Algebra of quantum $$ \mathcal{C} $$-polynomials

Algebra: Monomials and Polynomials

algebra is a theoretical course: we wonder more about why things are true than about how we can do things. Algebraists can at times be concerned more with elegance and beauty than applicability and efficiency. You may be tempted on many occasions to ask yourself the point of all this abstraction and theory. Who needs this stuff? Keep the examples above in mind; they show that algebra is not onl...

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

Symbolic-Numeric Algebra for Polynomials

DUAL PROPERTIES OF ORTHOGONAL POLYNOMIALS OF DISCRETE VARIABLES ASSOCIATED WITH THE QUANTUM ALGEBRA Uq(su(2))

We show that for every set of discrete polynomials yn(x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials zk(ξ(t)) of degrees k = s−a and k = b− s− 1. Here we do this for the classical and alternative Hahn and Racah polynomials as well as for their q-analogs. Also we establish the connection between classical and alternative f...

Computer Algebra of Polynomials and Rational Functions

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