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
*Permutation group triple product property: *(Reference Wikipedia)
Let {\displaystyle G}[image: G] be a non-trivial group. Three nonempty
subsets {\displaystyle S,T,U\subset G}[image: {\displaystyle S,T,U\subset
G}] are said to have the *triple product property* in {\displaystyle G}[image:
G] if for all elements {\displaystyle s,s'\in S}[image: {\displaystyle
s,s'\in S}], {\displaystyle t,t'\in T}[image: {\displaystyle t,t'\in T}],
{\displaystyle
u,u'\in U}[image: {\displaystyle u,u'\in U}] it is the case that
{\displaystyle s's^{-1}t't^{-1}u'u^{-1}=1\Rightarrow s'=s,t'=t,u'=u}[image:
{\displaystyle s's^{-1}t't^{-1}u'u^{-1}=1\Rightarrow s'=s,t'=t,u'=u}]
where {\displaystyle 1}[image: 1] is the identity of {\displaystyle G}[image:
G].
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 "T*wo 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;
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