‣ IsAutomorphismOfF2( arg ) | ( category ) |
Returns: true or false
‣ AutomorphismOfF2( F, list ) | ( operation ) |
Constructor of the automorphism object given a word of automorphisms.
‣ WordOfAutomorphismOfF2( aut ) | ( attribute ) |
Returns the left canonical form of the given automorphism.
‣ ImagesAutomorphismOfF2( aut ) | ( attribute ) |
Returns the images of the generators of \(F_2\) under the given automorphism.
‣ ImageByAutomorphismOfF2( aut, w ) | ( operation ) |
Returns the image of the given word under the given automorphism.
‣ IsIdentityAutomorphismOfF2( aut ) | ( property ) |
Returns: true or false
‣ MatrixRepresentationOfAutomorphismOfF2( aut ) | ( attribute ) |
Returns the image of an automorphism in \(\mathrm{GL}_2(\mathbb{Z})\) under the map \(\Psi\).
‣ IsSpecialAutomorphismOfF2( aut ) | ( property ) |
Returns: true or false
‣ IsConjugacyAutomorphismOfF2( aut ) | ( property ) |
Returns: true or false
‣ ConjugacyElementConjugacyAutomorphismOfF2( aut ) | ( attribute ) |
Getter of the element that determines a conjugacy automorphism.
‣ ConjugacyAutomorphismOfF2( F, w ) | ( operation ) |
Returns the automorphism determinated by conjugacy of the given word in \(F_2\)
‣ AutomorphismOfF2ByImages( F, u, v ) | ( operation ) |
Returns an automorphism such that the images of the basis elements are the given words \(u\) and \(v\). If the automorphism does not exist, it returns false.
‣ AutomorphismOfF2ByMatrix( F, M ) | ( operation ) |
Returns an automorphism whose image in \(\mathrm{GL}_2(\mathbb{Z})\) is the given matrix.
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