# How do I define a homomorphism of a graded commutative algebra?

Why does the following throw a `TypeError: images do not define a valid homomorphism`

?

```
E = GradedCommutativeAlgebra(QQ,'x,y',degrees=(1,1))
E.inject_variables()
f = E.hom([x,y])
```

I expected it to define $f$ to be the identity homomorphism of $E$. What is the right way to define a homomorphism of $E$? I'm more interested in the one that switches $x$ and $y$ than the identity homomorphism, but this seemed a more obvious version of the question.

I am working on implementing morphisms of graded commutative algebras. No promises about when it might be done, but what are you interested in doing with the morphisms? What features would you like to have?

@JohnPalmieri Extremely late response but I want to be able to compute the trace of an endomorphism of a cdga on the cohomology, (multi)degree by (multi)degree, assuming degreewise finite dimensionality.