Problem section (rotating fluids): a system of polynomial equations and a solution by an unusual method

ABSTRACT

A system of three third order polynomial equations with parameters is presented, along with its solution by the construction of a single carefully chosen determinant. This system displays some characteristics which may be common in practice, but are not dealt with effectively by most automatic solvers.

REFERENCES

• 1: J. W. Swift, "Convection in a Rotating Fluid Layer", in "Contemporary Mathematics Series", vol. 28, J. Marsden, ed., American Mathematical Society, 1984.
• 2: A. M. Soward, "Bifurcation and Stability of Finite Amplitude Convection in a Rotating Layer", submitted to Physica D.
• 3: F. S. Macaulay, "The Algebraic Theory of Modular Systems", Cambridge University Press, 1916, reprinted as "Cambridge Tracts in Mathematics and Mathematical Physics", No. 19, 1964.