15,433 research outputs found

    Factorization of quadratic polynomials in the ring of formal power series over Z\Z

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    We establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the ring Z[[x]]Z[[x]] of formal power series with integer coefficients. For n,m≥1n,m\ge 1 and pp prime, we show that pn+pmβx+αx2p^n+p^m\beta x+\alpha x^2 is reducible in Z[[x]]Z[[x]] if and only if it is reducible in Zp[x]Z_p[x], the ring of polynomials over the pp-adic integers.Comment: 15 page

    Factorization of Rational Curves in the Study Quadric and Revolute Linkages

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    Given a generic rational curve CC in the group of Euclidean displacements we construct a linkage such that the constrained motion of one of the links is exactly CC. 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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