solving a linear problem with (multivariate) polynomial coefficients

[Michele Zaffalon]

I am struggling to find a way of solving the following equation (simplified example)
```
f = x+1
g = 2*x+1
expr = a*f + b*g - 1
solve(expr, (a, b))
```
I would like to have `a=2`, `b=-1` which make `expr` identically zero.

I am interested in polynomials with higher powers: at the moment, I derive with respect to x, subs 0 for x, accumulate the result as column in a matrix and solve the linear problem associated. This method works for univariate polynomials, but it become impractical for multivariate linear systems, which is my ultimate goal, because of the need to derive with respect to all mixed terms x^m*y^n. (I also could not find a way of collecting the coefficients of the terms x^m*y^n.)

Is there a way to solve these linear problems?

Thank you,
michele

[Aaron Meurer]

Perhaps solve_undetermined_coeffs() can do what you want.

Aaron Meurer

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[Michele Zaffalon]

A few minutes after I posted my question, I found that Poly.coeffs does what I want and works for multivariate polynomials

```
lin = Poly(expr, x, y).coeffs()
solve(lin, [a,b,c,d,e])
```
with the following definitions
```
x, y = symbols("x, y")
a, b, c, d, e = symbols("a, b, c, d, e")

f = 3*x**2-2*y+1
g = x*y+x-2*y
h = x**2+2*y**2-2
j = x+3
k = x**2-x*y+2
expr = a*f + b*g + c*h + d*j + e*k - (7*x**2 + 2*x*y + 4*x - 4*y**2 - 14*y + 9)

```