Return all the expressions in equal relations?

Questions
1

Given several sets containing equal relations ( in “=” or “==” relations) such as

seit1={a1=a2=a3}

or {a1==a2==a3},
set2={a2=b1=b2, b3=b4},or {a2==b1==b2, b3==b4},
How to get all expressions in the equal relation (including its transitive relations), like a1,a2,a3,b1,b2? when input any one of expressions in the relation (any one among a1,a2,a3,b1,b2)?

2

You should test it further, but did you perhaps mean this (it doesn’t work with “=”)?

<< Combinatorica`

eqs = {a2 == b1 == b2, b3 == b4}
head = Head[eqs[[1]]];
eqs /. head -> List;
Apply[head, (KSubsets[#, 2] & /@ List @@@ eqs), {2}]
3

Thanks?

These sentences are truly what I need:

eqs = {a2 == b1 == b2, b3 == b4};
head = Head[eqs[[1]]];
eqs /. head -> List;

It outputs {{a2 , b1 , b2}, {b3, b4}}.

But now it is needed to print a2 , b1 , b2 when input any one of a2 , b1 , b2; or print b3 and b4 when input any one among b3 and b4.
I tried to write these sentences :

SList=eqs /. head -> List;

SList[[1]];

If [Containing[SList[[1]],Input[] , Print[SList[[1]]],F]

Here hope printing a2 , b1 , b2 when input any one of a2 , b1 , b2 by justifying the input is contained in { a2 , b1 , b2} . But it does not run.Why?
Should there be a better approach to print the items in the “==” relationship like a2 , b1 , b2 when input any one of them?

4

I am afraid I don’t quite understand what you mean. But perhaps this helps a bit:

Take your set of equations

eqs = {Equal[a, b, c, d, e], Equal[u, v]}

and consider the following function

test[x_] := 
 If[MemberQ[# =!= Symbol & /@ Head /@ List @@ x, True], Print[x], 
  Print["Nothing to print"]]

Then

test /@ eqs;

Now assign a value to, say d

d = 5;
test /@ eqs;

Clear d and assign a value to u

d =.
u = 2;
test /@ eqs;

Clear u again and find there are no values assigned

u =.
test /@ eqs;

Now assign two values

v = 3;
b = 5.6;
test /@ eqs;
5

Your help truly beneficial!
I tried to rewrite the programs as follows which are similar:

eqs = {a2 == b1 == b2, b3 == b4};

Slist = List @@@ eqs;

If[ContainsAll[Flatten[SList[[1]]], Input[]], Print[SList[[1]]], F]

When input one of a2 ,b1, b2 in a brace, say {b1} , the output will be all of a2 ,b1, b2 (in relationship equal with the input).

6

And? Does it work?
My Mathematica (Version 7) doesn’t know ContainsAll.
What do you think about this? (Type x=1 in the Input field to leave the loop.)

eqs = {a2 == b1 == b2, b3 == b4};
test[x_] := 
 If[MemberQ[# =!= Symbol & /@ Head /@ List @@ x, True], Print[x], 
  Print["Nothing to print"]]

x = 0;
While[ x == 0,
 Input[];
 test /@ eqs;
 ]
7

It works well ! You really have good feelings in Mathematica programming!
Input a2=3, it will output 3== b1 == b2.

I suppose it is same as the prohrams

eqs = {a2 == b1 == b2, b3 == b4};

Slist = List @@@ eqs;

If[ContainsAll[Flatten[Slist[[1]]], Input[]], Print[Slist[[1]]], F]

(Slist was wrong in above as SList)

I searched the function ContainsAll. It is introduced since 2015 in Mathematica version 10.2.