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Add a RandomValidInputForHomomorphism method #127

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ssiccha opened this issue Jul 5, 2019 · 1 comment · May be fixed by #235
Open

Add a RandomValidInputForHomomorphism method #127

ssiccha opened this issue Jul 5, 2019 · 1 comment · May be fixed by #235
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enhancement SummerSchoolMGR Work done during the Summer School on Matrix Group Recognition in Aachen in 2019

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@ssiccha
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ssiccha commented Jul 5, 2019 •
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This is based on the discussion in PR #76.

This can be used to extend the idea of PR #76. If a test is called with tryNonGroupElements := true, then currently random elements are created that have a very low probability to pass ValidateHomomInput (see #98). RandomValidInputForHomomorphismOfRecogNode should create elements that always pass ValidateHomomInput but will usually not be in the group that is represented by the recognition node.
@ssiccha ssiccha added enhancement SummerSchoolMGR Work done during the Summer School on Matrix Group Recognition in Aachen in 2019 labels Jul 5, 2019
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ssiccha commented Dec 17, 2020

To expand on this:
Say we do ri := RecogniseGroup(G);, ri is not a leaf, and phi := Homom(ri) is the reduction homomorphism computed by recog. Then, if we generate random elements which may not be in G, then most of the time phi will not be applicable to them. Thus we test whether phi correctly rejects non-group-elements, but we do not do so for all other nodes in the recognition tree.

But I just had a better and simpler idea than doing a RandomValidInputForHomomorphism. We can just do the generate random non-group-elements for each non-leaf node in the tree!

@ssiccha ssiccha linked a pull request Dec 17, 2020 that will close this issue
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enhancement SummerSchoolMGR Work done during the Summer School on Matrix Group Recognition in Aachen in 2019
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Add function RECOG.TryNonGroupElements ssiccha/recog
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