BMVsets

description:

[V1,V2,V3]=BMVsets(m,k) constructs the reduced monomial basis needed for the Gram matrix of (m,k) BMV polynomial with x^2 and y^2 as arguments.

See KLEP, Igor, SCHWEIGHOFER, Markus: Sums of hermitian squares and the BMV conjecture, J. Stat. Phys., 2008, vol. 133, pp. 739-760 for details.

arguments:

m and k are non-negative integers

output:

V1, V2, V3 are lists of corresponding monomials

possible usage:

BMVsets(m,k)

example:

>> [V1,V2,V3]=BMVsets(8,4)

V1 = 'y*y*y*y*x*x*x*x'

     'y*y*x*x*y*y*x*x'

     'y*y*x*x*x*x*y*y'

     'x*x*y*y*y*y*x*x'

     'x*x*y*y*x*x*y*y'

     'x*x*x*x*y*y*y*y'

V2 = 'x*y*y*y*y*x*x*x'

     'x*y*y*x*x*y*y*x'

     'x*x*x*y*y*y*y*x'

V3 = 'y*y*y*x*x*x*x*y'

     'y*x*x*y*y*x*x*y'

     'y*x*x*x*x*y*y*y'