61.17 Example of DCE Functions

We take the first example presentation above, run it and demonstrate the above functions on the result.

```    gap> k := S5Pres.groupK;;
gap> c := S5Pres.gens[1].name;;
gap> d := S5Pres.gens[2].name;;
gap> u := DCE(S5Pres);
#I Set up generators and inverses
#I Set up column structure: 4 columns
#I Pre-processed relators
#I Done subgroup generators
#I Also done relators in subgroup
#I Pushing at weight 3
#I      1 double 1 single 1 blanks
#I 1 DCEWord(K,[c, d])^3
#I   1 cases
#I 1 DCEWord(K,[(2,3), c])^3
#I   1 cases
#I Pushing at weight 5
#I      3 double 5 single 1 blanks
#I 2 DCEWord(K,[c, d])^3
#I   1 cases
#I 2 DCEWord(K,[(2,3), c])^3
#I   1 cases
#I 3 DCEWord(K,[c, d])^3
#I   2 cases
#I 3 DCEWord(K,[(2,3), c])^3
#I   3 cases
#I Pushing at weight 101
#I      3 double 5 single 0 blanks
#I 1 DCEWord(K,[c, c])
#I   1 cases
#I 1 DCEWord(K,[d, d])
#I   1 cases
#I Pushing at weight 103
#I      3 double 5 single 0 blanks
#I 2 DCEWord(K,[c, c])
#I   1 cases
#I 2 DCEWord(K,[d, d])
#I   1 cases
#I 3 DCEWord(K,[c, c])
#I   2 cases
#I 3 DCEWord(K,[d, d])
#I   1 cases
<< Double coset table "No name" closed 3 double 5 single >>
gap> u.degree;
5
gap> u.status;
"closed"
gap> u.dcct;
3
gap> a1 := DCEWord(k,(1,2));
DCEWord(K,[(1,2)])
gap> b1 := DCEWord(k,(2,3));
DCEWord(K,[(2,3)])
gap> c1 := DCEWord(k,c);
DCEWord(K,[c])
gap> d1 := DCEWord(k,d);
DCEWord(K,[d])
gap> DCEPerm(u,a1);
#I Done cosets, starting image
(4,5)
gap> DCEPerm(u,a1*c1*b1);
#I Done cosets, starting image
(2,4,5,3)
gap> DCEPerms(u);
#I Done cosets, starting image
#I Done cosets, starting image
#I Done cosets, starting image
#I Done cosets, starting image
[ (2,3), (1,2), (3,5), (3,4) ]
gap> DCEWrite(u,"s5.dct");
gap> u1 := DCESetup(S5Pres);
#I Set up generators and inverses
#I Set up column structure: 4 columns
#I Pre-processed relators
<< Double coset table "No name" Set up >>