RegularChains[SemiAlgebraicSetTools][PartialCylindricalAlgebraicDecomposition] - compute a partial cylindrical algebraic decomposition
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Calling Sequence
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PartialCylindricalAlgebraicDecomposition(p, lp, R)
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Parameters
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R
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polynomial ring
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p
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polynomial of R
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lp
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list of polynomials of R
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Description
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The command PartialCylindricalAlgebraicDecomposition returns llr a list of points in the Euclidean space of dimension d, where d the number of variables in R.
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Each point in llr is a sample point of a d dimensional connected open set, which is a cell of a Cylindrical Algebraic Decomposition (CAD) induced by the polynomial p and the polynomials in lp, under the variable projection order given by R. Recall that the variables in R are sorted in decreasing order.
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If lp is not an empty list, then the points which do not satisfy q > 0 for all polynomial q in lp are discarded; otherwise, the points are in one-to-one correspondence to all the d dimensional CAD cells.
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The coordinates of all these points are rational numbers, and the ith coordinate of each point of llr corresponds the ith variable of R.
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The base field of R is the field of rational numbers.
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Examples
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