... matrices1
These matrices can be computed during the Gröbner basis computation.
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... considered2
In fact this test set is related to the technique called saturation and explained more precisely in [5].
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...3
Note that this ordering is well-founded since we have a well-founded ordering on and .
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...4
Note that this ordering is well-founded since we have a well-founded ordering on and .
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... 5
Remember that .
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... 6
If not stated otherwise is the usual ordering on where .
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...7
Let . We call the positive numbers the remainders of . Then for each there are unique such that and is a remainder of . We get and in case and even . Further does not divide , if are different remainders of .
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... 8
if and otherwise.
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... property9
By Theorem 6 a set can be characterized as a prefix Gröbner basis if any element in its right ideal can be prefix reduced to zero using the set.
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