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Example:

A.<a,b> = FreeAlgebra(QQ, 2)
f = a + a * b - b * a
f.coefficient(a*b)

Throws:

AssertionError: a*b should be an element of Free monoid on 2 generators (a, b)

After some investigation:

c = f.monomial_coefficients()
type(list(c.keys())[0])
<class 'sage.monoids.free_monoid.FreeMonoid_with_category.element_class'>

But:

type(a*b)
<class 'sage.algebras.free_algebra.FreeAlgebra_generic_with_category.element_class'>

This might be a bug? I'm not sure. For now, the only 'solution' I have is something like this:

mon_keys = list(c.keys())
str_keys = [str(k) for k in c.keys()]
i = str_keys.index(str(a*b))
print(f[mon_keys[i]])

Which prints:

1

as expected.

Note that this is a playground example, in practice I need to get this result from a Lyndon word in the generators, hence some of the generalities that would otherwise seem slightly unneeded. Anyhow, Is there a way to avoid this ugly hack?

Example:

A.<a,b> = FreeAlgebra(QQ, 2)
f = a + a * b - b * a
f.coefficient(a*b)

Throws:

AssertionError: a*b should be an element of Free monoid on 2 generators (a, b)

After some investigation:

c = f.monomial_coefficients()
type(list(c.keys())[0])
<class 'sage.monoids.free_monoid.FreeMonoid_with_category.element_class'>

But:

type(a*b)
<class 'sage.algebras.free_algebra.FreeAlgebra_generic_with_category.element_class'>

This might be a bug? I'm not sure. For now, the only 'solution' I have is something like this:

mon_keys = list(c.keys())
str_keys = [str(k) for k in c.keys()]
i = str_keys.index(str(a*b))
print(f[mon_keys[i]])

Which prints:

1

as expected.

Note that this is a playground example, in practice I need to get this result from a Lyndon word in the generators, hence some of the generalities that would otherwise seem slightly unneeded. Anyhow, Is there a way to avoid this ugly hack?