return the list of inequations in a regular system
The command RepresentingInequations(rs, R) returns the inequations of the regular system rs, assuming that the polynomials of rs belong to R
This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form RepresentingInequations(..) only after executing the command with(RegularChains[ConstructibleSetTools]). However, it can always be accessed through the long form of the command by using RegularChains[ConstructibleSetTools][RepresentingInequations](..).
See ConstructibleSetTools and RegularChains for the related mathematical concepts, in particular for the ideas of a constructible set, a regular system and, a regular chain.
Define a polynomial ring.
Define a set of polynomials of R.
The command Triangularize (with lazard option) will decompose the common solutions of the polynomials system sys by means of regular chains.
Let rc be the first regular chain and h be a polynomial regarded as an inequation.
To obtain a regular system, check whether h is regular with respect to rc.
Since h is regular, you can build a regular system.
Notice that the inequation h is returned by the command RepresentingInequations.
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