Mathematical theory of saturation: Difference between revisions
OffsuitKnave (talk | contribs) m correct matrix entry |
Cmloegcmluin (talk | contribs) add Wolfram Language implementation |
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To test for saturation, we may take the wedge product of the generators. Wedging <26 41 60 72| with <12 19 28 34| gives us <<2 8 20 8 26 24||; this is not zero, so the rank of the group these generate is two. However the coefficients have a gcd of two, and hence the group is not saturated; for saturation, the coefficients must be relatively prime, with a gcd of one. | To test for saturation, we may take the wedge product of the generators. Wedging <26 41 60 72| with <12 19 28 34| gives us <<2 8 20 8 26 24||; this is not zero, so the rank of the group these generate is two. However the coefficients have a gcd of two, and hence the group is not saturated; for saturation, the coefficients must be relatively prime, with a gcd of one. | ||
= Wolfram Language implementation = | |||
<nowiki> | |||
rightReducingMatrix[m_] := Last[SmithDecomposition[m]] | |||
geneDefactor[m_] := Take[Inverse[rightReducingMatrix[m]], MatrixRank[m]] | |||
</nowiki> | |||
[[Category:math]] | [[Category:math]] | ||
[[Category:theory]] | [[Category:theory]] | ||