Solutions of pure equations in rational division algebras, II

Internal Symmetry from Division Algebras in Pure Spinor Geometry

The É. Cartan’s equations defining “simple” spinors (renamed “pure” by C. Chevalley) are interpreted as equations of motions for fermion multiplets in momentum spaces which, in a constructive approach based bilinearly on those spinors, result compact and Lorentzian, naturally ending up with a ten-dimension space. The equations found are most of those traditionally adopted ad hoc by theoretical ...

Triangulaizability of Algebras Over Division Rings

Rational Heuristics for Rational Solutions of Riccati Equations

We describe some new algorithm and heuristics for computing the polynomial and rational solutions of bounded degree of a class of ordinary di erential equations, which includes generalized Riccati equations. As a consequence, our methods can be used for factoring linear ordinary di erential equations. Since they generate systems of algebraic equations in at most n unknowns, where n is the order...

Rational solutions of first-order differential equations∗

We prove that degrees of rational solutions of an algebraic differential equation F (dw/dz,w, z) = 0 are bounded. For given F an upper bound for degrees can be determined explicitly. This implies that one can find all rational solutions by solving algebraic equations. Consider the differential equation F (w′, w, z) = 0, (w′ = dw/dz) (1) where F is a polynomial in three variables. Theorem 1 For ...

Exact Solutions of Linear Equations with Rational

1. Introduction. Sometimes one is interested in exact solutions of linear equations and cannot tolerate any errors at all, be it round-off errors, truncation errors or otherwise. In such situations division cannot be used. Eliminating variables by cross-multiplying leads to a tremendous growth in the size of intermediate results. This is well illustrated in an example of J. Barkley Rosser [5], ...