**The Kolchin Seminar in Differential Algebra**** **

**Saturday November 20**^{th}** 2004**

**Richard C. Churchill**

Hunter College

**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.

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**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.

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John Nahay

Swan Orchestral Systems

**Differential resolvents are complete and useful (Continued)**

**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.

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

**Click here for directions to Hunter
College and location of room **