The discussion focuses on finding the coefficients of the Taylor polynomial of degree two for the function z(x,y) around the point (0,0) using Python. The equation x + 2y + z + e^(2z) - 1 = 0 is central to the problem. Participants suggest using the SymPy library for symbolic differentiation, which facilitates the calculation of partial derivatives necessary for determining the Taylor coefficients.
PREREQUISITESMathematicians, data scientists, and Python developers interested in polynomial approximations and symbolic computation.
SimPy will do symbolic differentiation, including partial derivatives. See https://docs.sympy.org/latest/tutorial/calculus.htmlschniefen said:Summary: Consider the equation ##x+2y+z+e^{2z}-1=0##. Find the cocoefficients of the Taylor polynomial of degree two of the function ##z(x,y)## about the point ##(0,0)##.
To find the coefficients of the Taylor polynomial of degree two of the function ##z(x,y)## around the point ##(0,0)##, what would be a handy way of doing that in python? How would one find the derivatives of ##z(x,y)##?