cos(x)^2 = 1` (via trigonometric
>> simplification rules) and immediately return:
>> - `x` for the indefinite integral,
>> - `%pi` for the definite integral from 0 to `%pi`,
>> - `1` for `trigsimp` regardless of whether the exponent is symbolic or a
>> large integer.
>>
>> *Actual Behavior*
>> - Works only for indefinite integration with the large integer power.
>> - Hangs on definite integration and on `trigsimp` when the exponent is a
>> concrete large integer.
>>
>> *Additional Notes*
>> This appears to be a performance/scaling issue in the trigonometric
>> simplification or integration routines when dealing with very large integer
>> exponents. Maxima should apply the basic identity `sin^2 + cos^2 = 1`
>> early, before expanding the huge power.
>>
>> _______________________________________________
>> Maxima-discuss mailing list
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>> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>>
>

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