On Tuesday, 22 October 2019 23:23:44 UTC+2, Dima Pasechnik wrote:
>
> On Tue, Oct 22, 2019 at 9:51 PM 'Bill Hart' via sage-devel 
> <[email protected] <javascript:>> wrote: 
> > 
> > 
> > 
> > On Friday, 18 October 2019 15:21:05 UTC+2, Dima Pasechnik wrote: 
> >> 
> >> Hi, 
> >> well, Sage's functionality for modules over polynomial rings is quite 
> limited. 
> >> It assumes that a submodule of a free module is free. 
> > 
> > 
> > In what way does it assume this? There are limitations, but I'm not so 
> sure I would summarise them like this. 
>
> I am talking about Sage, not Singular. Singular's functionality to 
> work with modules over polynomial rings is not exposed in Sage at all. 
>
> In Sage every (sub)module comes with a basis. This works only for 
> modules over PIDs, if I recall 
> correctly. 
>

A submodule of a free module over a PID is free, of course.

But yes, Singular handles more general modules, at least over a polynomial 
ring. 

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