Parametrization of Pythagorean triples by a single triple of polynomials

It is well known that Pythagorean triples can be parametrized by two triples of polynomials with integer coefficients. We show that no single triple of polynomials with integer coefficients in any number of variables is sufficient, but that there exists a parametrization of Pythagorean triples by a single triple of integer-valued polynomials.Comment: to appear in J. Pure Appl. Algebr

Solving quadratic equations over polynomial rings of characteristic two

We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation an tn + ··· + a0 = 0 with coefficients ai in A, our problem is to find its roots in A. We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain a finite algorithm for solving a polynomial equation over A when A is F[x1,... ,xN ] or F(x1,... ,xN ) for any finite field F and any number N of variables. The case of quadratic equations in characteristic two is studied in detail

Similarity Classes of 3×33\times 3 Matrices over a Local Principal Ideal Ring

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.Mathematic

Similarity classes of 3x3 matrices over a local principal ideal ring

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.Comment: 14 pages, final version, to appear in Communications in Algebr

Leonid Vaserstein Interview

NOTE: to view these items please visit http://dynkincollection.library.cornell.eduInterview conducted by Eugene Dynkin with Leonid N. Vaserstein in August 1980. The interview is in two parts