Adresses issue with equality/hashing on module orderings

[RafaelDavidMohr]

Adds == and hashing for ModuleOrderings.

I don't know if this is the best solution, I essentially just circumvent what julia does by default when calling == on structs (which is to call === on every field) by instead calling == recursively on every field.

If this is potentially to dangerous, let me know. It does fix #3347 on my machine.

Tag: @ederc

[fieker]

Can't this be handled by matrices or similar like in the monomial Case?
Is there a canonical normal form for those orderings?

[thofma]

Hm, yes, I wonder whether this is correct:

mutable struct ModOrdering{T} <: AbsModOrdering
   gens::T
   ord::Symbol

If one only checks if gens and ord are equal, then this does not check equality of orderings.

[RafaelDavidMohr]

Can't this be handled by matrices or similar like in the monomial Case? Is there a canonical normal form for those orderings?

It can but it is more involved, see theorem 2 here. I decided against this because it would go substantially beyond the addressed issue to implement this and because, as far as I can tell, we don't support any functionality for such general matrix orderings.

If required, I am however happy to take a look at a canonical matrix form for the orderings we do support, maybe it's easier in this case.

[RafaelDavidMohr]

Hm, yes, I wonder whether this is correct:

mutable struct ModOrdering{T} <: AbsModOrdering
   gens::T
   ord::Symbol

If one only checks if gens and ord are equal, then this does not check equality of orderings.

I apologize I don't quite understand what you mean. Do you have an example?

[thofma]

I was thinking about the following situation: The polynomial ring has one variable and the module is free of rank one. Then :lex and :degrevlex and whatnot define all the same orderings, but the equality check proposed here should yield false?

[RafaelDavidMohr]

I was thinking about the following situation: The polynomial ring has one variable and the module is free of rank one. Then :lex and :degrevlex and whatnot define all the same orderings, but the equality check proposed here should yield false?

Yes, good point. Ok, I will think of something else.

[RafaelDavidMohr]

Brief update: I am working on this but this will take a while. We will need canonical representations of module orderings and they will take a while to implement.

[RafaelDavidMohr]

I've added equality and hashing by embedding the underlying module of the ordering in question into a new polynomial ring and computing the canonical matrix there, which is then used for equality checking and hashing.

While this is not a unique representation of the ordering, it catches at least all reasonable cases that I could come up with.

[lgoettgens]

I think that == should compare the underlying modules of the orderings as well. And then same for the hash: the field M should be used there as well

[ederc]

I'm not sure I completely understand why. If I have two different modules and I want to find out if both share the same ordering, how shall I do that? Note that also for MonomialOrdering we do not compare the corresponding rings.

[lgoettgens]

In that case, we should definitely keep it consistent and revert the change here. Sorry for the double work @RafaelDavidMohr

[RafaelDavidMohr]

No worries, it's reverted.