[isabelle-dev] Factorial ring

Florian Haftmann florian.haftmann at informatik.tu-muenchen.de
Thu Mar 10 11:18:57 CET 2016

Hi all,

since 4a5b81ff5992 in src/HOL/Number_Theory/Factorial_Ring.thy, there is
an abstract formalization of an factorial ring with a constructive
factorization operation:

	factorization a :: 'a => 'a multiset option

Maybe other algebraists can comment on this.  I would appreciate if we
can use this is a base to push abstract algebra forward.

Two remarks have to be made:
a) The development has no auxiliary operations; maybe borrowing ideas
like multiplicity and prime_factors from UniqueFactorization can turn
proofs more compact.
b) In private discussion there was the idea to define is_prime
generically in class algebraic_semidom, rather than to provide it is a
class parameter.  Class factorial_semiring would then just assume
finite_divisors (or maybe there is a more appropriate criterion?).



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