# egb(...,Algorithm=>...) -- algorithm choice for egb

## Description

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); i2 : egb({x_0+x_1}, Algorithm=>Buchberger) o2 = {x } 0 o2 : List i3 : use R; i4 : egb({x_0+x_1}, Algorithm=>Incremental) o4 = {x } 0 o4 : List i5 : use R; i6 : egb({x_0+x_1}, Algorithm=>Signature) -- TOTAL covered pairs = -6 o6 = {x + x , 2x } 1 0 0 o6 : List

## Further information

• Default value: Buchberger
• Function: egb -- computes equivariant Gröbner bases
• Option key: Algorithm -- an optional argument

## Functions with optional argument named Algorithm :

• egb(...,Algorithm=>...) -- algorithm choice for egb
• "gb(...,Algorithm=>...)" -- see gb -- compute a Gröbner basis
• "syz(...,Algorithm=>...)" -- see syz(Matrix) -- compute the syzygy matrix