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Gröbner Basis theory originated in the work of Buchberger [4] and is now considered to be one of the most important and useful areas of computer algebra. In 1993, Zharkov and Blinkov [13] proposed an alternative method of computing a commutative Gröbner Basis, namely the computation of an Involutive Basis. In the mid 1980's, Mora showed [11] that… (More)

- Erik J Norberg, John S Parker, Steven C Nicholes, Byungchae Kim, Uppiliappan Krishnamachari, Larry A Coldren +91 others
- 2011

An etched beam splitter (EBS) photonic coupler based on frustrated total internal reflection (FTIR) is designed, fabricated and characterized in the InP/InGaAsP material system. The EBS offers an ultra compact footprint (8x11 μm) and a complete range of bar/cross coupling ratio designs. A novel pre-etching process is developed to achieve sufficient depth of… (More)

Given a monoid string rewriting system M , one way of obtaining a complete rewriting system for M is to use the classical Knuth-Bendix critical pairs completion algorithm. It is well known that this algorithm is equivalent to computing a noncommutative Gröbner basis for M. This article develops an alternative approach, using noncommutative involutive basis… (More)

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