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Define a polynomial ring.
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| (1) |
Define a set of polynomials of R.
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The command Triangularize (with lazard option) decomposes the common solutions of the polynomial system
by means of regular chains.
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There are two groups of solutions, each of which is given by a regular chain. To view their equations, use the Equations command.
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Let
be the first regular chain, and
be the second one.
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Consider two polynomials
and
; regard them as inequations.
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To obtain a regular system, first check whether
is regular with respect to
, and
is regular with respect to
.
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Both of them are regular, thus you can build the following regular systems.
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![rs1 := RegularSystem(rc1, [h1], R)](/support/helpjp/helpview.aspx?si=6404/file06485/math182.png)
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The command RegularSystemDifference computes the set theoretical difference of two sets defined by regular systems. The output is a list of regular systems which forms a constructible set.
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To view the output, use the following sequence of commands.
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| (10) |
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| (13) |
Alternatively, you could use the Info command.
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| (14) |