The Gröbner fan of an ideal
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Publication:1117983
DOI10.1016/S0747-7171(88)80042-7zbMath0668.13017MaRDI QIDQ1117983
Lorenzo Robbiano, Ferdinando Mora
Publication date: 1988
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Symbolic computation and algebraic computation (68W30) Polynomial rings and ideals; rings of integer-valued polynomials (13F20)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the theory of graded structures
- New constructive methods in classical ideal theory
- A theorem on refining division orders by the reverse lexicographic order
- Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
- Classificazione dei semplici ordinamenti di un gruppo libero commutativo con \(n\) generatori
- Linear Inequalities and Related Systems. (AM-38)
