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1 Automorphisms
 1.1 Automorphisms
 1.2 Recognizing automorphisms

1 Automorphisms

1.1 Automorphisms

1.1-1 IsAutomorphismOfF2
‣ IsAutomorphismOfF2( arg )( filter )

Returns: true or false

1.1-2 AutomorphismOfF2
‣ AutomorphismOfF2( F, list )( operation )

Constructor of the automorphism object given a word of automorphisms.

1.1-3 WordOfAutomorphismOfF2
‣ WordOfAutomorphismOfF2( aut )( attribute )

Returns the word of the given automorphism.

1.1-4 ImagesAutomorphismOfF2
‣ ImagesAutomorphismOfF2( aut )( attribute )

Returns the images of the generators of \(F_2\) by the given automorphism.

1.1-5 ImageByAutomorphismOfF2
‣ ImageByAutomorphismOfF2( aut, w )( operation )

Returns the image of the given word by the given automorphism.

1.1-6 IsIdentityAutomorphismOfF2
‣ IsIdentityAutomorphismOfF2( aut )( property )

Returns: true or false

1.1-7 MatrixRepresentationOfAutomorphismOfF2
‣ MatrixRepresentationOfAutomorphismOfF2( aut )( attribute )

Returns the representation of an automorphism in \(\mathrm{GL}_2(\mathbb{Z})\).

1.1-8 IsSpecialAutomorphismOfF2
‣ IsSpecialAutomorphismOfF2( aut )( attribute )

Returns whether or not an automorphism is special, that is its representation in \(\mathrm{GL}_2(\mathbb{Z})\) has determinant 1.

1.1-9 IsConjugacyAutomorphismOfF2
‣ IsConjugacyAutomorphismOfF2( aut )( property )

Returns: true or false

1.1-10 ConjugacyElementConjugacyAutomorphismOfF2
‣ ConjugacyElementConjugacyAutomorphismOfF2( aut )( attribute )

Getter of the element that determines a conjugacy automorphism

1.1-11 ConjugacyAutomorphismOfF2
‣ ConjugacyAutomorphismOfF2( F, w )( operation )

Returns the automorphism determinated by the conjugacy of the given word in \(F_2\)

1.2 Recognizing automorphisms

1.2-1 AutomorphismOfF2ByImages
‣ AutomorphismOfF2ByImages( F, u, v )( operation )

Returns an automorphism such that the images of the basis are the given words u and v. If the automorphism does not exists, returns false.

1.2-2 AutomorphismOfF2ByMatrix
‣ AutomorphismOfF2ByMatrix( F, M )( operation )

Returns an automorphism that has the given matrix as image in \(\mathrm{GL}_2(\mathbb{Z})\).

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