Manuscript XVI-L@1 · XVI-L.tex · section · 35081099

Computational verification

L.1 The complete source as a jet polynomial › Computational verification · lines 434–450

Sample entries, copied from the output ( $σ_{α} = \partial_{α} σ_{ε}$ , $σ_{α β} = \partial_{α} \partial_{β} σ_{ε}$ ; slots $i, j$ are labelled by $(ab)$ ; multi-indices are written as $e_{α}$ ):

P^{0, 0; 00}_{C_{2}, (00) (00)} P^{0, e_{1}; 00}_{M_{2}, (00) (01)} P^{0, 2 e_{3}; 00}_{J_{3}, (00) (11)} = - \frac{3}{4} (σ_{11} + σ_{22} + σ_{33}), = - \frac{3}{2} σ_{0}, = - \frac{1}{4} σ_{ε}, P^{0, 0; 00}_{C_{2}, (00) (12)} P^{0, e_{2}; 00}_{M_{2}, (00) (02)} P^{0, e_{1} + e_{2}; 00}_{J_{3}, (00) (12)} = σ_{12}, = - \frac{3}{2} σ_{0}, = \frac{1}{2} σ_{ε}, P^{e_{3}, e_{3}; 00}_{J_{3}, (01) (01)} = - \frac{1}{2} σ_{ε} .

Displayed formulas in this passage

unlabeled · line 437
$P^{0, 0; 00}_{C_{2}, (00) (00)} P^{0, e_{1}; 00}_{M_{2}, (00) (01)} P^{0, 2 e_{3}; 00}_{J_{3}, (00) (11)} = - \frac{3}{4} (σ_{11} + σ_{22} + σ_{33}), = - \frac{3}{2} σ_{0}, = - \frac{1}{4} σ_{ε}, P^{0, 0; 00}_{C_{2}, (00) (12)} P^{0, e_{2}; 00}_{M_{2}, (00) (02)} P^{0, e_{1} + e_{2}; 00}_{J_{3}, (00) (12)} = σ_{12}, = - \frac{3}{2} σ_{0}, = \frac{1}{2} σ_{ε}, P^{e_{3}, e_{3}; 00}_{J_{3}, (01) (01)} = - \frac{1}{2} σ_{ε} .$

Nearby in this section

lemma: Lemma: Computational verification of L.1