Manuscript IX-C@1 · IX-C.tex · section · 03ce8e6b

Second-stage coefficient equations and associativity

Second-stage coefficient equations and associativity · lines 1090–1107

IX-C@1#eq:firstprescription, IX-C@1#eq:secondprescription, IX-C@1#eq:mixedprescription

If the two-edge functionals have been established, the intended placement prescriptions are

L_{1} (P_{L}, C) L_{2} (P_{L}, C) L_{1} (Q_{L}, C) = G_{13} + G_{23}, = G_{13, 23}, = G_{12, 23} + G_{12, 13}, R_{1} (A, P_{R}) R_{2} (A, P_{R}) R_{1} (A, Q_{R}) = G_{12} + G_{13}, = G_{12, 13}, = G_{12, 23} + G_{13, 23} .

These are labelled prescription equations until descent through $p_{L}, q_{L}, p_{R}, q_{R}$ , existence, and admission have been proved.

Displayed formulas in this passage

IX-C@1#eq:firstprescription · line 1094
$L_{1} (P_{L}, C) L_{2} (P_{L}, C) L_{1} (Q_{L}, C) = G_{13} + G_{23}, = G_{13, 23}, = G_{12, 23} + G_{12, 13}, R_{1} (A, P_{R}) R_{2} (A, P_{R}) R_{1} (A, Q_{R}) = G_{12} + G_{13}, = G_{12, 13}, = G_{12, 23} + G_{13, 23} .$
IX-C@1#eq:secondprescription · line 1094
$L_{1} (P_{L}, C) L_{2} (P_{L}, C) L_{1} (Q_{L}, C) = G_{13} + G_{23}, = G_{13, 23}, = G_{12, 23} + G_{12, 13}, R_{1} (A, P_{R}) R_{2} (A, P_{R}) R_{1} (A, Q_{R}) = G_{12} + G_{13}, = G_{12, 13}, = G_{12, 23} + G_{13, 23} .$
IX-C@1#eq:mixedprescription · line 1094
$L_{1} (P_{L}, C) L_{2} (P_{L}, C) L_{1} (Q_{L}, C) = G_{13} + G_{23}, = G_{13, 23}, = G_{12, 23} + G_{12, 13}, R_{1} (A, P_{R}) R_{2} (A, P_{R}) R_{1} (A, Q_{R}) = G_{12} + G_{13}, = G_{12, 13}, = G_{12, 23} + G_{13, 23} .$