[Maxima] The factor function is a little bit silly.

Alexey Beshenov al at beshenov.ru
Mon Apr 7 10:47:39 CDT 2008

On Monday 07 April 2008 15:45, J.C. Pizarro wrote:

> To fix this problem in the future: better artificial sustitution in the
> solving of factor or intelligent lazy computation as
> factor(expand(Alpha)) => Alpha.

You're passing a verb to factor(...), so it's not "silly" when Maxima 
evaluates it and does expansion of such huge polynomial.

Your rule is obviously wrong, e.g.

  factor(expand((x^2+4*x+4)^3)) => (x+2)^6

You can add your own rules of form

  factor(expand((f)^n)) => (factor(f))^n,

but I guess it's not very useful---why not to remove expand(...) when it's not 

> factor(expand((sqrt(x+a)+b)^10));
> i got once the imprecise solution
> 10 b x^4 sqrt(x+a) + 120 b^3 x^3 sqrt(x+a) + ... + 45 a^4 b^2 + a^5
> but i got many times (sqrt(x+a)+b)^10 .
> I think that the maxima system uses memoization that remember some internal
> answers of previous computations but it's non-deterministic.

Maybe you just have removed expand(...)?

  factor(expand((sqrt(x+a)+b)^10)) =>
    10*b*x^4*sqrt(x+a) + 120*b^3*x^3*sqrt(x+a) + ...,

  factor(sqrt(x+a)+b)^10) =>

Alexey Beshenov <al at beshenov.ru>
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