... Reinert1
The author was supported by the Deutsche Forschungsgemeinschaft (DFG).
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... convergent2
Convergent presentations for groups are string rewriting systems which are terminating and confluent.
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... ideals3
An ideal is called binomial if it has a basis solely consisting of polynomials of the form m1 -m2 where m1,m2 are monomials.
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...4
Notice that while is minimal with respect to , the ordering is not compatible with multiplication as then would imply .
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...v5
Those familiar with string rewriting systems should notice that prefix reducing a word u with a binomial where directly corresponds to prefix string reducing u with a rule followed by free reduction.
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... algorithm6
The FGLM Algorithm has been generalized to the setting of finitely presented groups in [5].
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... reduction7
We say a free reduced word prefix reduces to v (modulo free group reduction) using a rule if there exists such that and .
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... rule8
Notice that there are trivial rules among these where the left and right hand sides coincide as words and these of course have to be removed in order to make the system terminating.
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... computed9
The steps in the computation of the prefix Gröbner basis can be directly related to Nielsen transformations (see [23]).
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... basis10
The computation of the prefix Gröbner basis is related to the filling of the first line of the tables in TC and the deduction of equations
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...11
The set H realizes the addition of subgroup generators or in TC corresponds to marking the first and last slot of each relator table with the newly found coset representative .
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... subgroup12
This corresponds to the coset collapses in TC.
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