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RegularChains[ConstructibleSetTools][Union] - compute the union of two constructible sets
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Calling Sequence
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Union(cs1, cs2, R)
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Parameters
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cs1, cs2
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constructible sets
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R
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polynomial ring
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Description
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The command Union(cs1, cs2, R) returns a constructible set, the union of cs1 and cs2.
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There might be redundancy in the output.
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This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form Union(..) 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][Union](..).
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Examples
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Define a polynomial ring  first.
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![R := PolynomialRing([x, y])](/support/helpjp/helpview.aspx?si=6403/file06489/math87.png)
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Consider the following polynomials of  .
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Let cs1 be the solution set of  and  , and cs2 be the solution set of  and  .
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![cs1 := GeneralConstruct([F, G], [1], R)](/support/helpjp/helpview.aspx?si=6403/file06489/math133.png)
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![cs2 := GeneralConstruct([G, H], [1], R)](/support/helpjp/helpview.aspx?si=6403/file06489/math140.png)
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Use the command Union to obtain the union of these two solution sets.
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![{[[y-1], [1]], [[y+1], [1]], [[x, y], [1]], [[x, y-3], [1]], [[x-2, y+1], [1]], [[x-1, y-1], [1]], [[x-1, y+1], [1]], [[x+1, y-1], [1]]}](/support/helpjp/helpview.aspx?si=6403/file06489/math158.png)
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The Union command is not guaranteed to remove all the redundant components, for efficiency consideration. Use the MakePairwiseDisjoint command to remove them.
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![{[[y-1], [1]], [[y+1], [1]], [[x, y], [1]], [[x, y-3], [1]]}](/support/helpjp/helpview.aspx?si=6403/file06489/math182.png)
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Download Help Document
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