Quelle Pq Sprache: Shell

#Example: "Pq" . . . based on manual example illustrating `Pq' usage
#vars: F, a, b, procId1, procId2, procId3, procId4, G, R, H, rels;
#options:
F := FreeGroup("a", "b"); a := F.1; b := F.2;
#alt: do
#procId1 := PqStart( F );
#alt: sub <procId1> for <F>
Pq( F : Prime := 2, ClassBound := 3 );

## Now let us get a p-quotient of an fp group
G := F / [a^4, b^4];
#alt: do
#procId2 := PqStart( G );
#alt: sub <procId2> for <G>
Pq( G : Prime := 2, ClassBound := 3 );

## Now let's get a different p-quotient of the same group
#alt: sub <procId2> for <G>
Pq( G : Prime := 2, ClassBound := 3,
#alt: do
#              RedoPcp,
              Exponent := 4 );

## Now we'll get a p-quotient of another fp group
## which we will redo using the `Relators' option
R := [ a^25, Comm(Comm(b, a), a), b^5 ];
H := F / R;
#alt: do
#procId3 := PqStart( H );
#alt: sub <procId3> for <H>
Pq( H : Prime := 5, ClassBound := 5, Metabelian );

## Now we redo the previous example using the `Relators' option
F := FreeGroup("a", "b");
## `F' was defined for `Relators'. We use the same strings that GAP uses
## for printing the free group generators. It is *not* necessary to
## predefine: a := F.1; etc. (as it was above).
rels := [ "a^25", "[b, a, a]", "b^5" ];
R := PqGAPRelators(F, rels);
H := F / R;
#alt: sub <procId3> for <H>
Pq( H : Prime := 5, ClassBound := 5, Metabelian,
#alt: do
#              RedoPcp,
              Relators := rels );

## Above we could have just passed `F' (rather than `H'):
F := FreeGroup("a", "b");
rels := [ "a^25", "[b, a, a]", "b^5" ];
#alt: do
#procId4 := PqStart( F );
#alt: sub <procId4> for <F>
Pq( F : Prime := 5, ClassBound := 5, Metabelian,
        Relators := rels );

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