I wonder whether someone out there would give some ideas on how to implement a problem involving monomials (or polynomials if you wish).
dx/dt=f(x,y,z), dy/dt=g(x,y,z) and dz/dt=h(x,y,z) where f, g and h are polynomial functions of x,y,z.
For instance, I need a test that returns false in:
a) dx/dt=f(x,z), dydt=anything, dz/dt=h(x,z) or
b) dx/dt=f(x,y), dydt=g(x,y), dz/dt=anything.
c) dx/dt=anything, dy/dt=g(y,z), dz/dt=h(y,z)
that is, if two derivatives are related only between themselves, a false should be returned. An example where a false should be returned is
[x*y*theta+x*theta, x*y*theta, x*theta+y*theta+z*theta] = [f(x,y),g(x,y),h(x,y,z)] where theta .. theta are the coefficients.
PS. I am trying to avoid "for" in the solution in case I need to add another derivative but could not come up with a solution. In that case I need to test 3 variables instead of 2 and then 2 variables (as in the examples).