‣ ConjugacyGL2Z( A, B ) | ( function ) |
Decides whether a pair of 2x2 matrices in \(\mathrm{GL}_2(\mathbb{Z})\) are conjugate. If so returns the element \(C\) such that \(A=C^{-1}BC\).
‣ CentralizerGL2Z( A, B ) | ( function ) |
Given a matrix \(A\), computes a matrix \(C\) such that \(C_{\mathrm{GL}_2(\mathbb{Z})}(A) = \langle -C, C \rangle\) and an integer \(n\) such that \(C^n=A\).
‣ MembershipSubgroupSL2Z( gens, A ) | ( function ) |
Given a matrix \(A\), decides whether \(A\in\langle gens \rangle\) and if so computes a word \(w\) in the generators that represent \(A\).
‣ AreAutomorphicEquivalent( F, u, v ) | ( operation ) |
Decides whether u and v are automorphic equivalent in F.
‣ IsCyclicalyReducedWord( u ) | ( property ) |
Returns: true or false
‣ IsSubword( u, v ) | ( operation ) |
Returns whether the word v is a subword of u or not.
‣ IsPrefix( u, v ) | ( operation ) |
Returns whether the word v is a prefix of u or not.
‣ IsSuffix( u, v ) | ( operation ) |
Returns whether the word v is a suffix of u or not.
‣ RootFreeGroup( v ) | ( operation ) |
Returns a word \(w\) and an integer \(r\) such that \(w^r=v\) and \(r\) is maximal.
‣ NielsenReducedSet( V ) | ( function ) |
Given a sequence of elements \(V\) of a free group, returns a Nielsen reduced set \(W\) that is equivalent to \(V\).
‣ IsNielsenReducedSet( V ) | ( function ) |
Given a sequence of elements \(V\) of a free group, returns whether \(V\) is a Nielsen reduced set or not.
‣ InFreeSubgroup( V, w ) | ( function ) |
Given a sequence of elements \(V\) of a free group and a word \(w\), returns whether \(w\) is in the subgroup generated by \(V\) or not.
‣ IsSubgroupOfFreeSubgroup( V, W ) | ( function ) |
Given two sequence of elements \(V,W\) of a free group and a word \(w\), returns whether the subgroup generated by \(W\) is a subgroup of the group generated by \(V\) or not.
‣ IsNormalSubgroupOfFreeSubgroup( V, W ) | ( function ) |
Given two sequence of elements \(V,W\) of a free group and a word \(w\), returns whether the subgroup generated by \(W\) is a normal subgroup of the group generated by \(V\) or not.
‣ AreEquivalent( V, W ) | ( function ) |
Given two sequence of elements \(V,W\) of a free group and a word \(w\), returns whether \(V\) and \(W\) are equivalent or not.
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