Buchberger: This is a top level implementation of the equivariant Buchberger algorithm.
Incremental: This strategy uses Macaulay2's built in Gröbner basis algorithm gb. A Gröbner basis is computed for each truncated ideal. If no new elements are discovered up to Inc-action are discovered between the n truncation and the 2n-1 truncation for some n larger than the width of the generators, then the result is returned.
Signature: This is an implementation of an equivariant variant of the Gao-Volny-Wang signature based Gröbner basis algorithm. Experimental!
i1 : R = buildERing({symbol x}, {1}, QQ, 2);
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i2 : egb({x_0+x_1}, Algorithm=>Buchberger)
o2 = {x }
0
o2 : List
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i3 : use R; |
i4 : egb({x_0+x_1}, Algorithm=>Incremental)
o4 = {x }
0
o4 : List
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i5 : use R; |
i6 : egb({x_0+x_1}, Algorithm=>Signature)
-- TOTAL covered pairs = -6
o6 = {x + x , 2x }
1 0 0
o6 : List
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