15,433 research outputs found
Factorization of quadratic polynomials in the ring of formal power series over
We establish necessary and sufficient conditions for a quadratic polynomial
to be irreducible in the ring of formal power series with integer
coefficients. For and prime, we show that is reducible in if and only if it is reducible in , the
ring of polynomials over the -adic integers.Comment: 15 page
Factorization of Rational Curves in the Study Quadric and Revolute Linkages
Given a generic rational curve in the group of Euclidean displacements we
construct a linkage such that the constrained motion of one of the links is
exactly . Our construction is based on the factorization of polynomials over
dual quaternions. Low degree examples include the Bennett mechanisms and
contain new types of overconstrained 6R-chains as sub-mechanisms.Comment: Changed arxiv abstract, corrected some type
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