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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'