Admissible orders and linear forms
Volker Weispfenning · ACM SIGSAM Bulletin · 1987
Admissible orders on terms (power-products of finitely many indeterminates X 1 ,..., X n play a fundamental role in the definition and construction of Groebner bases for polynomial ideals (see [Bul). By passage to exponents, these orders may be construed as linear orders on [EQUATION] compatible with addition and with smallest element [EQUATION] = (0,...,0). Any such order extends uniquely to a linear order ) into an ordered group such that all elements of [EQUATION] are non-negative, Conversely, any restriction of such an order to [EQUATION] is an admissible order on [EQUATION]. So from now on an "admissible order" will be a linear group order on [EQUATION] with [EQUATION] >= 0.