Generator preimage: Difference between revisions
Cmloegcmluin (talk | contribs) |
Cmloegcmluin (talk | contribs) use descriptive names for the two methods |
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=Finding the transversal generators= | =Finding the transversal generators= | ||
Two methods for finding transversal generators have been developed. The first was developed by [[Gene Ward Smith]] sometime in or before June 2011. The second was developed by [[User:Sintel|Sintel]] in December 2021. | Two methods for finding transversal generators have been developed. The first was developed by [[Gene Ward Smith]] sometime in or before June 2011, which uses the [[Hermite normal form]]. The second was developed by [[User:Sintel|Sintel]] in December 2021, which uses the [[Smith normal form]]. | ||
== | == Method using the Smith Normal Form == | ||
So we want to find a generators matrix <math>G</math> for a mapping <math>M</math> where: | So we want to find a generators matrix <math>G</math> for a mapping <math>M</math> where: | ||
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</syntaxhighlight>}} | </syntaxhighlight>}} | ||
== | == Method using the Hermite Normal Form == | ||
We can find transversal generators for V by the following procedure: | We can find transversal generators for V by the following procedure: | ||