Add a hint about how to sort with a monomial ordering

[lgoettgens]

From slack:

@fingolfin : hmmm... should we perhaps define something like isless(ord) = (m1, m2) -> cmp(o, m1, m2) < 0 to make such things more convenient? So one can write sort(G; lt=isless(o)) But perhaps I am over-engineering again 🙂

@lgoettgens : That could break a lot of generic julia code, as that may expect isless to compare its arguments directly. So we would need a different name for that. But what we definitely could do, is add this line of code to the docstring of cmp

I opened this to not forget. If people have ideas what to do here, please chime in. (tagging triage to ask there for ideas)

[fingolfin]

I don't understand how this would break or even affect generic Julia code. AFAIK all such code expects a 2-arg isless. What I am suggesting is to have a convenient way to turn an "ordering" into a function that can be passed into places that want an "isless" / < function. Indeed, you omitted the example implementation I provided in that discussion:

isless(ord) = (m1, m2) -> cmp(ord, m1, m2) < 0 

So this unary method returns a binary method.

Of course we could do that under a different name, the main reason I thought to use isless(o) is that it's very easy to remember. But I also said:

But perhaps I am over-engineering again 🙂

[lgoettgens]

For similar functions like isequal and < there is a 1-arg method that is defined via partial application. I am not sure if this is the case for isless as well, but if yes, this would be an ambiguity for isless(ord) if that gives an ordering function for mpolys, or a partial application of ordering of orderings

[fingolfin]

Ok. Another option would be to just allow ord itself to be used as lt-competator, i.e. sort(x; lt=ord)

[joschmitt]

This is slightly orthogonal to the discussion about sorting, but would it make sense to have isless(::MPolyRingElem, ::MPolyRingElem; ordering::MonomialOrdering)? We seem to have isless for (some?) multivariate polynomials, I assume it compares with respect to the "internal ordering". Putting the ordering as a keyword argument would fit similar functions like leading_monomial etc. But maybe this is against Julia conventions?

(Every time I have to use cmp I have to read up what it does again, so I would like to have a foolproof way to compare monomials.)