| Knots |
PresentationKnotQuandle(gaussCode)
Inputs a Gauss Code of a knot (with the orientations; see GaussCodeOfPureCubicalKnot in HAP package) and outputs the generators and relators of the knot quandle associated (in the form of a record). |
PD2GC(PD)
Inputs a Planar Diagram of a knot; outputs the Gauss Code associated (with the orientations). |
PlanarDiagramKnot(n,k)
Returns a Planar Diagram for the k-th knot with n crossings (nUNKNOWNEntity(le)12) if it exists; fail otherwise. |
GaussCodeKnot(n,k)
Returns a Gauss Code (with orientations) for the k-th knot with n crossings (nUNKNOWNEntity(le)12) if it exists; fail otherwise. |
PresentationKnotQuandleKnot(n,k)
Returns generators and relators (in the form of a record) for the k-th knot with n crossings (nUNKNOWNEntity(le)12) if it exists; fail otherwise. |
NumberOfHomomorphisms(genRelQ,finiteQ)
Inputs generators and relators genRelQ of a knot quandle (in the form of a record, see above) and a finite quandle finiteQ; outputs the number of homomorphisms from the former to the latter. |
PartitionedNumberOfHomomorphisms(genRelQ,finiteQ)
Inputs generators and relators genRelQ of a knot quandle (in the form of a record, see above) and a finite connected quandle finiteQ; outputs a partition of the number of homomorphisms from the former to the latter. |
| Quandles |
ConjugationQuandle(G,n)
Inputs a finite group G and an integer n; outputs the associated n-fold conjugation quandle. |
FirstQuandleAxiomIsSatisfied(M) SecondQuandleAxiomIsSatisfied(M) ThirdQuandleAxiomIsSatisfied(M)
Inputs a finite magma M; returns true if M satisfy the first/second/third axiom of a quandle, false otherwise. |
IsQuandle(M)
Inputs a finite magma M; returns true if M is a quandle, false otherwise. |
Quandles(n)
Returns a list of all quandles of size n, nUNKNOWNEntity(le)6. If nUNKNOWNEntity(ge)7, it returns fail. |
Quandle(n,k)
Returns the k-th quandle of size n (nUNKNOWNEntity(le)6) if such a quandle exists, fail otherwise. |
IdQuandle(Q)
Inputs a quandle Q; and outputs a list of integers [n,k] such that Q is isomorphic to |
IsLatin(Q)
Inputs a finite quandle Q; returns true if Q is latin, false otherwise. |
IsConnectedQuandle(Q)
Inputs a finite quandle Q; returns true if Q is connected, false otherwise. |
ConnectedQuandles(n)
Returns a list of all connected quandles of size n. |
ConnectedQuandle(n,k)
Returns the k-th quandle of size n if such a quandle exists, fail otherwise. |
IdConnectedQuandle(Q)
Inputs a connected quandle Q; and outputs a list of integers [n,k] such that Q is isomorphic to |
IsQuandleEnvelope(Q,G,e,stigma)
Inputs a set Q, a permutation group G, an element e UNKNOWNEntity(isin) Q and an element stigma UNKNOWNEntity(isin) G; returns true if this structure describes a quandle envelope, false otherwise. |
QuandleQuandleEnveloppe(Q,G,e,stigma)
Inputs a set Q, a permutation group G, an element e UNKNOWNEntity(isin) Q and an element stigma UNKNOWNEntity(isin) G. If this structure describes a quandle envelope, the function returns the quandle from this quandle envelope; and fail otherwise. Nb: this quandle is a connected quandle. |
KnotInvariantCedric(genRelQ,n,m)
Inputs generators and relators of a knot quandle (in the form of a record, see above) and two integers n and m; outputs a list [n1,n2,...,nk] where nj is a partition of the number of homomorphisms from the considered knot quandle to the j-th connected quandle of size nUNKNOWNEntity(le)iUNKNOWNEntity(le)m. |
RightMultiplicationGroupAsPerm(Q)
Inputs a connected quandle Q; output its right multiplication group whose elements are permutations. |
RightMultiplicationGroup(Q)
Inputs a connected quandle Q; output its right multiplication group whose elements are mappings from Q to Q. |
AutomorphismGroupQuandleAsPerm(Q)
Inputs a connected quandle Q; outputs its automorphism group whose elements are permutations. |
AutomorphismGroupQuandle(Q)
Inputs a connected quandle Q; outputs its automorphism group whose elements are mappings from Q to Q. |
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