On Sun, Dec 03, 2023 at 09:24:51PM +0800, Qian Yun wrote:
> Should "froot(4*a^2,4)" return
> [exponent = 2, coef = 1, radicand = 2 a] instead of
> [exponent = 4, coef = 1, radicand = 4 a^2] ?
Probably. AFAICS easy modification to froot would do this:
one needs to separately handle content of polynomials
(numerator and denominator). OTOH there is question
how far should we go. 'zroot' internally used inside
PolynomialRoots needs to factor integers. For large
integers it is very expensive, so rather undesirable.
OTOH we can do essential root simplification by factoring
polynomials. When there is large integer content,
factoring polynomial is much cheaper than factoring
integers. By factoring polynomials we will not
simplify say 'sqrt(2048)' to '32*sqrt(2)', but it
is enough to guarantee independence of roots. And
by factoring polynomials we can simplify 'sqrt(2*sqrt(2) + 3)'
to '1 + sqrt(2)' which 'froot' can not do.
So, 'froot' is fairly incomplete simplifier. Its potential
advantage is that it may be less expensive than factoring.
But then we should avoid really expensive stuff in 'froot'.
--
Waldek Hebisch
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