A unification of Liouvillian extensions
We generalize Liouville's theory of elementary functions to a larger class of differential extensions. Elementary, Liouvillian and trigonometric extensions are all special cases of our extensions. In the transcendental case, we show how the rational ...
How to compute the Chow form of an unmixed polynomial ideal in single exponential time
LetK be a field andF1,?, Fm homogeneous polynomials in the indeterminatesX0,?, Xn with coefficients inK. We describe anefficiently parallelizable single exponential time algorithm which computes the Chow form of the idealI:= (F1,?, Fm), provided that I ...
On the construction of irreducible self-reciprocal polynomials over finite fields
The transformationf(x)?fQx?deg(f)f(x + 1/x) for f(x)? $$\mathbb{F}_q [x]$$ is studied. Simple criteria are given for the case that the irreducibility off is inherited by the self-reciprocal polynomialfQ. Infinite sequences of irreducible self-reciprocal ...
Some remarks on strong fibonacci pseudoprimes
Necessary and sufficient conditions are given for an odd composite integern to be a Fibonacci pseudoprime of themth kind for allm??. One consequence of this characterization is that any such pseudoprime has to be a Carmichael number.
Group codes on certain algebraic curves with many rational points
We construct a series of algebraic geometric codes using a class of curves which have many rational points. We obtain codes of lengthq2 over $$\mathbb{F}$$ q, whereq = 2q02 andq0 = 2n, such that dimension + minimal distance ?q2 + 1 ? q0(q ? 1). The codes ...