Question :
You can get a coefficient of a specific term by using coeff();
x, a = symbols("x, a")
expr = 3 + x + x**2 + a*x*2
expr.coeff(x)
# 2*a + 1
Here I want to extract all the coefficients of x, x**2 (and so on), like;
# for example
expr.coefficients(x)
# want {1: 3, x: (2*a + 1), x**2: 1}
There is a method as_coefficients_dict(), but it seems this doesn’t work in the way I want;
expr.as_coefficients_dict()
# {1: 3, x: 1, x**2: 1, a*x: 2}
expr.collect(x).as_coefficients_dict()
# {1: 3, x**2: 1, x*(2*a + 1): 1}
Answer #1:
The easiest way is to use Poly
>>> a = Poly(expr, x)
>>> a.coeffs()
[1, 2*a + 1, 3]
Answer #2:
all_coeffs() can be sometime better than using coeffs() for a Poly.
The difference lies in output of these both. coeffs() returns a list containing all coefficients which has a value and ignores those whose coefficient is 0 whereas all_coeffs() returns all coefficients including those whose coefficient is zero.
>>> a = Poly(x**3 + a*x**2 - b, x)
>>> a.coeffs()
[1, a, -b]
>>> a.all_coeffs()
[1, a, 0, -b]
Answer #3:
One thing you can do is use a dictionary comprehension like so:
dict = {x**p: expr.collect(x).coeff(x**p) for p in range(1,n)}
where n is the highest power+1. In this case n=3. So you would have the list [1,2]
This would give
dict = {x: (2*a+1), x**2: 1}
Then you can add in the single term with
dict[1] = 3
So
dict = {1:3,x:(2*a+1),x**2:1}
You may also try:
a = list(reversed(expr.collect(x).as_ordered_terms()))
dict = {x**p: a[p],coeff(x**p) for p in range(1,n)}
dict[1] = a[0] # Would only apply if there is single term such as the 3 in the example
where n is the highest power + 1.
Answer #4:
Collection of coefficients can be handled with Poly and then separation of the monomials into dependent and independent parts can be handled with Expr.as_independent:
>>> def codict(expr, *x):
... collected = Poly(expr, *x).as_expr()
... return dict(i.as_independent(*x)[::-1] for i in Add.make_args(collected))
...
>>> codict(y, x)
{1: 3, x**2: 1, x: 2*a + 1}
>>> codict(y+b*z,x,z)
{1: 3, x**2: 1, z: b, x: 2*a + 1}
