On 10/28/2013 10:04 AM, Fabio S. wrote: >> The problem with having Axiom "automatically" perform a >> irreducibility check is that the check could be time consuming.
That's true. >> Suppose you have a polynomial of high degree whose factorization >> takes, say, a couple of minutes. With an automatic irreducibility >> test, AXIOM would factor the polynomial every time you create the >> finite field, which is probably not what you would want. I haven't checked Axiom, but in FriCAS (I guess the documentation is still identical to the one in Axiom) it says for FiniteFieldExtensionByPolynomial: ... generated by the extension polynomial defpol which MUST be irreducible. However, if the parameters given to a domain D are identical, then Axiom should be smart enough to take the already created domain. In other words if you have a: FiniteExtensionFieldByPolynomial(F, defpol) := something b: FiniteExtensionFieldByPolynomial(F, defpol) := something_else then Axiom would create the extension domain only once. OK, I haven't checked this, but this is the idea. Of course there can be situations where FiniteExtensionFieldByPolynomial(F, defpol) would be used in a completely different context so that Axiom would have no chance to realize that this domain has already been computed, then it would create a second copy. Best thing probably is to do E := FiniteExtensionFieldByPolynomial(F, defpol) a: E := ... b: E := ... Ralf _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org https://lists.nongnu.org/mailman/listinfo/axiom-developer
