In [1]:S=BooleSet([x(0),x(1)*x(2)]) In [2]:S Out[2]:{{x(1),x(2)}, {x(0)}}
S is a set of sets of variables. Our usual interpretation is to identify it with a polynomial with corresponding terms:
In [3]:Polynomial(S) Out[3]:x(1)*x(2) + x(0)Another interpretation is to map a set of variables
In [4]:(x(1)*x(2)*x(3)).divisors() Out[4]:{{x(1),x(2),x(3)}, {x(1),x(2)}, {x(1),x(3)}, {x(1)}, {x(2),x(3)}, {x(2)}, {x(3)}, {}}
We distingish between procedures, which use subsets of the ambient space (like finding zeros of a polynomial), and such procedures, where only the dimension/involved unit vectors/variables matter. The first kind of procedures usually gets the ambient space itself, the second kind gets the monomial consisting of all involved variables.