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RegularChains[ConstructibleSetTools][RepresentingInequations] - return the list of inequations in a regular system
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Calling Sequence
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RepresentingInequations(rs, R)
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Parameters
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rs
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regular system
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R
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polynomial ring
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Description
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The command RepresentingInequations(rs, R) returns the inequations of the regular system rs, assuming that the polynomials of rs belong to R
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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](..).
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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.
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Examples
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Define a polynomial ring.
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![R := PolynomialRing([x, y, z])](/support/helpjp/helpview.aspx?si=6416/file06487/math94.png)
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Define a set of polynomials of R.
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![sys := [z*x^2+y+z, y^2+z]](/support/helpjp/helpview.aspx?si=6416/file06487/math105.png)
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![sys := [z*x^2+y+z, y^2+z]](/support/helpjp/helpview.aspx?si=6416/file06487/math108.png)
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The command Triangularize (with lazard option) will decompose the common solutions of the polynomials system  by means of regular chains.
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![dec := [regular_chain, regular_chain]](/support/helpjp/helpview.aspx?si=6416/file06487/math124.png)
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Let  be the first regular chain and  be a polynomial regarded as an inequation.
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![rc := dec[1]](/support/helpjp/helpview.aspx?si=6416/file06487/math134.png) 
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To obtain a regular system, check whether  is regular with respect to  .
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Since  is regular, you can build a regular system.
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![rs := RegularSystem(rc, [h], R)](/support/helpjp/helpview.aspx?si=6416/file06487/math162.png)
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Notice that the inequation  is returned by the command RepresentingInequations.
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![ineqs := [x+z]](/support/helpjp/helpview.aspx?si=6416/file06487/math178.png)
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