The Division Algorithm in Complex Bases

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The Division Algorithm in Complex Bases

Complex numbers can be represented in positional notation using certain Gaussian integers as bases and digit sets. We describe a long division algorithm to divide one Gaussian integer by another, so that the quotient is a periodic expansion in such a complex base. To divide by the Gaussian integer w in the complex base b, using a digit set D, the remainder must be in the set wT(b, D) \ Z[i], wh...

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Gröbner Bases is a technique that provides algorithmic solutions to a variety of problems in Commutative Algebra and Algebraic Geometry. In this introductory tutorial the basic algorithms as well as their generalization for computing Gröbner basis of a set of multivariate polynomials are presented. The Gröbner basis technique is applied to solve systems of polynomial equations in several variab...

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ژورنال

عنوان ژورنال: Canadian Mathematical Bulletin

سال: 1996

ISSN: 0008-4395,1496-4287

DOI: 10.4153/cmb-1996-006-1