"Source: Text/LieTheory/RootDtm.text";
"Line: 2633";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/LieTheory/RootDtm.text, line: 2633
// Example: H107E28 ()
print "Example: H107E28";
ei := GetEchoInput();
SetEchoInput(true);
R := RootDatum("A4B5" : Isogeny:="SC"); 
Q, S := DirectSumDecomposition( R );
R eq S;
assert $1;
R eq Q[1] join Q[2];
assert $1;
R eq &join DirectSumDecomposition(R);
assert $1;
R eq &+    DirectSumDecomposition(R);
assert not $1;
R1 := RootDatum("A3T2B4T3");
R2 := RootDatum("T3G2T4BC3");
R1 + R2;
R1 join R2;
G<a,b>:=FundamentalGroup("A1A1");
_,inj:=sub<G|a*b>;
R:=RootDatum("A1A1":Isogeny:=inj);
ad := RootDatum( "A1" : Isogeny:="Ad" );
sc := RootDatum( "A1" : Isogeny:="SC" );
IsIsomorphic( R, DirectSum(ad,ad) );
assert not $1;
IsIsomorphic( R, DirectSum(ad,sc) );
assert not $1;
IsIsomorphic( R, DirectSum(sc,sc) );
assert not $1;
Q, S := DirectSumDecomposition( R );  
R eq S;                             
assert not $1;
SetEchoInput(ei);
