[Maxima-bugs] [maxima:bugs] Re: #4814 Default GCD algorithm can't handle algebraic

[Stavros M. <mac...@us...>]

I agree that almost all of our users don't care and shouldn't care. There might be 0.1% of our users who care a lot because they know which algorithm is fastest or least likely to have a bug on their special huge case.

Maybe we should have ``gcd:default`` mean "do what you think is best". That probably means ``algebraic:true`` as well. That way ``gcd(x^2-1,x-sqrt(2)) => x+sqrt(2)``, which I think is what most users expect.



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**[bugs:#4814] Default GCD algorithm can't handle algebraic**

**Status:** closed
**Group:** None
**Labels:** gcd algebraic 
**Created:** Sun Jul 12, 2026 11:56 AM UTC by David Scherfgen
**Last Updated:** Sun Jul 12, 2026 03:08 PM UTC
**Owner:** nobody


>From the manual:

> To take the gcd when an algebraic is present, e.g., `gcd (x^2 - 2*sqrt(2)* x + 2, x - sqrt(2))`, the option variable `algebraic` must be `true` and `gcd` must not be `ez`.

This example doesn't work with the default `gcd` value of `spmod`:

~~~
(%i1) gcd (x^2 - 2*sqrt(2)* x + 2, x - sqrt(2)), algebraic;
(%o1)                             x - sqrt(2)
~~~

We should probably automatically select a different algorithm when algebraics are present.


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