[isabelle-dev] Proper sign of gcd / lcm on type int

[Florian Haftmann]

>> Both are ok in my view; ironically, lcm is used more often in
>> Isabelle/ML than gcd.  Providing an lcm in the manner of HOL is trivial,
>> though:
>>
>> 	Integer.gcd = PolyML.gcd
>> 	Integer.lcm = abs oo PolyML.lcm
> 
> These two lines are the plan. Is that a good one or a bad one?

I tinkered around with (a) fractions.gcd in Python and (b)
http://api.mathjs.org/

(a) has mixed signs for gcd
(b) has everything normalized

Maybe this is evidence that we are rather free in choosing our sign
rules, and then normalizing could be a legitimate choice, conceeding
that most practical occuring lcm computations concern non-negative
denominators.

Cheers,
	Florian

> 
> Presently, I have used PolyML.IntInf.gcd and PolyML.IntInf.lcm for
> rat.ML (see da38571dd5bd). It somehow violates our cozy Isabelle/ML
> library environment to refer to structure PolyML.
> 
> 
> BTW, AFP has special code generator setup for PolyML.IntInf.gcd here:
> 
> https://bitbucket.org/isa-afp/afp-devel/src/54c65361e6ed029f70572de89cfc5736153a0feb/thys/Gauss_Jordan/Code_Generation_IArrays_SML.thy?at=default&fileviewer=file-view-default#Code_Generation_IArrays_SML.thy-33
> 
> https://bitbucket.org/isa-afp/afp-devel/src/54c65361e6ed029f70572de89cfc5736153a0feb/thys/Echelon_Form/Examples_Echelon_Form_IArrays.thy?at=default&fileviewer=file-view-default#Examples_Echelon_Form_IArrays.thy-44
> 
> Luckily, this is only gcd and not lcm, so it coincides already.
> 
> 
> 	Makarius
> 
> 
> 
> 
> _______________________________________________
> isabelle-dev mailing list
> isabelle-dev at in.tum.de
> https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev
> 

-- 

PGP available:
http://isabelle.in.tum.de/~haftmann/pgp/florian_haftmann_at_informatik_tu_muenchen_de

-------------- next part --------------
A non-text attachment was scrubbed...
Name: signature.asc
Type: application/pgp-signature
Size: 819 bytes
Desc: OpenPGP digital signature
URL: <https://mailman46.in.tum.de/pipermail/isabelle-dev/attachments/20160601/979f6342/attachment.sig>