Re: GPUs. Was..Re: Should facts() show duplicate facts?

Using a combination of completing the square, *realroots*, *factor*, and
*polydecomp*, the arithmetic-geometric mean inequality, etc., I can handle
cases like this:

z^2-2*x*z+2*y^2+4*x*y+x^3+3*x^2
x^4*y^2+y^4*x^2-3*x^2*y^2+1 (Motzkin polynomial)


It's under control of an *effort* parameter to allow the user to limit
the computational
cost (similar to *maxmin_effort*).

*realroots *is also useful for improving on cases like
*min(x^2,x^3,x^4,x^5,x^6,x^7,x^8,x^9,x^10)
*=> *max(x^2,x^3,x^9,x^10)* (using *maxmin_effort* > 2) => *max(x^2,x^10)*
by using it to find the intersections (this particular case is easily
handled by *solve*, but messier cases are not).

            -s

On Fri, Aug 28, 2026 at 4:16 PM David Scherfgen <[email protected]>
wrote:

> Oh, that sounds interesting.
> I've been working on something like that, too.
> Can you show some example expressions of which your solution can determine
> the sign?
>
> Am Fr., 28. Aug. 2026 um 22:12 Uhr schrieb Stavros Macrakis <
> [email protected]>:
>
>> Yes, Maxima currently doesn't use numerical techniques to solve symbolic
>> problems. But there are some easy cases where it could.
>>
>> For example, *sign(x^6+2*x+2)* could use *nroots/realroots *to determine
>> (reliably!) that it has no real roots and is therefore always positive.
>> Similarly that *assume(x>-1/2), sign(x^6+3*x+2) => pos*.
>>
>> I'm actually working on some enhancements to *sign/is* that incorporate
>> this and other techniques.
>>
>>          -s
>>
>> On Fri, Aug 28, 2026 at 3:32 PM Richard Fateman <[email protected]>
>> wrote:
>>
>>> Exact arithmetic in finite fields would feed into modular arithmetic
>>> routines like gcd, factoring .. are there GPU routines for arbitrary
>>> precision integer arithmetic?
>>>
>>> Floating point evaluation is not heavily used in serial, so not clear
>>> how parallel would help.
>>> ....
>>>
>> _______________________________________________
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>>
>

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