### 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}
```