Roots of algebraic equations and Clifford algebra
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The author investigates roots of real polynomials inside the real two-dimensional Clifford algebra with generator \(\varepsilon\), \(\varepsilon^2=1\), calling the elements of this algebra hyperbolic. The corresponding numbers of real and hyperbolic roots of a polynomial are calculated. As applications, the intersection of a line with an algebraic plane curve is examined, and some remarks on linear differential equations with constant coefficients are given.
Clifford algebras, spinors, roots of real polynomials, linear differential equations, constant coefficients, Linear ordinary differential equations and systems, hyperbolic roots, Polynomials in real and complex fields: location of zeros (algebraic theorems), Clifford algebra, Real polynomials: location of zeros
Clifford algebras, spinors, roots of real polynomials, linear differential equations, constant coefficients, Linear ordinary differential equations and systems, hyperbolic roots, Polynomials in real and complex fields: location of zeros (algebraic theorems), Clifford algebra, Real polynomials: location of zeros
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