Rational Normal Forms and Minimal Decompositions of Hypergeometric Terms

Rational Normal Forms and Minimal Decompositions of Hypergeometric Terms

We describe a multiplicative normal form for rational functions which exhibits the shift structure of the factors, and investigate its properties. On the basis of this form we propose an algorithm which, given a rational function R, extracts a rational part F from the product of consecutive values of R: ∏n−1 k=n0 R(k) = F (n) ∏n−1 k=n0 V (k) where the numerator and denominator of the rational f...

Rational Canonical Forms and E cientRepresentations of Hypergeometric TermsS

We propose four multiplicative canonical forms that exhibit the shift structure of a given rational function. These forms in particular allow one to represent a hypergeometric term eeciently. Each of these representations is optimal in some sense.

Generic Algebras: Rational Parametrization and Normal Forms

For every algebraically closed field k of characteristic different from 2, we prove the following: (1) Generic finite dimensional (not necessarily associative) kalgebras of a fixed dimension, considered up to isomorphism, are parametrized by the values of a tuple of algebraically independent over k rational functions in the structure constants. (2) There exists an “algebraic normal form”, to wh...

Ideal decompositions and computation of tensor normal forms

Symmetry properties of r-times covariant tensors T can be described by certain linear subspaces W of the group ring K[Sr] of a symmetric group Sr. If for a class of tensors T such a W is known, the elements of the orthogonal subspace W⊥ of W within the dual space K[Sr] of K[Sr] yield linear identities needed for a treatment of the term combination problem for the coordinates of the T . We give ...

Minimal Polynomials and Jordan Normal Forms