Stuck solving a polynomial fitting problem using sympy

[tomi]

Hi, I have a problem with a polynomial fitting using sympy. I have asked the question on Stack Overflow but I got no feedback, so I thought that I would get some help here.

The core issue is in the args tuple from sympy.core.add.Add . If I define a polynomial function like p4 = a0 + a1x + ... an*x**n  and impose conditions on the function at symbolic points (xa, xb, ...) as well on the function derivative, I can get some other polynomials. For example, saying that the first derivative of p4 equals zero at a symbolic point xa

p4diff = diff(p4, x)

c4 = p4diff.subs(x, xa)

creates a basis for a linear combination of a0, a1, .. a4 valued with the xa symbol. For a polynomial of order 4, if I impose 4 such conditions, I can build for c0, c1,... c4 condition polynomials. As a result, I get a linear system of 4 equations for four polynomial coefficients a0,... a4. If the system has a unique solution, I have fitted a polynomial with the conditions c0, ... c4 to the interval [xa, xb]. This is the point where I'm stuck. I can't get to arrange the linear system for the solve_linear_system function using Matrix. Basically, it should look like this:

A = Matrix([a0 term from c0, a1 term from c0, ...., a4 term from c0, condition value], [.... c1 ...], ... , [ ... c4 ...]])

and then I can solve the system with solve_linear_system(A, a0, a1, a2, a3, a4), with the solution expressed with the symbols xa and xb. This way, I can fit the polynomial with the aforementioned conditions to any interval I = [xa, xb]. I could replace xa and xb with real values, but I need the symbolic solution - I am using it to construct a polynomial function in C++.

Any advice on this?


Thanks,
Tomislav

[Chris Smith]

I replied at SO.