Manuscript IX-Free-2@1 · IX-Free-2.tex · definition · abb2397a

Definition: Truncated partial product

The constructed truncated partial product · lines 1371–1384

IX-Free-2@1#def:product

For $d \in D_{decl}$ , set

⋆_{c} (d) = j = 0 \sum^{3} ℏ^{j} C_{j} (d) \in P_{Σ} \otimes_{C} C [ℏ] / (ℏ^{4}) .

Extend this map $C [ℏ] / (ℏ^{4})$ -linearly to

D_{decl} = D_{decl} \otimes_{C} C [ℏ] / (ℏ^{4}) .

A pair of formal functionals is admissible when its formal tensor lies in $D_{decl}$ . On such a pair, the partial product is obtained by this linearized map.

Displayed formulas in this passage

unlabeled · line 1374
$⋆_{c} (d) = j = 0 \sum^{3} ℏ^{j} C_{j} (d) \in P_{Σ} \otimes_{C} C [ℏ] / (ℏ^{4}) .$
unlabeled · line 1378
$D_{decl} = D_{decl} \otimes_{C} C [ℏ] / (ℏ^{4}) .$

Nearby in this section

section: The constructed truncated partial product
proposition: Proposition: Interface audit