‣ 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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