Definition: Minimal actual-functional carrier

Let ${\mathcal{P}}_{\Sigma ,\min }$ be the algebra of actual finite polynomial functionals generated, under ordinary pointwise multiplication, complex conjugation, and all fixed smooth directional derivatives, by:

1. ${\mathcal{P}}_{\mathrm{mc},\mathrm{pol}}$;

2. all sharp ${\mathcal{B}}_f$;

3. all linear sharp coordinate functionals ${\ell }_a$.

Identical functionals on smooth configurations are identified.