Acceleration of computation of φ-polynomials

Trajectory Planning Using High Order Polynomials under Acceleration Constraint

The trajectory planning, which is known as a movement from starting to end point by satisfying the constraints along the path is an essential part of robot motion planning. A common way to create trajectories is to deal with polynomials which have independent coefficients. This paper presents a trajectory formulation as well as a procedure to arrange the suitable trajectories for applications. ...

The computation of chromatic polynomials

The planar graph representing the truncated icosahedron is a cubic graph with 60 vertices and 90 edges. The computation of the chromatic polynomial of this graph is computed by enhancing the algorithm based on the classical Delete-Contract theorem as well as finding approaches for substantially modifying a computation tree during computation. The result itself is an interesting example of the t...

Efficient computation of Laguerre polynomials

An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials L (α) n (z) are presented. The standard threeterm recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for n large and α small, are used depending on the parameter region. Based on tests of contiguous relations in the parameter α and the degree n satisfi...

Quantum Computation of Jones’ Polynomials

It is one of the challenging problems to construct an efficient quantum algorithm which can compute the Jones’ polynomial for any knot or link obtained from closure or capping of a n-strand braid. We recapitulate the construction of braid-group Bn representations from vertex models. We perform orthogonal transformation involving quantum Clebsch-Gordan coefficient matrix on the qubit basis to ob...

Eecient Computation of Orthogonal Polynomials in Computer Algebra Eecient Computation of Orthogonal Polynomials in Computer Algebra