The Kolchin Seminar in Differential Algebra

Hunter College - Room HW706

Saturday November 20th 2004

Richard C. Churchill
Hunter College

An irreducibility criterion for linear differential operators
2:00 - 3:00PM

Abstract: The original English edition of van der Waerden's classic algebra text contains a generalization of the Eisenstein irreducibility criterion which is attributed to G. Dumas.  I formulate the argument in terms of Newton polygons and then adapt the method to obtain a sufficient condition for the irreducibility of an ordinary linear differential operator.


William Sit
City College
 An informal discussion on symbolic computation
3:30 - 4:30PM

Abstract: This may be considered a sequel to last Spring's talk on differential equation software.  The discussion will be different in that it will be concentrated on more general but ``elementary'' computations that seem to be unavailable from present-day, even leading-edge computer algebra systems.  Some special situations where progress has been made, for example in Gröbner basis with parameters, will be outlined. This is an open discussion and audience participation will be welcome. 


John Nahay
Swan Orchestral Systems
Differential resolvents are complete and useful (Continued)
5:00 - 6:00PM

Abstract: Is a q-th power differential resolvent of a polynomial a differential resolvent of the minimal polynomial of every solution of the resolvent?  The answer is yes. In this sense differential resolvents are complete. I proved this result in February 2004. We will choose various linear combinations over constants of the real-valued solutions of the resolvents of bi-quadratic equations to create funny-shaped ellipses I call "q-ellipses" and use the computer algebra system Mathematica to plot them. For fun, I will work backwards from the derived q-th power resolvent using Kovacic's algorithm to determine the values of q for which algebraic solutions exist (the answer: q must be rational). If there is time, I will use the resolvent to compute upper bounds on the number of extrema on these q-ellipses.



Coffee and tea will be served beginning at 1:30 PM
Room HW706

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