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SupposeNot / RAMP

Research Assistant for Maps and Polytopes
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Tests for internal and external self-duality #154

Closed CunningGabe closed 2 years ago

CunningGabe commented 2 years ago

c.f. my paper with Mark.

(Not to be confused with proper and improper self-duality, which is different)

Mixer2021 commented 2 years ago

Do we want this for non-reflexible maniplexes? We talked only about regular polytopes, but maybe this can be generalized at least to chiral?

CunningGabe commented 2 years ago

Yeah, I guess it makes sense for chiral - we can still ask whether the group automorphism that sends each si to s{n-i}^-1 is inner or outer. So let's just do it for chiral and reflexible for now.

Mixer2021 commented 2 years ago

Sounds good. I will add this tomorrow. Do we have the ability to grab the standard generators s_i if you are given a chiral maniplex?
Normal AutomorphismGroup(M) won't give the appropriate gens.

CunningGabe commented 2 years ago

It depends on how the chiral maniplex was built - for example, anything built from RotaryManiplex should give those generators, but random maniplexes that are later discovered to be chiral will not.

For example, compare AutomorphismGroup(ToroidalMap44([1,2])) with AutomorphismGroup(ToroidalMap44([1,2],[-2,1])).

It shouldn't be hard to make AutomorphismGroup try to put the group of a chiral maniplex in a standard form. I'll add an issue for that.

Mixer2021 commented 2 years ago

IsInternallySelfDual( M[, x] ) is done for the reflexible case, and is ready to go for chiral once the automorphism groups are well behaved.

CunningGabe commented 2 years ago

Done for chiral in 3c232bcecb2cc33737563b77dbb25aae1ddada7e.