As of release R2014a, there is no MATLAB function in the Symbolic Math Toolbox that can get the degree of a polynomial defined symbolically.
As a workaround you can use the MuPAD function "degree". To call the MuPAD engine from within MATLAB in order to use "degree", use the "feval" function as follows:
>> syms x y z
>> P = x^4 + 3*x^2*y^2 - z^3 + y + 1;
>> feval(symengine, 'degree', P)
ans =
4
To get the degree of "P" with respect to a specific variable, use the following:
>> syms x y z
>> P = x^4 + 3*x^2*y^2 - z^3 + y + 1;
>> feval(symengine, 'degree', P, y)
ans =
2
