Permutation group triple product property

[Mohit Gupta]

Hello everyone,

I was thinking of Implementing Permutation group triple product property as suggested by S.Y. Lee here (https://github.com/sympy/sympy/issues/18525). 

You can see more about it using these two links:

1.)https://en.wikipedia.org/wiki/Triple_product_property

2.)https://arxiv.org/pdf/1104.5097.pdf

So there is one algorithm mentioned in here (2.)https://arxiv.org/pdf/1104.5097.pdf Which is given below.

Here S, T, U are subgroups.

So I am expriencing some problem in implementation of this algorithm.

• As we can see intersection is used here and till now sympy does not contain any function for intersection of two groups.
• We can also see that here we are interested in finding whether the intersection of two subgroups is trivial or not so maybe se can avoid calculating intersection for of two groups.
• I was also thinking of using property "Two Normal Subgroups Intersecting Trivially Commute Each Other" (https://yutsumura.com/two-normal-subgroups-intersecting-trivially-commute-each-other/) but this will work only for Normal groups.

Can we have discussion that what should be the best approach here?

def test(S, T, U):
    if( T ∩ U = 1 ) then
        if( S ∩ T · U = 1 ) then
            return true;
    fi; fi;
    return false;

[S.Y. Lee]

I think that you should add a new method like **intersect**. I'm sure that intersections form a group, so it can be an another PermutationGroup, but union may not.