GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
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#A chap10.tst PatternClass package Ruth Hoffmann
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gap> START_TEST("PatternClass");
gap> LoadPackage("patternclass",false);
true
gap> SetAssertionLevel(1);
gap> a:=Automaton("det",4,3,[[2,4,3,3],[4,4,1,4],[3,1,2,4]],[1],[2]);
< deterministic automaton on 3 letters with 4 states >
gap> b:=LoopFreeAut(a);
< deterministic automaton on 3 letters with 5 states >
gap> Display(b);
| 1 2 3 4 5
--------------------
a | 2 4 5 3 5
b | 4 4 1 5 5
c | 3 1 2 5 5
Initial state: [ 1 ]
Accepting state: [ 2 ]
gap> a:=Automaton("det",4,3,[[2,4,3,3],[4,4,1,4],[3,1,2,4]],[1],[2]);
< deterministic automaton on 3 letters with 4 states >
gap> b:=LoopVertexFreeAut(a);
< deterministic automaton on 3 letters with 3 states >
gap> Display(b);
| 1 2 3
--------------
a | 2 2 1
b | 2 2 2
c | 3 2 2
Initial state: [ 3 ]
Accepting state: [ 1 ]
gap> STOP_TEST( "chap10.tst", 10000 );