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:

discriminant(...,Algorithm=>...) (missing documentation)
egb(...,Algorithm=>...) -- algorithm choice for egb
gb(...,Algorithm=>...) -- see gb -- compute a Gröbner basis
resultant(...,Algorithm=>...) (missing documentation)
syz(...,Algorithm=>...) -- see syz(Matrix) -- compute the syzygy matrix