Opened 4 years ago

Last modified 3 years ago

#26911 new enhancement

Add elimination for ideals over noncommutative rings

Reported by: Miguel Marco Owned by:
Priority: major Milestone:
Component: algebra Keywords:
Cc: Travis Scrimshaw, Simon King, John Perry Merged in:
Authors: Miguel Marco Reviewers:
Report Upstream: N/A Work issues:
Branch: u/mmarco/eliminate_noncommutative_ideal (Commits, GitHub, GitLab) Commit:
Dependencies: Stopgaps:

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Description (last modified by Miguel Marco)

This ticket adds the option of eliminating variables from noncommutative ideals.

Change History (11)

comment:1 Changed 4 years ago by Miguel Marco

Branch: u/mmarco/eliminate_noncommutative_ideal

comment:2 Changed 4 years ago by Miguel Marco

Authors: Miguel Marco
Branch: u/mmarco/eliminate_noncommutative_ideal
Cc: Travis Scrimshaw Simon King John Perry added
Component: PLEASE CHANGEalgebra
Description: modified (diff)
Type: PLEASE CHANGEenhancement

comment:3 Changed 4 years ago by Simon King

I'm puzzled. Didn't we already have this, of course in the case where Gröbnerbases of twosided ideals exist (such as G-Algebras that are implemented in Singular)?

comment:4 Changed 4 years ago by Miguel Marco

I also expected this to be already available, but I wasn't able to find it, so I implemented (it is just a matter of adding a method that wraps the corresponding singular call).

comment:5 Changed 4 years ago by Miguel Marco

By the way, I am tempted to implement this also for ideals over quotient rings (by lifting to the cover ring, adding the ideal that acts as kernel of the quotient, compute the elimination there and then project again). But i want to hear your thoughts on that because:

1) I am not completely sure if that mathematically makes sense. and 2) I am also not sure what should be the right class to implement it in.

So, what do you think?

comment:6 in reply to:  5 Changed 4 years ago by Simon King

Replying to mmarco:

By the way, I am tempted to implement this also for ideals over quotient rings (by lifting to the cover ring, adding the ideal that acts as kernel of the quotient, compute the elimination there and then project again). But i want to hear your thoughts on that because:

1) I am not completely sure if that mathematically makes sense.

I think so.

and 2) I am also not sure what should be the right class to implement it in.

So, what do you think?

I am VERY MUCH sure that it is implemented. Actually I clearly remember writing examples a couple of years ago for quotient rings of non-commutative rings. Of course, the general ideal containment problem for two-sided ideals in non-commutative rings is unsolvable. But the code contains slots for a "reduction()" method (or perhaps it was called "reduce()"). And IF that method is implemented, then quotient rings automatically are provided.

I don't have time to look into it right now, but I am sure everything can be found, for example, in sage.algebras.letterplace (it provides testing equality of cosets modulo two-sided weighted-homogeneous ideals).

Last edited 4 years ago by Simon King (previous) (diff)

comment:7 Changed 4 years ago by Simon King

Ouch. Maybe I was totally misunderstanding what this ticket is about. I thought it was about "reduction modulo Gröbner bases" ("computing normal forms"). Now I realise that you talk about elimination of variables, which of course is something completely different.

So, perhaps it is needed to disregard my previous comments...

comment:8 Changed 4 years ago by Miguel Marco

Branch: u/mmarco/eliminate_noncommutative_ideal

comment:9 Changed 4 years ago by Erik Bray

Milestone: sage-8.6sage-8.7

Retarging tickets optimistically to the next milestone. If you are responsible for this ticket (either its reporter or owner) and don't believe you are likely to complete this ticket before the next release (8.7) please retarget this ticket's milestone to sage-pending or sage-wishlist.

comment:10 Changed 4 years ago by Erik Bray

Milestone: sage-8.7sage-8.8

Ticket retargeted after milestone closed (if you don't believe this ticket is appropriate for the Sage 8.8 release please retarget manually)

comment:11 Changed 3 years ago by Erik Bray

Milestone: sage-8.8

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