CoCoA » CoCoALib

This would be quite useful. For the time being should we just add

define SqFree(f)
  return product(SqFreeFactor(f).factors);
enddefine;

Before checking in which name should I use?

Currently I have used radical in CoCoALib, and rad in CoCoA-5 (to avoid a clash with the fn radical defined in radical.cpkg).

Suggestions?

John Abbott wrote:

Currently I have used radical in CoCoALib, and rad in CoCoA-5 (to avoid a clash with the fn radical defined in radical.cpkg).

we could indeed use rad(I), rad(f),... which seems quite standard in all environments.

After spending some time thinking and writing, I realized that we would need a
IsSqFree(f) which could be considerably faster than computing and checking f=radical(f).
(especially when it isn't)

I like the idea of a fn IsSqFree; it certainly could be faster than testing equality with the radical (and also clearer?)

I find that IsSqFree is easier to understand than IsRadical for ringelems (and perhaps BigInt).
But then it is inconsistent to have IsSqFree as the test, and radical to compute the "maximal square-free factor".

Unfortunately, I also find SqFree to be a poor choice for the name of the fn which computes the "maximal square-free factor".

Not sure how to resolve this naming problem.

John Abbott wrote:

It seems that this issue is practically finished except for the questoon of the name of the function.
The main choice seems to be between: rad, radical or SqFree.

I vote for radical: I cannot see a similar function in Macaulay2; however in Singular it is called sqrfree and its result is by default the square free factorization (and with flag "3" the radical of the polynomial).