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The following example shows how to analyze the output of a comprehensive triangular decomposition.
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| (2) |
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The first part is a list of regular chains which form a pre-comprehensive triangular decomposition of F. The second part is a partition of the projection image of V(F) to the last coordinate. Each constructible set is associated with indices of regular chains in the first part.
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Consider a specialization point .
Try to figure out to which partition pt belongs.
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Then retrieve the indices of regular chains that specialize well at pt.
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| (8) |
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Thus you know that the regular chains in lrc_ind all specialize well at the point pt. Then you can do simple substitutions.
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| (10) |
Regular chains of form a triangular decomposition of F after specialization at pt.
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| (11) |