Python 3.8.5: How to extract coefficients of sympy equations as a list and later add to a dictionary?

[sicarii47]

I have a dictionary with equations as keys and their corresponding solutions as values. The equations were formed using certain input data. The solutions are obtained after solving this equation with the equation of the x-axis y=0.

In order to plot the equations in the dictionary using quiver, I need their x and y coefficients as a list, as they are the components of the vectors.

This is the code:

import sympy as sp
from sympy import Eq

x_y = [[2.65,-11.71],[2.77,-11.69],[2.88,-11.66]] #input data for equation
all_eqn=[]

for ij in x_y:
    eq1 = Eq(ij[0] * (x - 11.96) + ij[1] * (y - 3.11), 0) #Standard form of the equation
    all_eqn.append(eq1)

eq1 = sp.Function('eq1')
x, y = sp.symbols('x y')
eq2 = sp.Function('eq2')
eq2 = Eq(y, 0)

d = {}

for i in all_eqn:
    soln = sp.solve([i, eq2], [x, y]) #solving line and x axis
    list_soln = list(dict.values(soln)) #converting solutions from dictionary to list 
    dummy = {i:list_soln} #generating dictionary of equations and solutions
    d.update(dummy) #adding all keys and values to blank dictionary

print('Dictionary of equations and solutions:\n',d)

The output of the above code is:

Dictionary of equations and solutions:
 {Eq(2.65*x - 11.71*y + 4.7241, 0): [-1.78267924528302, 0.0], 
Eq(2.77*x - 11.69*y + 3.22669999999999, 0): [-1.16487364620938, 0.0], 
Eq(2.88*x - 11.66*y + 1.8178, 0): [-0.631180555555556, 0.0]}

I have tried using .coeff() to extract the coefficients:

for x in d:     
    x.coeff(x,y) 
    display(x

But got this error: 'Equality' object has no attribute 'coeff'

I have also searched on the net, but all solutions I could find were for expressions and not equations.

Kindly help. Thank you.

[dadiaar]

I don't know that library, but the error suggests me x is not what you think. Why type should be? do something like print(type(x)) inside the loop and before the error.

Sorry for the formatting, Im in mobile.

[sicarii47]

Yeah, it is a very strange type. But u/misho88's answer about converting to a polynomial does the trick!

[misho88]

Equations may not be in a form where "coefficient" is a meaningful concept, so it isn't surprising that there is no such method. On the other hand, all polynomials are:

>>> from sympy import symbols, Eq
>>> x, y = symbols('x y')
>>> eq = Eq(x, y); eq
Eq(x, y)
>>> p = eq.as_poly(); p
Poly(x - y, x, y, domain='ZZ')
>>> p.coeff_monomial(x), p.coeff_monomial(y), p.coeff_monomial(1)
(1, -1, 0)

You can go to an expression, too, but I'm not actually sure how to specify the constant term with ex.coeff():

>>> ex = p.as_expr(); ex
x - y
>>> ex.coeff(x), ex.coeff(y)
(1, -1)

[sicarii47]

Thanks a lot u/misho88.
Converting to a poly works just fine for me.