Noncommuting variables to the zeroth power

[kbarros]

Taking noncommuting variables to the zeroth power can lead to surprising results:

using DynamicPolynomials
@ncpolyvar a x
p = x^0 * a  # displays as `a`
p == a       # returns true (expected behavior)
a == p       # returns false (bug)

[exAClior]

A related bug with the following Minimal Working Example

using DynamicPolynomials
@ncpolyvar x y z
bases = monomials([x,y,z],2)
@assert z^0*y*x^0*z in bases

A dirty fix is possible with calling the following function on monomials

using DynamicPolynomials: Monomial
function remove_zero_degree(m::Monomial{C}) where {C}
    isconstant(m) && return m
    return prod([x[1]^x[2] for x in filter(!(iszero ∘ last), collect(zip(m.vars, m.z)))])
end
@assert remove_zero_degree(z^0*y*x^0*z) in bases

If desirable, I would be happy to make a PR on related parts of the library.

[blegat]

Thanks for the proposal, it would be best to fix the root of the issue which is that the equality should ignore the trailing zeros