A Multiplication Technique for the Factorization of Bivariate Quaternionic Polynomials

Abstract We consider bivariate polynomials over the skew field of quaternions, where indeterminates commute with all coefficients and each other. analyze existence univariate factorizations, that is, factorizations linear factors. A necessary condition for is factorization norm polynomial into a product polynomials. This however, not sufficient. Our central result states exist after multiplication suitable real as long fulfilled. present an algorithm computing this corresponding factorization. If original exists, input produces constant factor, thus giving posteriori factorizations. Some obtained in way are interest mechanism science. example curious closed-loop eight revolute joints.