gbFromOutputFile -- Read in a NCGroebnerBasis from a Bergman output file.

Synopsis

Usage:

Igb = gbFromOutputFile(A,fileName)
Inputs:
- A, an instance of the type NCPolynomialRing,
- fileName, a string,
Optional inputs:
- CacheBergmanGB => a Boolean value, default value true, specifies whether or not to cache the Groebner basis for later use
- MakeMonic => a Boolean value, default value true, specifies whether the Bergman output should be made monic
- ReturnIdeal => a Boolean value, default value false, specifies whether to return an NCIdeal or the NCGroebnerBasis
Outputs:
- Igb, an instance of the type NCGroebnerBasis, or an NCIdeal

Description

This command reads in a Groebner basis from a Bergman output file. It can be useful if you have performed a lengthy computation before, and wish to load in a previously computed result to do some computations.

The Groebner basis we are reading in for this example is located in the NCAlgebra auxiliary files directory. We are currently unable to compile this documentation node in a way that enables M2 to read the file. We give a text version of the session until the issue is resolved.

i1 : A=QQ{x56,x46,x36,x26,x16,x45,x35,x25,x15,x34,x24,x14,x23,x13,x12}

o1 = A

o1 : NCPolynomialRing

I = gbFromOutputFile(A,"NCAlgebra/FK.bo", ReturnIdeal=>true)

B=A/I

hilbertSeries(B,Order=>4)

In "Quadratic algebras, Dunkl elements, and Schubert calculus," Fomin and Kirillov introduce a family of noncommutative algebras E_n which may be thought of as the quadratic closure of the ring of "Bruhat operators" acting on a vector space whose basis is the symmetric group. In that paper, they provide Hilbert series for the algebras E_1, ..., E_5. The file loaded above is a Groebner basis of E_6 to degree 6. Thus B is isomorphic to E_6 in low degrees.

Ways to use gbFromOutputFile :

gbFromOutputFile(NCPolynomialRing,String)

For the programmer

The object gbFromOutputFile is a method function with options.