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gap> mat := [[1,0,0],[3,0,2],[0,5,4]]*Z(7^3);
[ [ Z(7^3), 0*Z(7), 0*Z(7) ], [ Z(7^3)^58, 0*Z(7), Z(7^3)^115 ],
[ 0*Z(7), Z(7^3)^286, Z(7^3)^229 ] ]
gap> phi1 := CorrelationOfProjectiveSpace(mat,GF(7^3));
<projective element with Frobenius with projectivespace isomorphism: <cmat 3x
3 over GF(7,3)>, F^0, IdentityMapping( <All elements of ProjectiveSpace(2,
343)> ) >
gap> frob := FrobeniusAutomorphism(GF(7^3));
FrobeniusAutomorphism( GF(7^3) )
gap> phi2 := CorrelationOfProjectiveSpace(mat,frob,GF(7^3));
<projective element with Frobenius with projectivespace isomorphism: <cmat 3x
3 over GF(7,3)>, F^7, IdentityMapping( <All elements of ProjectiveSpace(2,
343)> ) >
gap> delta := StandardDualityOfProjectiveSpace(ProjectiveSpace(2,GF(7^3)));
StandardDuality( AllElementsOfIncidenceStructure( ProjectiveSpace(
2,GF(7^3)) ) )
gap> phi3 := CorrelationOfProjectiveSpace(mat,GF(7^3),delta);
<projective element with Frobenius with projectivespace isomorphism: <cmat 3x
3 over GF(7,
3)>, F^0, StandardDuality( AllElementsOfIncidenceStructure( ProjectiveSpace(
2,GF(7^3)) ) ) >
gap> phi4 := CorrelationOfProjectiveSpace(mat,frob,GF(7^3),delta);
<projective element with Frobenius with projectivespace isomorphism: <cmat 3x
3 over GF(7,3)>, F^
7, StandardDuality( AllElementsOfIncidenceStructure( ProjectiveSpace(
2,GF(7^3)) ) ) >
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