Davenport, James

Nair, Akshar Sajive

Sankaran, Gregory

There are two relevant methods for CAD: McCallum [1984] which used order invariant CAD's and Lazard [Lazard1994, McCallumetal2019] which used lex-least invariant CADs, and doesn't have the nullification problem of McCallum [1984]. McCallum [1999] was the first to prove a CAD operator based on McCallum [1984], that took advantage of an equational constraint.In this paper, we do the same for Lazard's method. This takes in a lex-least invariant CAD of $\RR^{n-1}$ as input and outputs a sign invariant CAD of $\RR^n$: consequently, it cannot be used recursively, but only for $x_n$, the first variable to be projected. In the further steps of the projection phase, we use Lazard's original projection operator. Nonetheless, reducing the output in the first step has a domino effect throughout the remaining steps, which significantly reduces the complexity. The long-term goal is to find a general projection operator that takes advantage of the equality constraint and can be used recursively, and this operator gives an important first step in that direction.<br/

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On Benefits of Equality Constraints in Lex-Least Invariant CAD (Extended Abstract

https://purehost.bath.ac.uk/ws/files/197289894/SC2_SIAM_AK.pdf

On Benefits of Equality Constraints in Lex-Least Invariant CAD (Extended Abstract

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