How to extract all coefficients in sympy
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}
Answers:
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.
The easiest way is to use Poly
>>> a = Poly(expr, x)
>>> a.coeffs()
[1, 2*a + 1, 3]
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]
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()
i, d = collected.as_independent(*x, as_Add=True)
rv = dict(i.as_independent(*x, as_Mul=True)[::-1] for i in Add.make_args(d))
if i:
assert 1 not in rv
rv.update({S.One: i})
return rv
>>> var('a x z y')
(a, x, z, y)
>>> expr = 3 + x + x**2 + a*x*2
>>> codict(expr, x)
{x**2: 1, x: 2*a + 1, 1: 3}
>>> codict(expr+y+z, x)
{x**2: 1, x: 2*a + 1, 1: y + z + 3}
>>> codict(expr+y+z, x,y)
{y: 1, x**2: 1, x: 2*a + 1, 1: z + 3}
>>> codict(expr+y+z, x,y,z)
{y: 1, z: 1, x**2: 1, x: 2*a + 1, 1: 3}
Based on RDizzl3’s answer, I modified like this:
d_c = collect(my_poly, x)
# replace n by highest power + 1
dict = {x**p: d_c.coeff(x, p) for p in range(0,n)}
This does not skip the constant.
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}
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.
The easiest way is to use Poly
>>> a = Poly(expr, x)
>>> a.coeffs()
[1, 2*a + 1, 3]
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]
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()
i, d = collected.as_independent(*x, as_Add=True)
rv = dict(i.as_independent(*x, as_Mul=True)[::-1] for i in Add.make_args(d))
if i:
assert 1 not in rv
rv.update({S.One: i})
return rv
>>> var('a x z y')
(a, x, z, y)
>>> expr = 3 + x + x**2 + a*x*2
>>> codict(expr, x)
{x**2: 1, x: 2*a + 1, 1: 3}
>>> codict(expr+y+z, x)
{x**2: 1, x: 2*a + 1, 1: y + z + 3}
>>> codict(expr+y+z, x,y)
{y: 1, x**2: 1, x: 2*a + 1, 1: z + 3}
>>> codict(expr+y+z, x,y,z)
{y: 1, z: 1, x**2: 1, x: 2*a + 1, 1: 3}
Based on RDizzl3’s answer, I modified like this:
d_c = collect(my_poly, x)
# replace n by highest power + 1
dict = {x**p: d_c.coeff(x, p) for p in range(0,n)}
This does not skip the constant.