‣ ConjugacyGL2Z( A, B ) | ( function ) |
Decides whether two \(2 \times 2\) matrices in \(\mathrm{GL}_2(\mathbb{Z})\) are conjugate. If so, returns the element \(C\) such that \(A = C^{-1} B C\).
‣ CentralizerGL2Z( A, B ) | ( function ) |
Given a matrix \(A\), computes a matrix \(C\) and an integer \(n\) such that \(\mathrm{Cent}_{\mathrm{GL}_2(\mathbb{Z})}(A) = \langle -C, C \rangle\) and \(C^n = A\).
‣ MembershipSubgroupSL2Z( gens, A ) | ( function ) |
Given a matrix \(A\), decides whether \(A \in \langle \mathrm{gens} \rangle\) and, if so, computes a word \(w\) in the generators representing \(A\).
‣ AreAutomorphicEquivalent( F, u, v ) | ( operation ) |
Decides whether \(u\) and \(v\) are automorphically 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 \(u\).
‣ IsSuffix( u, v ) | ( operation ) |
Returns whether the word \(v\) is a suffix of \(u\).
‣ 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.
‣ 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 \(V\).
‣ IsSubgroupOfFreeSubgroup( V, W ) | ( function ) |
Given two sequences of elements \(V,W\) of a free group, returns whether the subgroup generated by \(W\) is a subgroup of the group generated by \(V\).
‣ IsNormalSubgroupOfFreeSubgroup( V, W ) | ( function ) |
Given two sequences of elements \(V,W\) of a free group, returns whether the subgroup generated by \(W\) is a normal subgroup of the group generated by \(V\).
‣ AreEquivalent( V, W ) | ( function ) |
Given two sequences of elements \(V,W\) of a free group, returns whether \(V\) and \(W\) are equivalent.
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