I was working out the second heuristic of the Maple paper along with Sean,
and the PR can be found here --> https://github.com/sympy/sympy/pull/2156
Firstly, the thing is I need to extract factors (according to the Maple
Paper)
a} that are algebraic
b} and are either a function of y alone or x alone
For example if h(x, y) = y**2*sin(x) , a guess for g(y) would be y**2
The problem is, the code that I've implemented extracts all factors.
Suppose h(x, y) = exp(y)*x**2 , then g(y) would give me exp(y) also.
Is there are a really good way to determine if an expression is algebraic
or not, thinking of something on the lines of .is_Polynomial() . Is
implementing something like .is_Algebraic() the best way forward?
Secondly, I don't really find the necessity of g(y) to be algebraic.
Because out of the ODE's that Sean gave me, one or two infinitesimals had
g(y) to be non-algebraic, and the infinitesimals seemed to satisfy the PDE.
Or maybe I am missing something.
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