> 
> Hi,
> 
> 
> What is the correct way to factor polynomials in spad code?
> 

ATM this is a mess.  Normally you need to determine correct
factorizer.  If you want something automatic, then
you may try GeneralizedMultivariateFactorize, but it works
on best effort basis: it may fail to produce factorization
if it can not find good factorizer.  If base ring is
Integer, then MultivariateFactorize contains apropriate
'factor'.

> 
> Assume I have some ring R (maybe Z):
> 
>   R : UniqueFactorizationDomain
> 

That is not enough: there fields F such that factorization
in SparseUnivariatePolynomial(F) is not computable.  So
we need more properties from R to be able to factor
polynomials.  This is at core of current mess.  There
was proposal to introduce additional property which
allows propagating polynomial factorization trough
type hierarchy (google for PolynomialFactorizationExplicit).
However, as I explaned in recent posts there is problem
with implementing it (both speed and correctness are
problematic).


-- 
                              Waldek Hebisch
[email protected] 

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