I am trying to solve an equation using an ansatz with a number of independent terms that all have different coefficients. Sympy is trying to find an answer in terms of the independent terms instead of just the coefficients, I feel like I am missing something but have tried everything I could think of/google.
To show a minimal problem I have the following example:
from sympy import *
x,y,z= symbols('x y z')
a1, a2, a3 = symbols('a1 a2 a3')
expr = a1*x + a2*y + a3*z + y
solve(expr,[a1,a2,a3])
the result is:
a1 = -a3 z/x; a2 = -1
What I would want to have is:
a1 = 0; a2 = -1; a3 = 0.
I feel like I am missing something, or is this plainly not possible with sympy.solve or another simple function. I could think of writing my own solver to solve the problem but if there is an 'easy' solution, that would be preferable.
The coefficients of x,y,z must be zero in order for the sum to be zero (as you have stated) so that can be stated as:
from sympy import *
v=x,y,z= symbols('x y z')
a1, a2, a3 = symbols('a1 a2 a3')
expr = a1*x + a2*y + a3*z + y
expanded = expr.expand()
coeffs = [expanded.coeff(vi) for vi in v] # you now have 3 equations
>>> solve(coeffs,[a1,a2,a3])
{a1: 0, a2: -1, a3: 0}