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'