7. Working with order 12 invariants

Fully expanded relations for the fourth step of order 12 invariants take up too much memory to be loaded at the same time in a typical PC. We provide two versions of the database for the hardest cases of this step and order:
    - Non expanded: these rules have not been fully `simplified' taking into account all the other relations. As a result, they are both somewhat smaller and slower to use. The corresponding files in the database end in the string `NE'.
    - Expanded: these rules have been fully expanded. They are bigger but faster.
We can control which version to use with the global variable $ExpandedCommuteOrder12Q:

The default value is False, meaning that Invar will load the non expanded version.

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For example, let us take this invariant:

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which is still independent after steps 2 and 3:

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It can be expanded using the NE-rules for step 4:

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but it is still not fully expanded, as this expression changes again under InvSimplify:

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The rules take less than 20 Mbytes:

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Now remove the rules

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and simplify again the invariant, now using the expanded rules. We get the fully expanded result

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but now the rules take more than 80 Mbytes:

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Tidy up:

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Created by Mathematica  (May 16, 2008)