与符号输出相对应的方程组

Question

Is it possible to solve a system of equations(linear or non linear) with sympy where the output is symbolic?

Example:

 1. f_m = a0 + a1*(-dx) + a2*(-dx)^2 
 2. f_c = a0
 3. f_p = a0 + a1*(dx) + a2*(dx)^2 

Solve for a2.

By the Mathematica command

Solve the solution is

a2 = (1/2)*(f_m - 2*f_c + f_p). 

Answer 1

This is a fundamental operation in Sympy, you should study the documention. Just to get you started:

import sympy as sp

f_m, f_c, f_p = sp.var('f_m, f_c, f_p')
a0, a1, a2 = sp.var('a0:3')
dx = sp.var('dx')

eq1 = sp.Eq(f_m, a0 + a1*(-dx) + a2*(-dx)**2)
eq2 = sp.Eq(f_c, a0)
eq3 = sp.Eq(f_p, a0 + a1*(dx) + a2*(dx)**2 )


sp.linsolve([eq1, eq2, eq3], (a0, a1, a2))
# sp.solve([eq1, eq2, eq3], (a0, a1, a2))  # also works

{(f_c, (-f_m + f_p)/(2*dx), (-2*f_c + f_m + f_p)/(2*dx**2))}