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334
Simplification of Cylindrical Algebraic Formulas
"... Abstract. For a set S of cells in a cylindrical algebraic decomposition of Rn, we introduce the notion of generalized cylindrical algebraic formula (GCAF) associated with S. We propose a multilevel heuristic algorithm for simplifying the cylindrical algebraic formula associated with S into a GCAF. ..."
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Abstract. For a set S of cells in a cylindrical algebraic decomposition of Rn, we introduce the notion of generalized cylindrical algebraic formula (GCAF) associated with S. We propose a multilevel heuristic algorithm for simplifying the cylindrical algebraic formula associated with S into a GCAF
Characterizing relativized cylindric algebras
 In Andreka et al. [AMN91
, 1991
"... We obtain the class NA of noncommutative cylindric algebras from the class CA of cylindric algebras by weakening the axiom C4 of commutativity of cylindrifications (to C ∗ 4, see below, and we obtain NCA from CA by omitting C4 completely). Some motivation for studying noncommutative cylindric algebr ..."
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Cited by 3 (0 self)
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We obtain the class NA of noncommutative cylindric algebras from the class CA of cylindric algebras by weakening the axiom C4 of commutativity of cylindrifications (to C ∗ 4, see below, and we obtain NCA from CA by omitting C4 completely). Some motivation for studying noncommutative cylindric
Cylindrical algebraic subdecompositions
 MATHEMATICS IN COMPUTER SCIENCE
, 2014
"... Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semialgebraic sets. In this paper we introduce cylindrical algebraic subdecompositions (subCADs), which are subsets of CADs containing al ..."
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Cited by 4 (4 self)
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Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semialgebraic sets. In this paper we introduce cylindrical algebraic subdecompositions (subCADs), which are subsets of CADs containing
On the Amalgamation Base of Cylindric Algebras
"... Let K be a class of algebras. A0 ∈ K is in the amalgamation base of K, briefly A0 ∈ APbase(K), if for all A1,A2 ∈ K and monomorphisms i1: A0 → A1 i2: A0 → A2 there exist D ∈ K and monomorphisms m1: A1 → D and m2: A2 → D such that m1 ◦ i1 = m2 ◦ i2. CAα stands for the class of cylindric algebras of d ..."
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Let K be a class of algebras. A0 ∈ K is in the amalgamation base of K, briefly A0 ∈ APbase(K), if for all A1,A2 ∈ K and monomorphisms i1: A0 → A1 i2: A0 → A2 there exist D ∈ K and monomorphisms m1: A1 → D and m2: A2 → D such that m1 ◦ i1 = m2 ◦ i2. CAα stands for the class of cylindric algebras
Improved Projection for Cylindrical Algebraic Decomposition
 Journal of Symbolic Computation
, 2001
"... This technical report is a preliminary version of a paper on improved projection for Cylindrical Algebraic Decomposition. It is being made available for ISSAC 2000 because of its bearing on [Bro00]. McCallum's projection operator for Cylindrical Algebraic Decomposition (CAD) [McC98, McC88, ..."
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Cited by 40 (2 self)
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This technical report is a preliminary version of a paper on improved projection for Cylindrical Algebraic Decomposition. It is being made available for ISSAC 2000 because of its bearing on [Bro00]. McCallum's projection operator for Cylindrical Algebraic Decomposition (CAD) [McC98, McC88
A Note on Cylindric Algebras
"... If two atomic cylindric set algebras of finite dimension> 1 are isomorphic, then baseminimality does not imply that they are lowerbase isomorphic. This contrasts the case of boolean algebras. ..."
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If two atomic cylindric set algebras of finite dimension> 1 are isomorphic, then baseminimality does not imply that they are lowerbase isomorphic. This contrasts the case of boolean algebras.
HOW TO USE CYLINDRICAL ALGEBRAIC DECOMPOSITION
 SÉMINAIRE LOTHARINGIEN DE COMBINATOIRE 65 (2011), ARTICLE B65A
, 2011
"... We take some items from a textbook on inequalities and show how to prove them with computer algebra using the Cylindrical Algebraic Decomposition algorithm. This is an example collection for standard applications of this algorithm, intended as a guide for potential users. ..."
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Cited by 1 (0 self)
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We take some items from a textbook on inequalities and show how to prove them with computer algebra using the Cylindrical Algebraic Decomposition algorithm. This is an example collection for standard applications of this algorithm, intended as a guide for potential users.
LAYERED CYLINDRICAL ALGEBRAIC DECOMPOSITION
"... Abstract. In this paper the idea of a Layered CAD is introduced, a truncation of a CAD to only high dimensional cells. Limiting to fulldimensional cells has already been investigated in the literature, but including another level can be beneficial for applications. A related topological property is ..."
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Cited by 3 (3 self)
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Abstract. In this paper the idea of a Layered CAD is introduced, a truncation of a CAD to only high dimensional cells. Limiting to fulldimensional cells has already been investigated in the literature, but including another level can be beneficial for applications. A related topological property is defined and related to robotics motion planning. The distribution of cell dimensions in a CAD is investigated and layered CAD ideas are combined with other research.
Connections between relation algebras and cylindric algebras
"... Abstract. We give an informal description of a recursive representabilitypreserving reduction of relation algebras to cylindric algebras. 1 ..."
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Abstract. We give an informal description of a recursive representabilitypreserving reduction of relation algebras to cylindric algebras. 1
Computing Cylindrical Algebraic Decomposition via Triangular Decomposition
, 2009
"... Cylindrical algebraic decomposition is one of the most important tools for computing with semialgebraic sets, while triangular decomposition is among the most important approaches for manipulating constructible sets. In this paper, for an arbitrary finite set F ⊂ R[y1,..., yn] we apply comprehensiv ..."
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Cited by 42 (14 self)
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Cylindrical algebraic decomposition is one of the most important tools for computing with semialgebraic sets, while triangular decomposition is among the most important approaches for manipulating constructible sets. In this paper, for an arbitrary finite set F ⊂ R[y1,..., yn] we apply
Results 1  10
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334